Each digit of pi treated as an integer,
Starting with 3 and x=0 and y=0.

3 down x=0 y=-3
1 left x=-1 y=-3
4 up x=-1 y=1
1 right x=0 y=1
5 down x=0 y=-4
9 right x=9 y=-4
2 up x=9 y=-2
6 left x=3 y=-2
5 D x=3 y=-7
3 L x=0 y=-7
5 U x=0 y=-2
8 R x=8 y=-2
9 D x=8 y=-11
7 R x=15 y=-11
9 U x=15 y=-2
3 L x=12 y=-2
2

Repeat that order of directions with each digit of pi.
What will be the x/y coordinates on the Cartesian coordinate plain
after 1,000,000 digits of pi?
How many times will it cross the x=0 axis and y=0 axis or where an
actual digit of pi ends up on x=0 and y=0?
Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully

We know pi's digits --->oo but the Cartesian coordinate plain will not
--->oo in any direction, in fact using the above method it will cross
or land on the x=0 or y=0 --->oo.
I used this repeated order D,L,U,R,D,R,U,L to accommodate all the single
numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
pattern of joining lines but it takes 140 iterations to complete the pattern.
Then it just retraces the lines in the next 140 iterations and so on --->oo.

0 D A zero so no change so x=0,y=0
1 L x=-1 y=0
2 U x=-1 y=2
3 R x=2 y=2
4 D x=2 y=-2
5 R x=7 y=-2
6 U x=7 y=4
7 L x=0 y=4
8 D x=0 y=-4
9 L x=-9 y=-4
0 U x=-9 y=-4
1 R x=-8 y=-4
2 D x=-8 y=-6
etc.
The numbers above from 0-9 repeated for each direction to 140 iterations produces a unique 140 x\y coordinates and then repeats that same unique x\y coordinates in the next 140 iterations and so-on.
When a zero or zeros like in pi are encountered it does not draw a line but uses only a direction change.

A simple concept, but interesting.

Dan

Dan joyce <danj4084@gmail.com> wrote:
> Each digit of pi treated as an integer,
> Starting with 3 and x=0 and y=0.
[snip coordinates example]
>
> Repeat that order of directions with each digit of pi.
> What will be the x/y coordinates on the Cartesian coordinate plain
> after 1,000,000 digits of pi?
> How many times will it cross the x=0 axis and y=0 axis or where an
> actual digit of pi ends up on x=0 and y=0?
> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
>
> We know pi's digits --->oo but the Cartesian coordinate plain will not
> --->oo in any direction, in fact using the above method it will cross
> or land on the x=0 or y=0 --->oo.
....
> When a zero or zeros like in pi are encountered it does not draw a line but uses only a direction change.

More clearly, it draws a line of length 0 for digit 0.

Here are some stats for the million-digit case:
Min Max Cross Zero Last @Orig
X: -2076 439 1074 563 -1648 1 #54073
Y: -752 1842 753 388 -574

In that output, you can see that X ranged from -2076 to 439, was zero
563 times, crossed the Y axis at least 1074 times. The trace returned
to the (0,0) origin 1 time, at digit 54073, and ended at (-1648,-574).

Also Y ranged from -752 to 1842, was zero 388 times, and crossed the X
axis at least 753 times. Note, these cross counts are lower bounds.
If more than two zero locations occur in a row, my program may miss an
axis crossing. For example, if x goes -1, 0, 0, 1 the program will
correctly count one crossing, but if x goes -1, 0, 0, 0, 1, it should
but won't, and if x goes 1, 0, 0, 0, 1, it shouldn't and doesn't.

Some more outputs (which took 0.3 minutes; 2 minutes; and 4.3 minutes,
respectively, with >99% of the time being the computation of pi and the
other <1% walking the digits.

Got pi to 10100111 digits, will process 10100100
Min Max Cross Zero Last @Orig
X: -5411 548 3493 1865 -2416 1 #54073
Y: -2953 7863 3308 1684 6714

Got pi to 50000011 digits, will process 50000000
Min Max Cross Zero Last @Orig
X: -14627 548 3697 1943 -5764 1 #54073
Y: -4316 12484 6477 3362 -332

Got pi to 100100009 digits, will process 100100000
Min Max Cross Zero Last @Orig
X: -14627 20240 7388 3841 -5522 1 #54073
Y: -33180 12484 6953 3590 -27829

On Monday, April 17, 2023 at 2:09:51 AM UTC-4, James Waldby wrote:
> Dan joyce <danj...@gmail.com> wrote:
> > Each digit of pi treated as an integer,
> > Starting with 3 and x=0 and y=0.
> [snip coordinates example]
> >
> > Repeat that order of directions with each digit of pi.
> > What will be the x/y coordinates on the Cartesian coordinate plain
> > after 1,000,000 digits of pi?
> > How many times will it cross the x=0 axis and y=0 axis or where an
> > actual digit of pi ends up on x=0 and y=0?
> > Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
> >
> > We know pi's digits --->oo but the Cartesian coordinate plain will not
> > --->oo in any direction, in fact using the above method it will cross
> > or land on the x=0 or y=0 --->oo.
> ...
> > When a zero or zeros like in pi are encountered it does not draw a line but uses only a direction change.
> More clearly, it draws a line of length 0 for digit 0.
Right.
> Here are some stats for the million-digit case:
> Min Max Cross Zero Last @Orig
> X: -2076 439 1074 563 -1648 1 #54073
> Y: -752 1842 753 388 -574
>
> In that output, you can see that X ranged from -2076 to 439, was zero
> 563 times, crossed the Y axis at least 1074 times. The trace returned
> to the (0,0) origin 1 time, at digit 54073, and ended at (-1648,-574).
>
> Also Y ranged from -752 to 1842, was zero 388 times, and crossed the X
> axis at least 753 times. Note, these cross counts are lower bounds.
> If more than two zero locations occur in a row, my program may miss an
> axis crossing. For example, if x goes -1, 0, 0, 1 the program will
> correctly count one crossing, but if x goes -1, 0, 0, 0, 1, it should
> but won't, and if x goes 1, 0, 0, 0, 1, it shouldn't and doesn't.
>
> Some more outputs (which took 0.3 minutes; 2 minutes; and 4.3 minutes,
> respectively, with >99% of the time being the computation of pi and the
> other <1% walking the digits.
>
> Got pi to 10100111 digits, will process 10100100
> Min Max Cross Zero Last @Orig
> X: -5411 548 3493 1865 -2416 1 #54073
> Y: -2953 7863 3308 1684 6714
>
> Got pi to 50000011 digits, will process 50000000
> Min Max Cross Zero Last @Orig
> X: -14627 548 3697 1943 -5764 1 #54073
> Y: -4316 12484 6477 3362 -332
>
> Got pi to 100100009 digits, will process 100100000
> Min Max Cross Zero Last @Orig
> X: -14627 20240 7388 3841 -5522 1 #54073
> Y: -33180 12484 6953 3590 -27829

You can Shure bring out some fascinating stuff with your coding skills.
Sadly to say I lost it on the cognitive skills needed for something like this.
Nicely done!
Pi's digits continue on --->oo but are bounded by x\y coordinates to never wander off in any
direction --->oo on the Cartesians Coordinate plain.
What's your thoughts on this?
I have a screen shot of a very small sampling of 25,001 digits of pi using a pixel count
as the line length. Of coerce computer screens don't have that high of a resolution to
stand a much larger sampling of pi's digits to keep everything on the screen.
Using the same repeated D,LU,R,D,R,U,L direction at the end of 25001digits It appears
the lines form a very general narrow upward band of lines giving a rapid increase of
+x and +y from a larger mass of lines already in the in +x and +y range.
Even at that small a sample of pi's digits I cut the pixel size down to 0.75. to keep everything
on screen.

Thanks for your interesting input.
Dan

On Tuesday, April 18, 2023 at 9:42:33 AM UTC+10, Dan joyce wrote:
> On Monday, April 17, 2023 at 2:09:51 AM UTC-4, James Waldby wrote:
> > Dan joyce <danj...@gmail.com> wrote:
> > > Each digit of pi treated as an integer,
> > > Starting with 3 and x=0 and y=0.
> > [snip coordinates example]
> > >
> > > Repeat that order of directions with each digit of pi.
> > > What will be the x/y coordinates on the Cartesian coordinate plain
> > > after 1,000,000 digits of pi?
> > > How many times will it cross the x=0 axis and y=0 axis or where an
> > > actual digit of pi ends up on x=0 and y=0?
> > > Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
> > >
> > > We know pi's digits --->oo but the Cartesian coordinate plain will not
> > > --->oo in any direction, in fact using the above method it will cross
> > > or land on the x=0 or y=0 --->oo.
> > ...
> > > When a zero or zeros like in pi are encountered it does not draw a line but uses only a direction change.
> > More clearly, it draws a line of length 0 for digit 0.
> Right.
> > Here are some stats for the million-digit case:
> > Min Max Cross Zero Last @Orig
> > X: -2076 439 1074 563 -1648 1 #54073
> > Y: -752 1842 753 388 -574
> >
> > In that output, you can see that X ranged from -2076 to 439, was zero
> > 563 times, crossed the Y axis at least 1074 times. The trace returned
> > to the (0,0) origin 1 time, at digit 54073, and ended at (-1648,-574).
> >
> > Also Y ranged from -752 to 1842, was zero 388 times, and crossed the X
> > axis at least 753 times. Note, these cross counts are lower bounds.
> > If more than two zero locations occur in a row, my program may miss an
> > axis crossing. For example, if x goes -1, 0, 0, 1 the program will
> > correctly count one crossing, but if x goes -1, 0, 0, 0, 1, it should
> > but won't, and if x goes 1, 0, 0, 0, 1, it shouldn't and doesn't.
> >
> > Some more outputs (which took 0.3 minutes; 2 minutes; and 4.3 minutes,
> > respectively, with >99% of the time being the computation of pi and the
> > other <1% walking the digits.
> >
> > Got pi to 10100111 digits, will process 10100100
> > Min Max Cross Zero Last @Orig
> > X: -5411 548 3493 1865 -2416 1 #54073
> > Y: -2953 7863 3308 1684 6714
> >
> > Got pi to 50000011 digits, will process 50000000
> > Min Max Cross Zero Last @Orig
> > X: -14627 548 3697 1943 -5764 1 #54073
> > Y: -4316 12484 6477 3362 -332
> >
> > Got pi to 100100009 digits, will process 100100000
> > Min Max Cross Zero Last @Orig
> > X: -14627 20240 7388 3841 -5522 1 #54073
> > Y: -33180 12484 6953 3590 -27829
> You can Shure bring out some fascinating stuff with your coding skills.
> Sadly to say I lost it on the cognitive skills needed for something like this.
> Nicely done!
> Pi's digits continue on --->oo but are bounded by x\y coordinates to never wander off in any
> direction --->oo on the Cartesians Coordinate plain.
> What's your thoughts on this?

How can it not? the central colored in square increases in size
or atleast the central outermost square increases in size -->oo

I dont believe in RANDOM WALK HYPOTHESIS that he crosses 0,0
INF times.

I think it forms a SKETCH that approaches INF-X -INF-X INF-Y -INF-Y
but it may be an INTERPRETATION of complete-infinity Vs potential-infinity

If you have billion step walks traced onto a picture would be interesting

On Monday, April 17, 2023 at 8:58:20 PM UTC-4, Graham Cooper wrote:
> On Tuesday, April 18, 2023 at 9:42:33 AM UTC+10, Dan joyce wrote:
> > On Monday, April 17, 2023 at 2:09:51 AM UTC-4, James Waldby wrote:
> > > Dan joyce <danj...@gmail.com> wrote:
> > > > Each digit of pi treated as an integer,
> > > > Starting with 3 and x=0 and y=0.
> > > [snip coordinates example]
> > > >
> > > > Repeat that order of directions with each digit of pi.
> > > > What will be the x/y coordinates on the Cartesian coordinate plain
> > > > after 1,000,000 digits of pi?
> > > > How many times will it cross the x=0 axis and y=0 axis or where an
> > > > actual digit of pi ends up on x=0 and y=0?
> > > > Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
> > > >
> > > > We know pi's digits --->oo but the Cartesian coordinate plain will not
> > > > --->oo in any direction, in fact using the above method it will cross
> > > > or land on the x=0 or y=0 --->oo.
> > > ...
> > > > When a zero or zeros like in pi are encountered it does not draw a line but uses only a direction change.
> > > More clearly, it draws a line of length 0 for digit 0.
> > Right.
> > > Here are some stats for the million-digit case:
> > > Min Max Cross Zero Last @Orig
> > > X: -2076 439 1074 563 -1648 1 #54073
> > > Y: -752 1842 753 388 -574
> > >
> > > In that output, you can see that X ranged from -2076 to 439, was zero
> > > 563 times, crossed the Y axis at least 1074 times. The trace returned
> > > to the (0,0) origin 1 time, at digit 54073, and ended at (-1648,-574)..
> > >
> > > Also Y ranged from -752 to 1842, was zero 388 times, and crossed the X
> > > axis at least 753 times. Note, these cross counts are lower bounds.
> > > If more than two zero locations occur in a row, my program may miss an
> > > axis crossing. For example, if x goes -1, 0, 0, 1 the program will
> > > correctly count one crossing, but if x goes -1, 0, 0, 0, 1, it should
> > > but won't, and if x goes 1, 0, 0, 0, 1, it shouldn't and doesn't.
> > >
> > > Some more outputs (which took 0.3 minutes; 2 minutes; and 4.3 minutes,
> > > respectively, with >99% of the time being the computation of pi and the
> > > other <1% walking the digits.
> > >
> > > Got pi to 10100111 digits, will process 10100100
> > > Min Max Cross Zero Last @Orig
> > > X: -5411 548 3493 1865 -2416 1 #54073
> > > Y: -2953 7863 3308 1684 6714
> > >
> > > Got pi to 50000011 digits, will process 50000000
> > > Min Max Cross Zero Last @Orig
> > > X: -14627 548 3697 1943 -5764 1 #54073
> > > Y: -4316 12484 6477 3362 -332
> > >
> > > Got pi to 100100009 digits, will process 100100000
> > > Min Max Cross Zero Last @Orig
> > > X: -14627 20240 7388 3841 -5522 1 #54073
> > > Y: -33180 12484 6953 3590 -27829
> > You can Shure bring out some fascinating stuff with your coding skills.
> > Sadly to say I lost it on the cognitive skills needed for something like this.
> > Nicely done!
> > Pi's digits continue on --->oo but are bounded by x\y coordinates to never wander off in any
> > direction --->oo on the Cartesians Coordinate plain.
> > What's your thoughts on this?
> How can it not? the central colored in square increases in size
> or atleast the central outermost square increases in size -->oo
>
> I dont believe in RANDOM WALK HYPOTHESIS that he crosses 0,0
> INF times.
>
> I think it forms a SKETCH that approaches INF-X -INF-X INF-Y -INF-Y
> but it may be an INTERPRETATION of complete-infinity Vs potential-infinity
>
> If you have billion step walks traced onto a picture would be interesting

I am just thinking of the average mean of the pi digits.
My thoughts are it creates a bounded limit on the x\y coordinates.
I could be dead wrong on my hypothesis.

On Tuesday, April 18, 2023 at 1:35:12 PM UTC+10, Dan joyce wrote:
> > > Pi's digits continue on --->oo but are bounded by x\y coordinates to never wander off in any
> > > direction --->oo on the Cartesians Coordinate plain.
> > > What's your thoughts on this?
> > How can it not? the central colored in square increases in size
> > or atleast the central outermost square increases in size -->oo
> >
> > I dont believe in RANDOM WALK HYPOTHESIS that he crosses 0,0
> > INF times.
> >
> > I think it forms a SKETCH that approaches INF-X -INF-X INF-Y -INF-Y
> > but it may be an INTERPRETATION of complete-infinity Vs potential-infinity
> >
> > If you have billion step walks traced onto a picture would be interesting
> I am just thinking of the average mean of the pi digits.
> My thoughts are it creates a bounded limit on the x\y coordinates.
> I could be dead wrong on my hypothesis.

a 1dimension example is clearer

Assume 2 people are betting against each other by tossing a coin.

the profit goes up down up down ...
in never ending cycle
in larger and larger profits both ways

if one person has a finite bank and the other an infinite bank
then the infinite bank always wins

similarly, the random walker will always cross any Y

On 4/16/2023 2:00 PM, Dan joyce wrote:
> Each digit of pi treated as an integer,
> Starting with 3 and x=0 and y=0.
>
> 3 down x=0 y=-3
> 1 left x=-1 y=-3
> 4 up x=-1 y=1
> 1 right x=0 y=1
> 5 down x=0 y=-4
> 9 right x=9 y=-4
> 2 up x=9 y=-2
> 6 left x=3 y=-2
> 5 D x=3 y=-7
> 3 L x=0 y=-7
> 5 U x=0 y=-2
> 8 R x=8 y=-2
> 9 D x=8 y=-11
> 7 R x=15 y=-11
> 9 U x=15 y=-2
> 3 L x=12 y=-2
> 2
>
> Repeat that order of directions with each digit of pi.
> What will be the x/y coordinates on the Cartesian coordinate plain
> after 1,000,000 digits of pi?
> How many times will it cross the x=0 axis and y=0 axis or where an
> actual digit of pi ends up on x=0 and y=0?
> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
>
> We know pi's digits --->oo but the Cartesian coordinate plain will not
> --->oo in any direction, in fact using the above method it will cross
> or land on the x=0 or y=0 --->oo.
>
> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the single
> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
> pattern of joining lines but it takes 140 iterations to complete the pattern.
> Then it just retraces the lines in the next 140 iterations and so on --->oo.
>
> 0 D A zero so no change so x=0,y=0
> 1 L x=-1 y=0
> 2 U x=-1 y=2
> 3 R x=2 y=2
> 4 D x=2 y=-2
> 5 R x=7 y=-2
> 6 U x=7 y=4
> 7 L x=0 y=4
> 8 D x=0 y=-4
> 9 L x=-9 y=-4
> 0 U x=-9 y=-4
> 1 R x=-8 y=-4
> 2 D x=-8 y=-6
> etc.
> The numbers above from 0-9 repeated for each direction to 140 iterations produces a unique 140 x\y coordinates and then repeats that same unique x\y coordinates in the next 140 iterations and so-on.
> When a zero or zeros like in pi are encountered it does not draw a line but uses only a direction change.
>
>
> A simple concept, but interesting.

It should end up looking like a brownian motion:

https://en.wikipedia.org/wiki/Brownian_motion

On Sunday, April 16, 2023 at 2:00:04 PM UTC-7, Dan joyce wrote:
> Each digit of pi treated as an integer,
> Starting with 3 and x=0 and y=0.
>
> 3 down x=0 y=-3
> 1 left x=-1 y=-3
> 4 up x=-1 y=1
> 1 right x=0 y=1
> 5 down x=0 y=-4
> 9 right x=9 y=-4
> 2 up x=9 y=-2
> 6 left x=3 y=-2
> 5 D x=3 y=-7
> 3 L x=0 y=-7
> 5 U x=0 y=-2
> 8 R x=8 y=-2
> 9 D x=8 y=-11
> 7 R x=15 y=-11
> 9 U x=15 y=-2
> 3 L x=12 y=-2
> 2
>
> Repeat that order of directions with each digit of pi.
> What will be the x/y coordinates on the Cartesian coordinate plain
> after 1,000,000 digits of pi?
> How many times will it cross the x=0 axis and y=0 axis or where an
> actual digit of pi ends up on x=0 and y=0?
> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
>
> We know pi's digits --->oo but the Cartesian coordinate plain will not
> --->oo in any direction, in fact using the above method it will cross
> or land on the x=0 or y=0 --->oo.
>
> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the single
> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
> pattern of joining lines but it takes 140 iterations to complete the pattern.
> Then it just retraces the lines in the next 140 iterations and so on --->oo.
>
> 0 D A zero so no change so x=0,y=0
> 1 L x=-1 y=0
> 2 U x=-1 y=2
> 3 R x=2 y=2
> 4 D x=2 y=-2
> 5 R x=7 y=-2
> 6 U x=7 y=4
> 7 L x=0 y=4
> 8 D x=0 y=-4
> 9 L x=-9 y=-4
> 0 U x=-9 y=-4
> 1 R x=-8 y=-4
> 2 D x=-8 y=-6
> etc.
> The numbers above from 0-9 repeated for each direction to 140 iterations produces a unique 140 x\y coordinates and then repeats that same unique x\y coordinates in the next 140 iterations and so-on.
> When a zero or zeros like in pi are encountered it does not draw a line but uses only a direction change.
>
>
> A simple concept, but interesting.
>
> Dan

Digits are not very accurate.
Round math can only go so far...
Where PI is a transcendental with infinite digits.
Man has uncertainty limit about transcendental instead.
How is PI verified?

On 4/19/2023 10:36 AM, mitchr...@gmail.com wrote:
> On Sunday, April 16, 2023 at 2:00:04 PM UTC-7, Dan joyce wrote:
>> Each digit of pi treated as an integer,
>> Starting with 3 and x=0 and y=0.
>>
>> 3 down x=0 y=-3
>> 1 left x=-1 y=-3
>> 4 up x=-1 y=1
>> 1 right x=0 y=1
>> 5 down x=0 y=-4
>> 9 right x=9 y=-4
>> 2 up x=9 y=-2
>> 6 left x=3 y=-2
>> 5 D x=3 y=-7
>> 3 L x=0 y=-7
>> 5 U x=0 y=-2
>> 8 R x=8 y=-2
>> 9 D x=8 y=-11
>> 7 R x=15 y=-11
>> 9 U x=15 y=-2
>> 3 L x=12 y=-2
>> 2
>>
>> Repeat that order of directions with each digit of pi.
>> What will be the x/y coordinates on the Cartesian coordinate plain
>> after 1,000,000 digits of pi?
>> How many times will it cross the x=0 axis and y=0 axis or where an
>> actual digit of pi ends up on x=0 and y=0?
>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
>>
>> We know pi's digits --->oo but the Cartesian coordinate plain will not
>> --->oo in any direction, in fact using the above method it will cross
>> or land on the x=0 or y=0 --->oo.
>>
>> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the single
>> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
>> pattern of joining lines but it takes 140 iterations to complete the pattern.
>> Then it just retraces the lines in the next 140 iterations and so on --->oo.
>>
>> 0 D A zero so no change so x=0,y=0
>> 1 L x=-1 y=0
>> 2 U x=-1 y=2
>> 3 R x=2 y=2
>> 4 D x=2 y=-2
>> 5 R x=7 y=-2
>> 6 U x=7 y=4
>> 7 L x=0 y=4
>> 8 D x=0 y=-4
>> 9 L x=-9 y=-4
>> 0 U x=-9 y=-4
>> 1 R x=-8 y=-4
>> 2 D x=-8 y=-6
>> etc.
>> The numbers above from 0-9 repeated for each direction to 140 iterations produces a unique 140 x\y coordinates and then repeats that same unique x\y coordinates in the next 140 iterations and so-on.
>> When a zero or zeros like in pi are encountered it does not draw a line but uses only a direction change.
>>
>>
>> A simple concept, but interesting.
>>
>> Dan
>
> Digits are not very accurate.

How many accurate base-10 symbols of pi can you generate?

> Round math can only go so far...
> Where PI is a transcendental with infinite digits.
> Man has uncertainty limit about transcendental instead.
> How is PI verified?

On 4/18/2023 7:11 PM, Chris M. Thomasson wrote:
> On 4/16/2023 2:00 PM, Dan joyce wrote:
>> Each digit of pi treated as an integer,
>> Starting with 3 and x=0 and y=0.
>>
>> 3 down  x=0 y=-3
>> 1 left  x=-1 y=-3
>> 4 up    x=-1 y=1
>> 1 right x=0  y=1
>> 5 down  x=0  y=-4
>> 9 right x=9  y=-4
>> 2 up    x=9  y=-2
>> 6 left  x=3  y=-2
>> 5 D     x=3  y=-7
>> 3 L     x=0  y=-7
>> 5 U     x=0  y=-2
>> 8 R     x=8  y=-2
>> 9 D     x=8  y=-11
>> 7 R     x=15 y=-11
>> 9 U     x=15 y=-2
>> 3 L     x=12 y=-2
>> 2
>>
>> Repeat that order of directions with each digit of pi.
>> What will be the x/y coordinates on the Cartesian coordinate plain
>> after 1,000,000 digits of pi?
>> How many times will it cross the x=0 axis and y=0 axis or where an
>> actual digit of pi ends up on x=0 and y=0?
>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
>>
>> We know pi's digits --->oo but the Cartesian coordinate plain will not
>> --->oo in any direction, in fact using the above method it will cross
>> or land on the x=0 or y=0 --->oo.
>> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the single
>> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
>> pattern of joining lines but it takes 140 iterations to complete the
>> pattern.
>> Then it just retraces the lines in the next 140 iterations and so on
>> --->oo.
>>
>> 0 D  A zero so no change so x=0,y=0
>> 1 L x=-1 y=0
>> 2 U x=-1 y=2
>> 3 R x=2  y=2
>> 4 D x=2  y=-2
>> 5 R x=7  y=-2
>> 6 U x=7  y=4
>> 7 L x=0  y=4
>> 8 D x=0  y=-4
>> 9 L x=-9 y=-4
>> 0 U x=-9 y=-4
>> 1 R x=-8 y=-4
>> 2 D x=-8 y=-6
>> etc.
>> The numbers above from 0-9 repeated for each direction to 140
>> iterations produces a unique 140 x\y coordinates and then repeats that
>> same unique x\y coordinates in the next 140 iterations and so-on.
>> When a zero or zeros like in pi are encountered it does not draw a
>> line but uses only a direction change.

Wait a minute. I am missing where it "changes direction" when a zero
digit is encountered. You say x=0, y=0 so are you resetting the origin,
or just treat the zero as a non-movement like encounter? In other words
the current point is left alone when a zero digit is observed?

>>
>>
>> A simple concept, but interesting.
>
> It should end up looking like a brownian motion:
>
> https://en.wikipedia.org/wiki/Brownian_motion
>

On Wednesday, April 19, 2023 at 4:10:57 PM UTC-4, Chris M. Thomasson wrote:
> On 4/18/2023 7:11 PM, Chris M. Thomasson wrote:
> > On 4/16/2023 2:00 PM, Dan joyce wrote:
> >> Each digit of pi treated as an integer,
> >> Starting with 3 and x=0 and y=0.
> >>
> >> 3 down x=0 y=-3
> >> 1 left x=-1 y=-3
> >> 4 up x=-1 y=1
> >> 1 right x=0 y=1
> >> 5 down x=0 y=-4
> >> 9 right x=9 y=-4
> >> 2 up x=9 y=-2
> >> 6 left x=3 y=-2
> >> 5 D x=3 y=-7
> >> 3 L x=0 y=-7
> >> 5 U x=0 y=-2
> >> 8 R x=8 y=-2
> >> 9 D x=8 y=-11
> >> 7 R x=15 y=-11
> >> 9 U x=15 y=-2
> >> 3 L x=12 y=-2
> >> 2
> >>
> >> Repeat that order of directions with each digit of pi.
> >> What will be the x/y coordinates on the Cartesian coordinate plain
> >> after 1,000,000 digits of pi?
> >> How many times will it cross the x=0 axis and y=0 axis or where an
> >> actual digit of pi ends up on x=0 and y=0?
> >> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
> >>
> >> We know pi's digits --->oo but the Cartesian coordinate plain will not
> >> --->oo in any direction, in fact using the above method it will cross
> >> or land on the x=0 or y=0 --->oo.
> >> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the single
> >> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
> >> pattern of joining lines but it takes 140 iterations to complete the
> >> pattern.
> >> Then it just retraces the lines in the next 140 iterations and so on
> >> --->oo.
> >>
> >> 0 D A zero so no change so x=0,y=0
> >> 1 L x=-1 y=0
> >> 2 U x=-1 y=2
> >> 3 R x=2 y=2
> >> 4 D x=2 y=-2
> >> 5 R x=7 y=-2
> >> 6 U x=7 y=4
> >> 7 L x=0 y=4
> >> 8 D x=0 y=-4
> >> 9 L x=-9 y=-4
> >> 0 U x=-9 y=-4
> >> 1 R x=-8 y=-4
> >> 2 D x=-8 y=-6
> >> etc.
> >> The numbers above from 0-9 repeated for each direction to 140
> >> iterations produces a unique 140 x\y coordinates and then repeats that
> >> same unique x\y coordinates in the next 140 iterations and so-on.
> >> When a zero or zeros like in pi are encountered it does not draw a
> >> line but uses only a direction change.
> Wait a minute. I am missing where it "changes direction" when a zero
> digit is encountered. You say x=0, y=0 so are you resetting the origin,
> or just treat the zero as a non-movement like encounter? In other words
> the current point is left alone when a zero digit is observed?

Say a zero lands on the up direction after a digit >0 draws a line on the left direction but
now a line is NOT drawn on the up direction because of the zero. So say the next integer
after the zero is >o it just retraces the left direction but now going in the right direction over the left direction over laying either partially or same length or longer (a larger digit that traced over the left direction)..
When you consider the order of directions --- D,L,U,R,D,R,U,L repeat --->oo
-----------------------------------------------------------------------------^ a zero it retraces over the previous L drawn by
an integer >o. so wherever the retraced line ends up on the previous L line drawn it will
intersect on that line or beyond and go in the down direction. after the retrace it goes to the D
direction.
If multiple zeros are encountered it is easy to figure out what happens.
That up arrow above in my example should point from under the U.

> >> A simple concept, but interesting.
> >
> > It should end up looking like a brownian motion:
> >
> > https://en.wikipedia.org/wiki/Brownian_motion
> >

On 4/19/2023 2:34 PM, Dan joyce wrote:
> On Wednesday, April 19, 2023 at 4:10:57 PM UTC-4, Chris M. Thomasson wrote:
>> On 4/18/2023 7:11 PM, Chris M. Thomasson wrote:
>>> On 4/16/2023 2:00 PM, Dan joyce wrote:
>>>> Each digit of pi treated as an integer,
>>>> Starting with 3 and x=0 and y=0.
>>>>
>>>> 3 down x=0 y=-3
>>>> 1 left x=-1 y=-3
>>>> 4 up x=-1 y=1
>>>> 1 right x=0 y=1
>>>> 5 down x=0 y=-4
>>>> 9 right x=9 y=-4
>>>> 2 up x=9 y=-2
>>>> 6 left x=3 y=-2
>>>> 5 D x=3 y=-7
>>>> 3 L x=0 y=-7
>>>> 5 U x=0 y=-2
>>>> 8 R x=8 y=-2
>>>> 9 D x=8 y=-11
>>>> 7 R x=15 y=-11
>>>> 9 U x=15 y=-2
>>>> 3 L x=12 y=-2
>>>> 2
>>>>
>>>> Repeat that order of directions with each digit of pi.
>>>> What will be the x/y coordinates on the Cartesian coordinate plain
>>>> after 1,000,000 digits of pi?
>>>> How many times will it cross the x=0 axis and y=0 axis or where an
>>>> actual digit of pi ends up on x=0 and y=0?
>>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
>>>>
>>>> We know pi's digits --->oo but the Cartesian coordinate plain will not
>>>> --->oo in any direction, in fact using the above method it will cross
>>>> or land on the x=0 or y=0 --->oo.
>>>> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the single
>>>> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
>>>> pattern of joining lines but it takes 140 iterations to complete the
>>>> pattern.
>>>> Then it just retraces the lines in the next 140 iterations and so on
>>>> --->oo.
>>>>

>>>> etc.
>>>> The numbers above from 0-9 repeated for each direction to 140
>>>> iterations produces a unique 140 x\y coordinates and then repeats that
>>>> same unique x\y coordinates in the next 140 iterations and so-on.
>>>> When a zero or zeros like in pi are encountered it does not draw a
>>>> line but uses only a direction change.
>> Wait a minute. I am missing where it "changes direction" when a zero
>> digit is encountered. You say x=0, y=0 so are you resetting the origin,
>> or just treat the zero as a non-movement like encounter? In other words
>> the current point is left alone when a zero digit is observed?
>
> Say a zero lands on the up direction after a digit >0 draws a line on the left direction but
> now a line is NOT drawn on the up direction because of the zero. So say the next integer
> after the zero is >o it just retraces the left direction but now going in the right direction over the left direction over laying either partially or same length or longer (a larger digit that traced over the left direction).
> When you consider the order of directions --- D,L,U,R,D,R,U,L repeat --->oo
[...]

Is this close? Using only a 5-ary symbol system for simplicity:

Say we define in a 2d plane the following normalized directions:

neutral = { 0, 0 }
up = { 0, 1 }
down = { 0, -1 }
left = { -1, 0 }
right = { 1, 0 }

where:

0 = neutral
1 = up
2 = down
3 = left
4 = right

So, a number

10133402

If we started with a point z at point { 0, 0 },

it would be:

z = { 0, 0 }

// iterate the digits

1: z = z + up = { 0, 1 }
0: z = z + neutral = { 0, 1 }
1: z = z + up = { 0, 2 }
3: z = z + left = { -1, 2 }
3: z = z + left = { -2, 2 }
4: z = z + right = { -1, 2 }
0: z = z + neutral = { -1, 2 }
2: z = z + down = { -1, 1 }

I only used a 5-ary set of symbols, but it would work.

On Wednesday, April 19, 2023 at 6:07:35 PM UTC-4, Chris M. Thomasson wrote:
> On 4/19/2023 2:34 PM, Dan joyce wrote:
> > On Wednesday, April 19, 2023 at 4:10:57 PM UTC-4, Chris M. Thomasson wrote:
> >> On 4/18/2023 7:11 PM, Chris M. Thomasson wrote:
> >>> On 4/16/2023 2:00 PM, Dan joyce wrote:
> >>>> Each digit of pi treated as an integer,
> >>>> Starting with 3 and x=0 and y=0.
> >>>>
> >>>> 3 down x=0 y=-3
> >>>> 1 left x=-1 y=-3
> >>>> 4 up x=-1 y=1
> >>>> 1 right x=0 y=1
> >>>> 5 down x=0 y=-4
> >>>> 9 right x=9 y=-4
> >>>> 2 up x=9 y=-2
> >>>> 6 left x=3 y=-2
> >>>> 5 D x=3 y=-7
> >>>> 3 L x=0 y=-7
> >>>> 5 U x=0 y=-2
> >>>> 8 R x=8 y=-2
> >>>> 9 D x=8 y=-11
> >>>> 7 R x=15 y=-11
> >>>> 9 U x=15 y=-2
> >>>> 3 L x=12 y=-2
> >>>> 2
> >>>>
> >>>> Repeat that order of directions with each digit of pi.
> >>>> What will be the x/y coordinates on the Cartesian coordinate plain
> >>>> after 1,000,000 digits of pi?
> >>>> How many times will it cross the x=0 axis and y=0 axis or where an
> >>>> actual digit of pi ends up on x=0 and y=0?
> >>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
> >>>>
> >>>> We know pi's digits --->oo but the Cartesian coordinate plain will not
> >>>> --->oo in any direction, in fact using the above method it will cross
> >>>> or land on the x=0 or y=0 --->oo.
> >>>> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the single
> >>>> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
> >>>> pattern of joining lines but it takes 140 iterations to complete the
> >>>> pattern.
> >>>> Then it just retraces the lines in the next 140 iterations and so on
> >>>> --->oo.
> >>>>
> >>>> etc.
> >>>> The numbers above from 0-9 repeated for each direction to 140
> >>>> iterations produces a unique 140 x\y coordinates and then repeats that
> >>>> same unique x\y coordinates in the next 140 iterations and so-on.
> >>>> When a zero or zeros like in pi are encountered it does not draw a
> >>>> line but uses only a direction change.
> >> Wait a minute. I am missing where it "changes direction" when a zero
> >> digit is encountered. You say x=0, y=0 so are you resetting the origin,
> >> or just treat the zero as a non-movement like encounter? In other words
> >> the current point is left alone when a zero digit is observed?
> >
> > Say a zero lands on the up direction after a digit >0 draws a line on the left direction but
> > now a line is NOT drawn on the up direction because of the zero. So say the next integer
> > after the zero is >o it just retraces the left direction but now going in the right direction over the left direction over laying either partially or same length or longer (a larger digit that traced over the left direction).
> > When you consider the order of directions --- D,L,U,R,D,R,U,L repeat --->oo
> [...]
>
> Is this close? Using only a 5-ary symbol system for simplicity:
>
> Say we define in a 2d plane the following normalized directions:
>
> neutral = { 0, 0 }
> up = { 0, 1 }
> down = { 0, -1 }
> left = { -1, 0 }
> right = { 1, 0 }
>
> where:
>
> 0 = neutral
> 1 = up
> 2 = down
> 3 = left
> 4 = right
>
>
> So, a number
>
> 10133402
>
> If we started with a point z at point { 0, 0 },
>
> it would be:
>
> z = { 0, 0 }
>
> // iterate the digits
>
> 1: z = z + up = { 0, 1 }
> 0: z = z + neutral = { 0, 1 }
> 1: z = z + up = { 0, 2 }
> 3: z = z + left = { -1, 2 }
> 3: z = z + left = { -2, 2 }
> 4: z = z + right = { -1, 2 }
> 0: z = z + neutral = { -1, 2 }
> 2: z = z + down = { -1, 1 }
>
> I only used a 5-ary set of symbols, but it would work.

You are using the digit length as a direction where I am using the order of direction
to point that next integer to ---- D,LU,R,D,R,U,L
We have to cover the 10 positions that are in pi. 0-9. So counting 0 as a neutral digit
and adding the other 9 = 10.

On 4/19/2023 3:23 PM, Dan joyce wrote:
> On Wednesday, April 19, 2023 at 6:07:35 PM UTC-4, Chris M. Thomasson wrote:
>> On 4/19/2023 2:34 PM, Dan joyce wrote:
>>> On Wednesday, April 19, 2023 at 4:10:57 PM UTC-4, Chris M. Thomasson wrote:
>>>> On 4/18/2023 7:11 PM, Chris M. Thomasson wrote:
>>>>> On 4/16/2023 2:00 PM, Dan joyce wrote:
>>>>>> Each digit of pi treated as an integer,
>>>>>> Starting with 3 and x=0 and y=0.
>>>>>>
>>>>>> 3 down x=0 y=-3
>>>>>> 1 left x=-1 y=-3
>>>>>> 4 up x=-1 y=1
>>>>>> 1 right x=0 y=1
>>>>>> 5 down x=0 y=-4
>>>>>> 9 right x=9 y=-4
>>>>>> 2 up x=9 y=-2
>>>>>> 6 left x=3 y=-2
>>>>>> 5 D x=3 y=-7
>>>>>> 3 L x=0 y=-7
>>>>>> 5 U x=0 y=-2
>>>>>> 8 R x=8 y=-2
>>>>>> 9 D x=8 y=-11
>>>>>> 7 R x=15 y=-11
>>>>>> 9 U x=15 y=-2
>>>>>> 3 L x=12 y=-2
>>>>>> 2
>>>>>>
>>>>>> Repeat that order of directions with each digit of pi.
>>>>>> What will be the x/y coordinates on the Cartesian coordinate plain
>>>>>> after 1,000,000 digits of pi?
>>>>>> How many times will it cross the x=0 axis and y=0 axis or where an
>>>>>> actual digit of pi ends up on x=0 and y=0?
>>>>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
>>>>>>
>>>>>> We know pi's digits --->oo but the Cartesian coordinate plain will not
>>>>>> --->oo in any direction, in fact using the above method it will cross
>>>>>> or land on the x=0 or y=0 --->oo.
>>>>>> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the single
>>>>>> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
>>>>>> pattern of joining lines but it takes 140 iterations to complete the
>>>>>> pattern.
>>>>>> Then it just retraces the lines in the next 140 iterations and so on
>>>>>> --->oo.
>>>>>>
>>>>>> etc.
>>>>>> The numbers above from 0-9 repeated for each direction to 140
>>>>>> iterations produces a unique 140 x\y coordinates and then repeats that
>>>>>> same unique x\y coordinates in the next 140 iterations and so-on.
>>>>>> When a zero or zeros like in pi are encountered it does not draw a
>>>>>> line but uses only a direction change.
>>>> Wait a minute. I am missing where it "changes direction" when a zero
>>>> digit is encountered. You say x=0, y=0 so are you resetting the origin,
>>>> or just treat the zero as a non-movement like encounter? In other words
>>>> the current point is left alone when a zero digit is observed?
>>>
>>> Say a zero lands on the up direction after a digit >0 draws a line on the left direction but
>>> now a line is NOT drawn on the up direction because of the zero. So say the next integer
>>> after the zero is >o it just retraces the left direction but now going in the right direction over the left direction over laying either partially or same length or longer (a larger digit that traced over the left direction).
>>> When you consider the order of directions --- D,L,U,R,D,R,U,L repeat --->oo
>> [...]
>>
>> Is this close? Using only a 5-ary symbol system for simplicity:
>>
>> Say we define in a 2d plane the following normalized directions:
>>
>> neutral = { 0, 0 }
>> up = { 0, 1 }
>> down = { 0, -1 }
>> left = { -1, 0 }
>> right = { 1, 0 }
>>
>> where:
>>
>> 0 = neutral
>> 1 = up
>> 2 = down
>> 3 = left
>> 4 = right
>>
>>
>> So, a number
>>
>> 10133402
>>
>> If we started with a point z at point { 0, 0 },
>>
>> it would be:
>>
>> z = { 0, 0 }
>>
>> // iterate the digits
>>
>> 1: z = z + up = { 0, 1 }
>> 0: z = z + neutral = { 0, 1 }
>> 1: z = z + up = { 0, 2 }
>> 3: z = z + left = { -1, 2 }
>> 3: z = z + left = { -2, 2 }
>> 4: z = z + right = { -1, 2 }
>> 0: z = z + neutral = { -1, 2 }
>> 2: z = z + down = { -1, 1 }
>>
>> I only used a 5-ary set of symbols, but it would work.
>
> You are using the digit length as a direction where I am using the order of direction
> to point that next integer to ---- D,LU,R,D,R,U,L

What is the LU? I think left and up. So z = z + left + up

LU seems to be treated as a single digit with the commas in your
direction list. Or is LU a normal vector like:

north_east = normalize({-1, 1}) ?

Fwiw, in my system, those directions would generate the following number

23142413

It generates D, L, U, R, D, R, U, L

Where:

z = { 0, 0 }

2: z = z + down = { 0, -1 }
3: z = z + left = { -1, -1 }
1: z = z + up = { -1, 0 }
4: z = z + right = { 0, 0 }
2: z = z + down = { 0, -1 }
4: z = z + right = { 1, -1 }
1: z = z + up = { 1, 0 }
3: z = z + left = { 0, 0 }

So zero ends up where at its original origin. Can you correct my system?
I don't think I made a mistake. I typed this into the newsreader.

> We have to cover the 10 positions that are in pi. 0-9. So counting 0 as a neutral digit
> and adding the other 9 = 10.

On 4/19/2023 3:39 PM, Chris M. Thomasson wrote:
> On 4/19/2023 3:23 PM, Dan joyce wrote:
>> On Wednesday, April 19, 2023 at 6:07:35 PM UTC-4, Chris M. Thomasson
>> wrote:
>>> On 4/19/2023 2:34 PM, Dan joyce wrote:
>>>> On Wednesday, April 19, 2023 at 4:10:57 PM UTC-4, Chris M. Thomasson
>>>> wrote:
>>>>> On 4/18/2023 7:11 PM, Chris M. Thomasson wrote:
>>>>>> On 4/16/2023 2:00 PM, Dan joyce wrote:
>>>>>>> Each digit of pi treated as an integer,
>>>>>>> Starting with 3 and x=0 and y=0.
>>>>>>>
>>>>>>> 3 down x=0 y=-3
>>>>>>> 1 left x=-1 y=-3
>>>>>>> 4 up x=-1 y=1
>>>>>>> 1 right x=0 y=1
>>>>>>> 5 down x=0 y=-4
>>>>>>> 9 right x=9 y=-4
>>>>>>> 2 up x=9 y=-2
>>>>>>> 6 left x=3 y=-2
>>>>>>> 5 D x=3 y=-7
>>>>>>> 3 L x=0 y=-7
>>>>>>> 5 U x=0 y=-2
>>>>>>> 8 R x=8 y=-2
>>>>>>> 9 D x=8 y=-11
>>>>>>> 7 R x=15 y=-11
>>>>>>> 9 U x=15 y=-2
>>>>>>> 3 L x=12 y=-2
>>>>>>> 2
>>>>>>>
>>>>>>> Repeat that order of directions with each digit of pi.
>>>>>>> What will be the x/y coordinates on the Cartesian coordinate plain
>>>>>>> after 1,000,000 digits of pi?
>>>>>>> How many times will it cross the x=0 axis and y=0 axis or where an
>>>>>>> actual digit of pi ends up on x=0 and y=0?
>>>>>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2
>>>>>>> respectfully
>>>>>>>
>>>>>>> We know pi's digits --->oo but the Cartesian coordinate plain
>>>>>>> will not
>>>>>>> --->oo in any direction, in fact using the above method it will
>>>>>>> cross
>>>>>>> or land on the x=0 or y=0 --->oo.
>>>>>>> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the
>>>>>>> single
>>>>>>> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
>>>>>>> pattern of joining lines but it takes 140 iterations to complete the
>>>>>>> pattern.
>>>>>>> Then it just retraces the lines in the next 140 iterations and so on
>>>>>>> --->oo.
>>>>>>>
>>>>>>> etc.
>>>>>>> The numbers above from 0-9 repeated for each direction to 140
>>>>>>> iterations produces a unique 140 x\y coordinates and then repeats
>>>>>>> that
>>>>>>> same unique x\y coordinates in the next 140 iterations and so-on.
>>>>>>> When a zero or zeros like in pi are encountered it does not draw a
>>>>>>> line but uses only a direction change.
>>>>> Wait a minute. I am missing where it "changes direction" when a zero
>>>>> digit is encountered. You say x=0, y=0 so are you resetting the
>>>>> origin,
>>>>> or just treat the zero as a non-movement like encounter? In other
>>>>> words
>>>>> the current point is left alone when a zero digit is observed?
>>>>
>>>> Say a zero lands on the up direction after a digit >0 draws a line
>>>> on the left direction but
>>>> now a line is NOT drawn on the up direction because of the zero. So
>>>> say the next integer
>>>> after the zero is >o it just retraces the left direction but now
>>>> going in the right direction over the left direction over laying
>>>> either partially or same length or longer (a larger digit that
>>>> traced over the left direction).
>>>> When you consider the order of directions --- D,L,U,R,D,R,U,L repeat
>>>> --->oo
>>> [...]
>>>
>>> Is this close? Using only a 5-ary symbol system for simplicity:
>>>
>>> Say we define in a 2d plane the following normalized directions:
>>>
>>> neutral = { 0, 0 }
>>> up = { 0, 1 }
>>> down = { 0, -1 }
>>> left = { -1, 0 }
>>> right = { 1, 0 }
>>>
>>> where:
>>>
>>> 0 = neutral
>>> 1 = up
>>> 2 = down
>>> 3 = left
>>> 4 = right
>>>
>>>
>>> So, a number
>>>
>>> 10133402
>>>
>>> If we started with a point z at point { 0, 0 },
>>>
>>> it would be:
>>>
>>> z = { 0, 0 }
>>>
>>> // iterate the digits
>>>
>>> 1: z = z + up = { 0, 1 }
>>> 0: z = z + neutral = { 0, 1 }
>>> 1: z = z + up = { 0, 2 }
>>> 3: z = z + left = { -1, 2 }
>>> 3: z = z + left = { -2, 2 }
>>> 4: z = z + right = { -1, 2 }
>>> 0: z = z + neutral = { -1, 2 }
>>> 2: z = z + down = { -1, 1 }
>>>
>>> I only used a 5-ary set of symbols, but it would work.
>>
>> You are using the digit length as a direction where I am using the
>> order of direction
>> to point that next integer to  ---- D,LU,R,D,R,U,L
>
> What is the LU? I think left and up. So z = z + left + up
>
> LU seems to be treated as a single digit with the commas in your
> direction list. Or is LU a normal vector like:
>

> north_east = normalize({-1, 1}) ?
^^^^^^^^^^^^^^^^^^^^^^^^^^
[..]

Humm.. I don't think I should necessarily normalize the north_east vector.

north_east = {-1, 1}

Or, in this case I should define it as:

left_up = {-1, 1}

;^)

On Wednesday, April 19, 2023 at 1:02:53 PM UTC-7, Chris M. Thomasson wrote:
> On 4/19/2023 10:36 AM, mitchr...@gmail.com wrote:
> > On Sunday, April 16, 2023 at 2:00:04 PM UTC-7, Dan joyce wrote:
> >> Each digit of pi treated as an integer,
> >> Starting with 3 and x=0 and y=0.
> >>
> >> 3 down x=0 y=-3
> >> 1 left x=-1 y=-3
> >> 4 up x=-1 y=1
> >> 1 right x=0 y=1
> >> 5 down x=0 y=-4
> >> 9 right x=9 y=-4
> >> 2 up x=9 y=-2
> >> 6 left x=3 y=-2
> >> 5 D x=3 y=-7
> >> 3 L x=0 y=-7
> >> 5 U x=0 y=-2
> >> 8 R x=8 y=-2
> >> 9 D x=8 y=-11
> >> 7 R x=15 y=-11
> >> 9 U x=15 y=-2
> >> 3 L x=12 y=-2
> >> 2
> >>
> >> Repeat that order of directions with each digit of pi.
> >> What will be the x/y coordinates on the Cartesian coordinate plain
> >> after 1,000,000 digits of pi?
> >> How many times will it cross the x=0 axis and y=0 axis or where an
> >> actual digit of pi ends up on x=0 and y=0?
> >> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
> >>
> >> We know pi's digits --->oo but the Cartesian coordinate plain will not
> >> --->oo in any direction, in fact using the above method it will cross
> >> or land on the x=0 or y=0 --->oo.
> >>
> >> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the single
> >> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
> >> pattern of joining lines but it takes 140 iterations to complete the pattern.
> >> Then it just retraces the lines in the next 140 iterations and so on --->oo.
> >>
> >> 0 D A zero so no change so x=0,y=0
> >> 1 L x=-1 y=0
> >> 2 U x=-1 y=2
> >> 3 R x=2 y=2
> >> 4 D x=2 y=-2
> >> 5 R x=7 y=-2
> >> 6 U x=7 y=4
> >> 7 L x=0 y=4
> >> 8 D x=0 y=-4
> >> 9 L x=-9 y=-4
> >> 0 U x=-9 y=-4
> >> 1 R x=-8 y=-4
> >> 2 D x=-8 y=-6
> >> etc.
> >> The numbers above from 0-9 repeated for each direction to 140 iterations produces a unique 140 x\y coordinates and then repeats that same unique x\y coordinates in the next 140 iterations and so-on.
> >> When a zero or zeros like in pi are encountered it does not draw a line but uses only a direction change.
> >>
> >>
> >> A simple concept, but interesting.
> >>
> >> Dan
> >
> > Digits are not very accurate.
> How many accurate base-10 symbols of pi can you generate?

That is the right question. So How do you verify?
Can you prove you can verify more than a few?
where is your proof of PI accuracy?
There is no accurate PI formula.

Mitchell Raemsch

> > Round math can only go so far...
> > Where PI is a transcendental with infinite digits.
> > Man has uncertainty limit about transcendental instead.
> > How is PI verified?

On Wednesday, April 19, 2023 at 6:43:43 PM UTC-4, Chris M. Thomasson wrote:
> On 4/19/2023 3:39 PM, Chris M. Thomasson wrote:
> > On 4/19/2023 3:23 PM, Dan joyce wrote:
> >> On Wednesday, April 19, 2023 at 6:07:35 PM UTC-4, Chris M. Thomasson
> >> wrote:
> >>> On 4/19/2023 2:34 PM, Dan joyce wrote:
> >>>> On Wednesday, April 19, 2023 at 4:10:57 PM UTC-4, Chris M. Thomasson
> >>>> wrote:
> >>>>> On 4/18/2023 7:11 PM, Chris M. Thomasson wrote:
> >>>>>> On 4/16/2023 2:00 PM, Dan joyce wrote:
> >>>>>>> Each digit of pi treated as an integer,
> >>>>>>> Starting with 3 and x=0 and y=0.
> >>>>>>>
> >>>>>>> 3 down x=0 y=-3
> >>>>>>> 1 left x=-1 y=-3
> >>>>>>> 4 up x=-1 y=1
> >>>>>>> 1 right x=0 y=1
> >>>>>>> 5 down x=0 y=-4
> >>>>>>> 9 right x=9 y=-4
> >>>>>>> 2 up x=9 y=-2
> >>>>>>> 6 left x=3 y=-2
> >>>>>>> 5 D x=3 y=-7
> >>>>>>> 3 L x=0 y=-7
> >>>>>>> 5 U x=0 y=-2
> >>>>>>> 8 R x=8 y=-2
> >>>>>>> 9 D x=8 y=-11
> >>>>>>> 7 R x=15 y=-11
> >>>>>>> 9 U x=15 y=-2
> >>>>>>> 3 L x=12 y=-2
> >>>>>>> 2
> >>>>>>>
> >>>>>>> Repeat that order of directions with each digit of pi.
> >>>>>>> What will be the x/y coordinates on the Cartesian coordinate plain
> >>>>>>> after 1,000,000 digits of pi?
> >>>>>>> How many times will it cross the x=0 axis and y=0 axis or where an
> >>>>>>> actual digit of pi ends up on x=0 and y=0?
> >>>>>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2
> >>>>>>> respectfully
> >>>>>>>
> >>>>>>> We know pi's digits --->oo but the Cartesian coordinate plain
> >>>>>>> will not
> >>>>>>> --->oo in any direction, in fact using the above method it will
> >>>>>>> cross
> >>>>>>> or land on the x=0 or y=0 --->oo.
> >>>>>>> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the
> >>>>>>> single
> >>>>>>> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
> >>>>>>> pattern of joining lines but it takes 140 iterations to complete the
> >>>>>>> pattern.
> >>>>>>> Then it just retraces the lines in the next 140 iterations and so on
> >>>>>>> --->oo.
> >>>>>>>
> >>>>>>> etc.
> >>>>>>> The numbers above from 0-9 repeated for each direction to 140
> >>>>>>> iterations produces a unique 140 x\y coordinates and then repeats
> >>>>>>> that
> >>>>>>> same unique x\y coordinates in the next 140 iterations and so-on.
> >>>>>>> When a zero or zeros like in pi are encountered it does not draw a
> >>>>>>> line but uses only a direction change.
> >>>>> Wait a minute. I am missing where it "changes direction" when a zero
> >>>>> digit is encountered. You say x=0, y=0 so are you resetting the
> >>>>> origin,
> >>>>> or just treat the zero as a non-movement like encounter? In other
> >>>>> words
> >>>>> the current point is left alone when a zero digit is observed?
> >>>>
> >>>> Say a zero lands on the up direction after a digit >0 draws a line
> >>>> on the left direction but
> >>>> now a line is NOT drawn on the up direction because of the zero. So
> >>>> say the next integer
> >>>> after the zero is >o it just retraces the left direction but now
> >>>> going in the right direction over the left direction over laying
> >>>> either partially or same length or longer (a larger digit that
> >>>> traced over the left direction).
> >>>> When you consider the order of directions --- D,L,U,R,D,R,U,L repeat
> >>>> --->oo
> >>> [...]
> >>>
> >>> Is this close? Using only a 5-ary symbol system for simplicity:
> >>>
> >>> Say we define in a 2d plane the following normalized directions:
> >>>
> >>> neutral = { 0, 0 }
> >>> up = { 0, 1 }
> >>> down = { 0, -1 }
> >>> left = { -1, 0 }
> >>> right = { 1, 0 }
> >>>
> >>> where:
> >>>
> >>> 0 = neutral
> >>> 1 = up
> >>> 2 = down
> >>> 3 = left
> >>> 4 = right
> >>>
> >>>
> >>> So, a number
> >>>
> >>> 10133402
> >>>
> >>> If we started with a point z at point { 0, 0 },
> >>>
> >>> it would be:
> >>>
> >>> z = { 0, 0 }
> >>>
> >>> // iterate the digits
> >>>
> >>> 1: z = z + up = { 0, 1 }
> >>> 0: z = z + neutral = { 0, 1 }
> >>> 1: z = z + up = { 0, 2 }
> >>> 3: z = z + left = { -1, 2 }
> >>> 3: z = z + left = { -2, 2 }
> >>> 4: z = z + right = { -1, 2 }
> >>> 0: z = z + neutral = { -1, 2 }
> >>> 2: z = z + down = { -1, 1 }
> >>>
> >>> I only used a 5-ary set of symbols, but it would work.
> >>
> >> You are using the digit length as a direction where I am using the
> >> order of direction
> >> to point that next integer to ---- D,LU,R,D,R,U,L
> >
> > What is the LU? I think left and up. So z = z + left + up
> >
> > LU seems to be treated as a single digit with the commas in your
> > direction list. Or is LU a normal vector like:
> >
>
>
> > north_east = normalize({-1, 1}) ?
> ^^^^^^^^^^^^^^^^^^^^^^^^^^
> [..]
>
> Humm.. I don't think I should necessarily normalize the north_east vector..
>
> north_east = {-1, 1}
>
> Or, in this case I should define it as:
>
> left_up = {-1, 1}
>
> ;^)
You could also set a 10 sided n-gon drawing to the center of each line on the inner
circle that would give 10 directions from the end of the last known direction.
The naming convention for each direction could be, starting at the top line
going down the right side of the inner circle -- x, x1,x2 stopping at 1/4 circle
Then going down from x on the left top -- -x1, -x2 =5 directions for the top half.
On the bottom half right side-- y, y1, y2 left side bottom half-- -y1,-y2
Just another brainstorm.

On 4/19/2023 3:51 PM, Dan joyce wrote:
> On Wednesday, April 19, 2023 at 6:43:43 PM UTC-4, Chris M. Thomasson wrote:
>> On 4/19/2023 3:39 PM, Chris M. Thomasson wrote:
>>> On 4/19/2023 3:23 PM, Dan joyce wrote:
>>>> On Wednesday, April 19, 2023 at 6:07:35 PM UTC-4, Chris M. Thomasson
>>>> wrote:
>>>>> On 4/19/2023 2:34 PM, Dan joyce wrote:
>>>>>> On Wednesday, April 19, 2023 at 4:10:57 PM UTC-4, Chris M. Thomasson
>>>>>> wrote:
>>>>>>> On 4/18/2023 7:11 PM, Chris M. Thomasson wrote:
>>>>>>>> On 4/16/2023 2:00 PM, Dan joyce wrote:
>>>>>>>>> Each digit of pi treated as an integer,
>>>>>>>>> Starting with 3 and x=0 and y=0.
>>>>>>>>>
>>>>>>>>> 3 down x=0 y=-3
>>>>>>>>> 1 left x=-1 y=-3
>>>>>>>>> 4 up x=-1 y=1
>>>>>>>>> 1 right x=0 y=1
>>>>>>>>> 5 down x=0 y=-4
>>>>>>>>> 9 right x=9 y=-4
>>>>>>>>> 2 up x=9 y=-2
>>>>>>>>> 6 left x=3 y=-2
>>>>>>>>> 5 D x=3 y=-7
>>>>>>>>> 3 L x=0 y=-7
>>>>>>>>> 5 U x=0 y=-2
>>>>>>>>> 8 R x=8 y=-2
>>>>>>>>> 9 D x=8 y=-11
>>>>>>>>> 7 R x=15 y=-11
>>>>>>>>> 9 U x=15 y=-2
>>>>>>>>> 3 L x=12 y=-2
>>>>>>>>> 2
>>>>>>>>>
>>>>>>>>> Repeat that order of directions with each digit of pi.
>>>>>>>>> What will be the x/y coordinates on the Cartesian coordinate plain
>>>>>>>>> after 1,000,000 digits of pi?
>>>>>>>>> How many times will it cross the x=0 axis and y=0 axis or where an
>>>>>>>>> actual digit of pi ends up on x=0 and y=0?
>>>>>>>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2
>>>>>>>>> respectfully
>>>>>>>>>
>>>>>>>>> We know pi's digits --->oo but the Cartesian coordinate plain
>>>>>>>>> will not
>>>>>>>>> --->oo in any direction, in fact using the above method it will
>>>>>>>>> cross
>>>>>>>>> or land on the x=0 or y=0 --->oo.
>>>>>>>>> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the
>>>>>>>>> single
>>>>>>>>> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
>>>>>>>>> pattern of joining lines but it takes 140 iterations to complete the
>>>>>>>>> pattern.
>>>>>>>>> Then it just retraces the lines in the next 140 iterations and so on
>>>>>>>>> --->oo.
>>>>>>>>>
>>>>>>>>> etc.
>>>>>>>>> The numbers above from 0-9 repeated for each direction to 140
>>>>>>>>> iterations produces a unique 140 x\y coordinates and then repeats
>>>>>>>>> that
>>>>>>>>> same unique x\y coordinates in the next 140 iterations and so-on.
>>>>>>>>> When a zero or zeros like in pi are encountered it does not draw a
>>>>>>>>> line but uses only a direction change.
>>>>>>> Wait a minute. I am missing where it "changes direction" when a zero
>>>>>>> digit is encountered. You say x=0, y=0 so are you resetting the
>>>>>>> origin,
>>>>>>> or just treat the zero as a non-movement like encounter? In other
>>>>>>> words
>>>>>>> the current point is left alone when a zero digit is observed?
>>>>>>
>>>>>> Say a zero lands on the up direction after a digit >0 draws a line
>>>>>> on the left direction but
>>>>>> now a line is NOT drawn on the up direction because of the zero. So
>>>>>> say the next integer
>>>>>> after the zero is >o it just retraces the left direction but now
>>>>>> going in the right direction over the left direction over laying
>>>>>> either partially or same length or longer (a larger digit that
>>>>>> traced over the left direction).
>>>>>> When you consider the order of directions --- D,L,U,R,D,R,U,L repeat
>>>>>> --->oo
>>>>> [...]
>>>>>
>>>>> Is this close? Using only a 5-ary symbol system for simplicity:
>>>>>
>>>>> Say we define in a 2d plane the following normalized directions:
>>>>>
>>>>> neutral = { 0, 0 }
>>>>> up = { 0, 1 }
>>>>> down = { 0, -1 }
>>>>> left = { -1, 0 }
>>>>> right = { 1, 0 }
>>>>>
>>>>> where:
>>>>>
>>>>> 0 = neutral
>>>>> 1 = up
>>>>> 2 = down
>>>>> 3 = left
>>>>> 4 = right
>>>>>
>>>>>
>>>>> So, a number
>>>>>
>>>>> 10133402
>>>>>
>>>>> If we started with a point z at point { 0, 0 },
>>>>>
>>>>> it would be:
>>>>>
>>>>> z = { 0, 0 }
>>>>>
>>>>> // iterate the digits
>>>>>
>>>>> 1: z = z + up = { 0, 1 }
>>>>> 0: z = z + neutral = { 0, 1 }
>>>>> 1: z = z + up = { 0, 2 }
>>>>> 3: z = z + left = { -1, 2 }
>>>>> 3: z = z + left = { -2, 2 }
>>>>> 4: z = z + right = { -1, 2 }
>>>>> 0: z = z + neutral = { -1, 2 }
>>>>> 2: z = z + down = { -1, 1 }
>>>>>
>>>>> I only used a 5-ary set of symbols, but it would work.
>>>>
>>>> You are using the digit length as a direction where I am using the
>>>> order of direction
>>>> to point that next integer to ---- D,LU,R,D,R,U,L
>>>
>>> What is the LU? I think left and up. So z = z + left + up
>>>
>>> LU seems to be treated as a single digit with the commas in your
>>> direction list. Or is LU a normal vector like:
>>>
>>
>>
>>> north_east = normalize({-1, 1}) ?
>> ^^^^^^^^^^^^^^^^^^^^^^^^^^
>> [..]
>>
>> Humm.. I don't think I should necessarily normalize the north_east vector.
>>
>> north_east = {-1, 1}
>>
>> Or, in this case I should define it as:
>>
>> left_up = {-1, 1}
>>
>> ;^)
> You could also set a 10 sided n-gon drawing to the center of each line on the inner
> circle that would give 10 directions from the end of the last known direction.
> The naming convention for each direction could be, starting at the top line
> going down the right side of the inner circle -- x, x1,x2 stopping at 1/4 circle
> Then going down from x on the left top -- -x1, -x2 =5 directions for the top half.
> On the bottom half right side-- y, y1, y2 left side bottom half-- -y1,-y2
> Just another brainstorm.

Humm... For some reason, these rules kind of remind me of playing the
chaos game with an n-gon.

https://en.wikipedia.org/wiki/Chaos_game

On Wednesday, April 19, 2023 at 6:56:26 PM UTC-4, Chris M. Thomasson wrote:
> On 4/19/2023 3:51 PM, Dan joyce wrote:
> > On Wednesday, April 19, 2023 at 6:43:43 PM UTC-4, Chris M. Thomasson wrote:
> >> On 4/19/2023 3:39 PM, Chris M. Thomasson wrote:
> >>> On 4/19/2023 3:23 PM, Dan joyce wrote:
> >>>> On Wednesday, April 19, 2023 at 6:07:35 PM UTC-4, Chris M. Thomasson
> >>>> wrote:
> >>>>> On 4/19/2023 2:34 PM, Dan joyce wrote:
> >>>>>> On Wednesday, April 19, 2023 at 4:10:57 PM UTC-4, Chris M. Thomasson
> >>>>>> wrote:
> >>>>>>> On 4/18/2023 7:11 PM, Chris M. Thomasson wrote:
> >>>>>>>> On 4/16/2023 2:00 PM, Dan joyce wrote:
> >>>>>>>>> Each digit of pi treated as an integer,
> >>>>>>>>> Starting with 3 and x=0 and y=0.
> >>>>>>>>>
> >>>>>>>>> 3 down x=0 y=-3
> >>>>>>>>> 1 left x=-1 y=-3
> >>>>>>>>> 4 up x=-1 y=1
> >>>>>>>>> 1 right x=0 y=1
> >>>>>>>>> 5 down x=0 y=-4
> >>>>>>>>> 9 right x=9 y=-4
> >>>>>>>>> 2 up x=9 y=-2
> >>>>>>>>> 6 left x=3 y=-2
> >>>>>>>>> 5 D x=3 y=-7
> >>>>>>>>> 3 L x=0 y=-7
> >>>>>>>>> 5 U x=0 y=-2
> >>>>>>>>> 8 R x=8 y=-2
> >>>>>>>>> 9 D x=8 y=-11
> >>>>>>>>> 7 R x=15 y=-11
> >>>>>>>>> 9 U x=15 y=-2
> >>>>>>>>> 3 L x=12 y=-2
> >>>>>>>>> 2
> >>>>>>>>>
> >>>>>>>>> Repeat that order of directions with each digit of pi.
> >>>>>>>>> What will be the x/y coordinates on the Cartesian coordinate plain
> >>>>>>>>> after 1,000,000 digits of pi?
> >>>>>>>>> How many times will it cross the x=0 axis and y=0 axis or where an
> >>>>>>>>> actual digit of pi ends up on x=0 and y=0?
> >>>>>>>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2
> >>>>>>>>> respectfully
> >>>>>>>>>
> >>>>>>>>> We know pi's digits --->oo but the Cartesian coordinate plain
> >>>>>>>>> will not
> >>>>>>>>> --->oo in any direction, in fact using the above method it will
> >>>>>>>>> cross
> >>>>>>>>> or land on the x=0 or y=0 --->oo.
> >>>>>>>>> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the
> >>>>>>>>> single
> >>>>>>>>> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
> >>>>>>>>> pattern of joining lines but it takes 140 iterations to complete the
> >>>>>>>>> pattern.
> >>>>>>>>> Then it just retraces the lines in the next 140 iterations and so on
> >>>>>>>>> --->oo.
> >>>>>>>>>
> >>>>>>>>> etc.
> >>>>>>>>> The numbers above from 0-9 repeated for each direction to 140
> >>>>>>>>> iterations produces a unique 140 x\y coordinates and then repeats
> >>>>>>>>> that
> >>>>>>>>> same unique x\y coordinates in the next 140 iterations and so-on.
> >>>>>>>>> When a zero or zeros like in pi are encountered it does not draw a
> >>>>>>>>> line but uses only a direction change.
> >>>>>>> Wait a minute. I am missing where it "changes direction" when a zero
> >>>>>>> digit is encountered. You say x=0, y=0 so are you resetting the
> >>>>>>> origin,
> >>>>>>> or just treat the zero as a non-movement like encounter? In other
> >>>>>>> words
> >>>>>>> the current point is left alone when a zero digit is observed?
> >>>>>>
> >>>>>> Say a zero lands on the up direction after a digit >0 draws a line
> >>>>>> on the left direction but
> >>>>>> now a line is NOT drawn on the up direction because of the zero. So
> >>>>>> say the next integer
> >>>>>> after the zero is >o it just retraces the left direction but now
> >>>>>> going in the right direction over the left direction over laying
> >>>>>> either partially or same length or longer (a larger digit that
> >>>>>> traced over the left direction).
> >>>>>> When you consider the order of directions --- D,L,U,R,D,R,U,L repeat
> >>>>>> --->oo
> >>>>> [...]
> >>>>>
> >>>>> Is this close? Using only a 5-ary symbol system for simplicity:
> >>>>>
> >>>>> Say we define in a 2d plane the following normalized directions:
> >>>>>
> >>>>> neutral = { 0, 0 }
> >>>>> up = { 0, 1 }
> >>>>> down = { 0, -1 }
> >>>>> left = { -1, 0 }
> >>>>> right = { 1, 0 }
> >>>>>
> >>>>> where:
> >>>>>
> >>>>> 0 = neutral
> >>>>> 1 = up
> >>>>> 2 = down
> >>>>> 3 = left
> >>>>> 4 = right
> >>>>>
> >>>>>
> >>>>> So, a number
> >>>>>
> >>>>> 10133402
> >>>>>
> >>>>> If we started with a point z at point { 0, 0 },
> >>>>>
> >>>>> it would be:
> >>>>>
> >>>>> z = { 0, 0 }
> >>>>>
> >>>>> // iterate the digits
> >>>>>
> >>>>> 1: z = z + up = { 0, 1 }
> >>>>> 0: z = z + neutral = { 0, 1 }
> >>>>> 1: z = z + up = { 0, 2 }
> >>>>> 3: z = z + left = { -1, 2 }
> >>>>> 3: z = z + left = { -2, 2 }
> >>>>> 4: z = z + right = { -1, 2 }
> >>>>> 0: z = z + neutral = { -1, 2 }
> >>>>> 2: z = z + down = { -1, 1 }
> >>>>>
> >>>>> I only used a 5-ary set of symbols, but it would work.
> >>>>
> >>>> You are using the digit length as a direction where I am using the
> >>>> order of direction
> >>>> to point that next integer to ---- D,LU,R,D,R,U,L
> >>>
> >>> What is the LU? I think left and up. So z = z + left + up
> >>>
> >>> LU seems to be treated as a single digit with the commas in your
> >>> direction list. Or is LU a normal vector like:
> >>>
> >>
> >>
> >>> north_east = normalize({-1, 1}) ?
> >> ^^^^^^^^^^^^^^^^^^^^^^^^^^
> >> [..]
> >>
> >> Humm.. I don't think I should necessarily normalize the north_east vector.
> >>
> >> north_east = {-1, 1}
> >>
> >> Or, in this case I should define it as:
> >>
> >> left_up = {-1, 1}
> >>
> >> ;^)
> > You could also set a 10 sided n-gon drawing to the center of each line on the inner
> > circle that would give 10 directions from the end of the last known direction.
> > The naming convention for each direction could be, starting at the top line
> > going down the right side of the inner circle -- x, x1,x2 stopping at 1/4 circle
> > Then going down from x on the left top -- -x1, -x2 =5 directions for the top half.
> > On the bottom half right side-- y, y1, y2 left side bottom half-- -y1,-y2
> > Just another brainstorm.
> Humm... For some reason, these rules kind of remind me of playing the
> chaos game with an n-gon.
>
> https://en.wikipedia.org/wiki/Chaos_game

On Wednesday, April 19, 2023 at 7:14:57 PM UTC-4, Dan joyce wrote:
> On Wednesday, April 19, 2023 at 6:56:26 PM UTC-4, Chris M. Thomasson wrote:
> > On 4/19/2023 3:51 PM, Dan joyce wrote:
> > > On Wednesday, April 19, 2023 at 6:43:43 PM UTC-4, Chris M. Thomasson wrote:
> > >> On 4/19/2023 3:39 PM, Chris M. Thomasson wrote:
> > >>> On 4/19/2023 3:23 PM, Dan joyce wrote:
> > >>>> On Wednesday, April 19, 2023 at 6:07:35 PM UTC-4, Chris M. Thomasson
> > >>>> wrote:
> > >>>>> On 4/19/2023 2:34 PM, Dan joyce wrote:
> > >>>>>> On Wednesday, April 19, 2023 at 4:10:57 PM UTC-4, Chris M. Thomasson
> > >>>>>> wrote:
> > >>>>>>> On 4/18/2023 7:11 PM, Chris M. Thomasson wrote:
> > >>>>>>>> On 4/16/2023 2:00 PM, Dan joyce wrote:
> > >>>>>>>>> Each digit of pi treated as an integer,
> > >>>>>>>>> Starting with 3 and x=0 and y=0.
> > >>>>>>>>>
> > >>>>>>>>> 3 down x=0 y=-3
> > >>>>>>>>> 1 left x=-1 y=-3
> > >>>>>>>>> 4 up x=-1 y=1
> > >>>>>>>>> 1 right x=0 y=1
> > >>>>>>>>> 5 down x=0 y=-4
> > >>>>>>>>> 9 right x=9 y=-4
> > >>>>>>>>> 2 up x=9 y=-2
> > >>>>>>>>> 6 left x=3 y=-2
> > >>>>>>>>> 5 D x=3 y=-7
> > >>>>>>>>> 3 L x=0 y=-7
> > >>>>>>>>> 5 U x=0 y=-2
> > >>>>>>>>> 8 R x=8 y=-2
> > >>>>>>>>> 9 D x=8 y=-11
> > >>>>>>>>> 7 R x=15 y=-11
> > >>>>>>>>> 9 U x=15 y=-2
> > >>>>>>>>> 3 L x=12 y=-2
> > >>>>>>>>> 2
> > >>>>>>>>>
> > >>>>>>>>> Repeat that order of directions with each digit of pi.
> > >>>>>>>>> What will be the x/y coordinates on the Cartesian coordinate plain
> > >>>>>>>>> after 1,000,000 digits of pi?
> > >>>>>>>>> How many times will it cross the x=0 axis and y=0 axis or where an
> > >>>>>>>>> actual digit of pi ends up on x=0 and y=0?
> > >>>>>>>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2
> > >>>>>>>>> respectfully
> > >>>>>>>>>
> > >>>>>>>>> We know pi's digits --->oo but the Cartesian coordinate plain
> > >>>>>>>>> will not
> > >>>>>>>>> --->oo in any direction, in fact using the above method it will
> > >>>>>>>>> cross
> > >>>>>>>>> or land on the x=0 or y=0 --->oo.
> > >>>>>>>>> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the
> > >>>>>>>>> single
> > >>>>>>>>> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
> > >>>>>>>>> pattern of joining lines but it takes 140 iterations to complete the
> > >>>>>>>>> pattern.
> > >>>>>>>>> Then it just retraces the lines in the next 140 iterations and so on
> > >>>>>>>>> --->oo.
> > >>>>>>>>>
> > >>>>>>>>> etc.
> > >>>>>>>>> The numbers above from 0-9 repeated for each direction to 140
> > >>>>>>>>> iterations produces a unique 140 x\y coordinates and then repeats
> > >>>>>>>>> that
> > >>>>>>>>> same unique x\y coordinates in the next 140 iterations and so-on.
> > >>>>>>>>> When a zero or zeros like in pi are encountered it does not draw a
> > >>>>>>>>> line but uses only a direction change.
> > >>>>>>> Wait a minute. I am missing where it "changes direction" when a zero
> > >>>>>>> digit is encountered. You say x=0, y=0 so are you resetting the
> > >>>>>>> origin,
> > >>>>>>> or just treat the zero as a non-movement like encounter? In other
> > >>>>>>> words
> > >>>>>>> the current point is left alone when a zero digit is observed?
> > >>>>>>
> > >>>>>> Say a zero lands on the up direction after a digit >0 draws a line
> > >>>>>> on the left direction but
> > >>>>>> now a line is NOT drawn on the up direction because of the zero. So
> > >>>>>> say the next integer
> > >>>>>> after the zero is >o it just retraces the left direction but now
> > >>>>>> going in the right direction over the left direction over laying
> > >>>>>> either partially or same length or longer (a larger digit that
> > >>>>>> traced over the left direction).
> > >>>>>> When you consider the order of directions --- D,L,U,R,D,R,U,L repeat
> > >>>>>> --->oo
> > >>>>> [...]
> > >>>>>
> > >>>>> Is this close? Using only a 5-ary symbol system for simplicity:
> > >>>>>
> > >>>>> Say we define in a 2d plane the following normalized directions:
> > >>>>>
> > >>>>> neutral = { 0, 0 }
> > >>>>> up = { 0, 1 }
> > >>>>> down = { 0, -1 }
> > >>>>> left = { -1, 0 }
> > >>>>> right = { 1, 0 }
> > >>>>>
> > >>>>> where:
> > >>>>>
> > >>>>> 0 = neutral
> > >>>>> 1 = up
> > >>>>> 2 = down
> > >>>>> 3 = left
> > >>>>> 4 = right
> > >>>>>
> > >>>>>
> > >>>>> So, a number
> > >>>>>
> > >>>>> 10133402
> > >>>>>
> > >>>>> If we started with a point z at point { 0, 0 },
> > >>>>>
> > >>>>> it would be:
> > >>>>>
> > >>>>> z = { 0, 0 }
> > >>>>>
> > >>>>> // iterate the digits
> > >>>>>
> > >>>>> 1: z = z + up = { 0, 1 }
> > >>>>> 0: z = z + neutral = { 0, 1 }
> > >>>>> 1: z = z + up = { 0, 2 }
> > >>>>> 3: z = z + left = { -1, 2 }
> > >>>>> 3: z = z + left = { -2, 2 }
> > >>>>> 4: z = z + right = { -1, 2 }
> > >>>>> 0: z = z + neutral = { -1, 2 }
> > >>>>> 2: z = z + down = { -1, 1 }
> > >>>>>
> > >>>>> I only used a 5-ary set of symbols, but it would work.
> > >>>>
> > >>>> You are using the digit length as a direction where I am using the
> > >>>> order of direction
> > >>>> to point that next integer to ---- D,LU,R,D,R,U,L
> > >>>
> > >>> What is the LU? I think left and up. So z = z + left + up
> > >>>
> > >>> LU seems to be treated as a single digit with the commas in your
> > >>> direction list. Or is LU a normal vector like:
> > >>>
> > >>
> > >>
> > >>> north_east = normalize({-1, 1}) ?
> > >> ^^^^^^^^^^^^^^^^^^^^^^^^^^
> > >> [..]
> > >>
> > >> Humm.. I don't think I should necessarily normalize the north_east vector.
> > >>
> > >> north_east = {-1, 1}
> > >>
> > >> Or, in this case I should define it as:
> > >>
> > >> left_up = {-1, 1}
> > >>
> > >> ;^)
> > > You could also set a 10 sided n-gon drawing to the center of each line on the inner
> > > circle that would give 10 directions from the end of the last known direction.
> > > The naming convention for each direction could be, starting at the top line
> > > going down the right side of the inner circle -- x, x1,x2 stopping at 1/4 circle
> > > Then going down from x on the left top -- -x1, -x2 =5 directions for the top half.
> > > On the bottom half right side-- y, y1, y2 left side bottom half-- -y1,-y2
> > > Just another brainstorm.
> > Humm... For some reason, these rules kind of remind me of playing the
> > chaos game with an n-gon.
> >
> > https://en.wikipedia.org/wiki/Chaos_game
> There is no pictorial of 10 sided fractal?

On 4/19/2023 4:14 PM, Dan joyce wrote:
> On Wednesday, April 19, 2023 at 6:56:26 PM UTC-4, Chris M. Thomasson wrote:
>> On 4/19/2023 3:51 PM, Dan joyce wrote:
>>> On Wednesday, April 19, 2023 at 6:43:43 PM UTC-4, Chris M. Thomasson wrote:
>>>> On 4/19/2023 3:39 PM, Chris M. Thomasson wrote:
>>>>> On 4/19/2023 3:23 PM, Dan joyce wrote:
>>>>>> On Wednesday, April 19, 2023 at 6:07:35 PM UTC-4, Chris M. Thomasson
>>>>>> wrote:
>>>>>>> On 4/19/2023 2:34 PM, Dan joyce wrote:
>>>>>>>> On Wednesday, April 19, 2023 at 4:10:57 PM UTC-4, Chris M. Thomasson
>>>>>>>> wrote:
>>>>>>>>> On 4/18/2023 7:11 PM, Chris M. Thomasson wrote:
>>>>>>>>>> On 4/16/2023 2:00 PM, Dan joyce wrote:
>>>>>>>>>>> Each digit of pi treated as an integer,
>>>>>>>>>>> Starting with 3 and x=0 and y=0.
>>>>>>>>>>>
>>>>>>>>>>> 3 down x=0 y=-3
>>>>>>>>>>> 1 left x=-1 y=-3
>>>>>>>>>>> 4 up x=-1 y=1
>>>>>>>>>>> 1 right x=0 y=1
>>>>>>>>>>> 5 down x=0 y=-4
>>>>>>>>>>> 9 right x=9 y=-4
>>>>>>>>>>> 2 up x=9 y=-2
>>>>>>>>>>> 6 left x=3 y=-2
>>>>>>>>>>> 5 D x=3 y=-7
>>>>>>>>>>> 3 L x=0 y=-7
>>>>>>>>>>> 5 U x=0 y=-2
>>>>>>>>>>> 8 R x=8 y=-2
>>>>>>>>>>> 9 D x=8 y=-11
>>>>>>>>>>> 7 R x=15 y=-11
>>>>>>>>>>> 9 U x=15 y=-2
>>>>>>>>>>> 3 L x=12 y=-2
>>>>>>>>>>> 2
>>>>>>>>>>>
>>>>>>>>>>> Repeat that order of directions with each digit of pi.
>>>>>>>>>>> What will be the x/y coordinates on the Cartesian coordinate plain
>>>>>>>>>>> after 1,000,000 digits of pi?
>>>>>>>>>>> How many times will it cross the x=0 axis and y=0 axis or where an
>>>>>>>>>>> actual digit of pi ends up on x=0 and y=0?
>>>>>>>>>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2
>>>>>>>>>>> respectfully
>>>>>>>>>>>
>>>>>>>>>>> We know pi's digits --->oo but the Cartesian coordinate plain
>>>>>>>>>>> will not
>>>>>>>>>>> --->oo in any direction, in fact using the above method it will
>>>>>>>>>>> cross
>>>>>>>>>>> or land on the x=0 or y=0 --->oo.
>>>>>>>>>>> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the
>>>>>>>>>>> single
>>>>>>>>>>> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
>>>>>>>>>>> pattern of joining lines but it takes 140 iterations to complete the
>>>>>>>>>>> pattern.
>>>>>>>>>>> Then it just retraces the lines in the next 140 iterations and so on
>>>>>>>>>>> --->oo.
>>>>>>>>>>>
>>>>>>>>>>> etc.
>>>>>>>>>>> The numbers above from 0-9 repeated for each direction to 140
>>>>>>>>>>> iterations produces a unique 140 x\y coordinates and then repeats
>>>>>>>>>>> that
>>>>>>>>>>> same unique x\y coordinates in the next 140 iterations and so-on.
>>>>>>>>>>> When a zero or zeros like in pi are encountered it does not draw a
>>>>>>>>>>> line but uses only a direction change.
>>>>>>>>> Wait a minute. I am missing where it "changes direction" when a zero
>>>>>>>>> digit is encountered. You say x=0, y=0 so are you resetting the
>>>>>>>>> origin,
>>>>>>>>> or just treat the zero as a non-movement like encounter? In other
>>>>>>>>> words
>>>>>>>>> the current point is left alone when a zero digit is observed?
>>>>>>>>
>>>>>>>> Say a zero lands on the up direction after a digit >0 draws a line
>>>>>>>> on the left direction but
>>>>>>>> now a line is NOT drawn on the up direction because of the zero. So
>>>>>>>> say the next integer
>>>>>>>> after the zero is >o it just retraces the left direction but now
>>>>>>>> going in the right direction over the left direction over laying
>>>>>>>> either partially or same length or longer (a larger digit that
>>>>>>>> traced over the left direction).
>>>>>>>> When you consider the order of directions --- D,L,U,R,D,R,U,L repeat
>>>>>>>> --->oo
>>>>>>> [...]
>>>>>>>
>>>>>>> Is this close? Using only a 5-ary symbol system for simplicity:
>>>>>>>
>>>>>>> Say we define in a 2d plane the following normalized directions:
>>>>>>>
>>>>>>> neutral = { 0, 0 }
>>>>>>> up = { 0, 1 }
>>>>>>> down = { 0, -1 }
>>>>>>> left = { -1, 0 }
>>>>>>> right = { 1, 0 }
>>>>>>>
>>>>>>> where:
>>>>>>>
>>>>>>> 0 = neutral
>>>>>>> 1 = up
>>>>>>> 2 = down
>>>>>>> 3 = left
>>>>>>> 4 = right
>>>>>>>
>>>>>>>
>>>>>>> So, a number
>>>>>>>
>>>>>>> 10133402
>>>>>>>
>>>>>>> If we started with a point z at point { 0, 0 },
>>>>>>>
>>>>>>> it would be:
>>>>>>>
>>>>>>> z = { 0, 0 }
>>>>>>>
>>>>>>> // iterate the digits
>>>>>>>
>>>>>>> 1: z = z + up = { 0, 1 }
>>>>>>> 0: z = z + neutral = { 0, 1 }
>>>>>>> 1: z = z + up = { 0, 2 }
>>>>>>> 3: z = z + left = { -1, 2 }
>>>>>>> 3: z = z + left = { -2, 2 }
>>>>>>> 4: z = z + right = { -1, 2 }
>>>>>>> 0: z = z + neutral = { -1, 2 }
>>>>>>> 2: z = z + down = { -1, 1 }
>>>>>>>
>>>>>>> I only used a 5-ary set of symbols, but it would work.
>>>>>>
>>>>>> You are using the digit length as a direction where I am using the
>>>>>> order of direction
>>>>>> to point that next integer to ---- D,LU,R,D,R,U,L
>>>>>
>>>>> What is the LU? I think left and up. So z = z + left + up
>>>>>
>>>>> LU seems to be treated as a single digit with the commas in your
>>>>> direction list. Or is LU a normal vector like:
>>>>>
>>>>
>>>>
>>>>> north_east = normalize({-1, 1}) ?
>>>> ^^^^^^^^^^^^^^^^^^^^^^^^^^
>>>> [..]
>>>>
>>>> Humm.. I don't think I should necessarily normalize the north_east vector.
>>>>
>>>> north_east = {-1, 1}
>>>>
>>>> Or, in this case I should define it as:
>>>>
>>>> left_up = {-1, 1}
>>>>
>>>> ;^)
>>> You could also set a 10 sided n-gon drawing to the center of each line on the inner
>>> circle that would give 10 directions from the end of the last known direction.
>>> The naming convention for each direction could be, starting at the top line
>>> going down the right side of the inner circle -- x, x1,x2 stopping at 1/4 circle
>>> Then going down from x on the left top -- -x1, -x2 =5 directions for the top half.
>>> On the bottom half right side-- y, y1, y2 left side bottom half-- -y1,-y2
>>> Just another brainstorm.
>> Humm... For some reason, these rules kind of remind me of playing the
>> chaos game with an n-gon.
>>
>> https://en.wikipedia.org/wiki/Chaos_game
>
> There is no pictorial of 10 sided fractal?

On 4/19/2023 3:49 PM, mitchr...@gmail.com wrote:
> On Wednesday, April 19, 2023 at 1:02:53 PM UTC-7, Chris M. Thomasson wrote:
>> On 4/19/2023 10:36 AM, mitchr...@gmail.com wrote:
>>> On Sunday, April 16, 2023 at 2:00:04 PM UTC-7, Dan joyce wrote:
>>>> Each digit of pi treated as an integer,
>>>> Starting with 3 and x=0 and y=0.
>>>>
>>>> 3 down x=0 y=-3
>>>> 1 left x=-1 y=-3
>>>> 4 up x=-1 y=1
>>>> 1 right x=0 y=1
>>>> 5 down x=0 y=-4
>>>> 9 right x=9 y=-4
>>>> 2 up x=9 y=-2
>>>> 6 left x=3 y=-2
>>>> 5 D x=3 y=-7
>>>> 3 L x=0 y=-7
>>>> 5 U x=0 y=-2
>>>> 8 R x=8 y=-2
>>>> 9 D x=8 y=-11
>>>> 7 R x=15 y=-11
>>>> 9 U x=15 y=-2
>>>> 3 L x=12 y=-2
>>>> 2
>>>>
>>>> Repeat that order of directions with each digit of pi.
>>>> What will be the x/y coordinates on the Cartesian coordinate plain
>>>> after 1,000,000 digits of pi?
>>>> How many times will it cross the x=0 axis and y=0 axis or where an
>>>> actual digit of pi ends up on x=0 and y=0?
>>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
>>>>
>>>> We know pi's digits --->oo but the Cartesian coordinate plain will not
>>>> --->oo in any direction, in fact using the above method it will cross
>>>> or land on the x=0 or y=0 --->oo.
>>>>
>>>> I used this repeated order D,L,U,R,D,R,U,L to accommodate all the single
>>>> numbers of pi 0,1,2,3,4,5,6,7,8,9 that gives a small repeated
>>>> pattern of joining lines but it takes 140 iterations to complete the pattern.
>>>> Then it just retraces the lines in the next 140 iterations and so on --->oo.
>>>>
>>>> 0 D A zero so no change so x=0,y=0
>>>> 1 L x=-1 y=0
>>>> 2 U x=-1 y=2
>>>> 3 R x=2 y=2
>>>> 4 D x=2 y=-2
>>>> 5 R x=7 y=-2
>>>> 6 U x=7 y=4
>>>> 7 L x=0 y=4
>>>> 8 D x=0 y=-4
>>>> 9 L x=-9 y=-4
>>>> 0 U x=-9 y=-4
>>>> 1 R x=-8 y=-4
>>>> 2 D x=-8 y=-6
>>>> etc.
>>>> The numbers above from 0-9 repeated for each direction to 140 iterations produces a unique 140 x\y coordinates and then repeats that same unique x\y coordinates in the next 140 iterations and so-on.
>>>> When a zero or zeros like in pi are encountered it does not draw a line but uses only a direction change.
>>>>
>>>>
>>>> A simple concept, but interesting.
>>>>
>>>> Dan
>>>
>>> Digits are not very accurate.
>> How many accurate base-10 symbols of pi can you generate?
>
> That is the right question. So How do you verify?
> Can you prove you can verify more than a few?
> where is your proof of PI accuracy?
> There is no accurate PI formula.

Well, there is atan(1) * 4 = pi

;^)

Time to implement a cordic. We can get it accurate up to a large number
of digits, but we cannot get all of them because they go on forever.

On 4/17/2023 5:58 PM, Graham Cooper wrote:
> On Tuesday, April 18, 2023 at 9:42:33 AM UTC+10, Dan joyce wrote:
>> On Monday, April 17, 2023 at 2:09:51 AM UTC-4, James Waldby wrote:
>>> Dan joyce <danj...@gmail.com> wrote:
>>>> Each digit of pi treated as an integer,
>>>> Starting with 3 and x=0 and y=0.
>>> [snip coordinates example]
>>>>
>>>> Repeat that order of directions with each digit of pi.
>>>> What will be the x/y coordinates on the Cartesian coordinate plain
>>>> after 1,000,000 digits of pi?
>>>> How many times will it cross the x=0 axis and y=0 axis or where an
>>>> actual digit of pi ends up on x=0 and y=0?
>>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
>>>>
>>>> We know pi's digits --->oo but the Cartesian coordinate plain will not
>>>> --->oo in any direction, in fact using the above method it will cross
>>>> or land on the x=0 or y=0 --->oo.
>>> ...
>>>> When a zero or zeros like in pi are encountered it does not draw a line but uses only a direction change.
>>> More clearly, it draws a line of length 0 for digit 0.
>> Right.
>>> Here are some stats for the million-digit case:
>>> Min Max Cross Zero Last @Orig
>>> X: -2076 439 1074 563 -1648 1 #54073
>>> Y: -752 1842 753 388 -574
>>>
>>> In that output, you can see that X ranged from -2076 to 439, was zero
>>> 563 times, crossed the Y axis at least 1074 times. The trace returned
>>> to the (0,0) origin 1 time, at digit 54073, and ended at (-1648,-574).
>>>
>>> Also Y ranged from -752 to 1842, was zero 388 times, and crossed the X
>>> axis at least 753 times. Note, these cross counts are lower bounds.
>>> If more than two zero locations occur in a row, my program may miss an
>>> axis crossing. For example, if x goes -1, 0, 0, 1 the program will
>>> correctly count one crossing, but if x goes -1, 0, 0, 0, 1, it should
>>> but won't, and if x goes 1, 0, 0, 0, 1, it shouldn't and doesn't.
>>>
>>> Some more outputs (which took 0.3 minutes; 2 minutes; and 4.3 minutes,
>>> respectively, with >99% of the time being the computation of pi and the
>>> other <1% walking the digits.
>>>
>>> Got pi to 10100111 digits, will process 10100100
>>> Min Max Cross Zero Last @Orig
>>> X: -5411 548 3493 1865 -2416 1 #54073
>>> Y: -2953 7863 3308 1684 6714
>>>
>>> Got pi to 50000011 digits, will process 50000000
>>> Min Max Cross Zero Last @Orig
>>> X: -14627 548 3697 1943 -5764 1 #54073
>>> Y: -4316 12484 6477 3362 -332
>>>
>>> Got pi to 100100009 digits, will process 100100000
>>> Min Max Cross Zero Last @Orig
>>> X: -14627 20240 7388 3841 -5522 1 #54073
>>> Y: -33180 12484 6953 3590 -27829
>> You can Shure bring out some fascinating stuff with your coding skills.
>> Sadly to say I lost it on the cognitive skills needed for something like this.
>> Nicely done!
>> Pi's digits continue on --->oo but are bounded by x\y coordinates to never wander off in any
>> direction --->oo on the Cartesians Coordinate plain.
>> What's your thoughts on this?
>
> How can it not? the central colored in square increases in size
> or atleast the central outermost square increases in size -->oo
>
> I dont believe in RANDOM WALK HYPOTHESIS that he crosses 0,0
> INF times.
>
> I think it forms a SKETCH that approaches INF-X -INF-X INF-Y -INF-Y
> but it may be an INTERPRETATION of complete-infinity Vs potential-infinity
>
> If you have billion step walks traced onto a picture would be interesting
>

Love the following on the following page:

nonprimes = <3 5 7 9 15 17 25 ..>

http://www.new-math.com/

non prime means non prime right? Or, is that a typo?

Any odd integer added to another odd integer is an even integer

Is a number divisible by 2? Ring a bell?

On 4/19/2023 8:28 PM, Chris M. Thomasson wrote:
> On 4/17/2023 5:58 PM, Graham Cooper wrote:
>> On Tuesday, April 18, 2023 at 9:42:33 AM UTC+10, Dan joyce wrote:
>>> On Monday, April 17, 2023 at 2:09:51 AM UTC-4, James Waldby wrote:
>>>> Dan joyce <danj...@gmail.com> wrote:
>>>>> Each digit of pi treated as an integer,
>>>>> Starting with 3 and x=0 and y=0.
>>>> [snip coordinates example]
>>>>>
>>>>> Repeat that order of directions with each digit of pi.
>>>>> What will be the x/y coordinates on the Cartesian coordinate plain
>>>>> after 1,000,000 digits of pi?
>>>>> How many times will it cross the x=0 axis and y=0 axis or where an
>>>>> actual digit of pi ends up on x=0 and y=0?
>>>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
>>>>>
>>>>> We know pi's digits --->oo but the Cartesian coordinate plain will not
>>>>> --->oo in any direction, in fact using the above method it will cross
>>>>> or land on the x=0 or y=0 --->oo.
>>>> ...
>>>>> When a zero or zeros like in pi are encountered it does not draw a
>>>>> line but uses only a direction change.
>>>> More clearly, it draws a line of length 0 for digit 0.
>>> Right.
>>>> Here are some stats for the million-digit case:
>>>> Min Max Cross Zero Last @Orig
>>>> X: -2076 439 1074 563 -1648 1 #54073
>>>> Y: -752 1842 753 388 -574
>>>>
>>>> In that output, you can see that X ranged from -2076 to 439, was zero
>>>> 563 times, crossed the Y axis at least 1074 times. The trace returned
>>>> to the (0,0) origin 1 time, at digit 54073, and ended at (-1648,-574).
>>>>
>>>> Also Y ranged from -752 to 1842, was zero 388 times, and crossed the X
>>>> axis at least 753 times. Note, these cross counts are lower bounds.
>>>> If more than two zero locations occur in a row, my program may miss an
>>>> axis crossing. For example, if x goes -1, 0, 0, 1 the program will
>>>> correctly count one crossing, but if x goes -1, 0, 0, 0, 1, it should
>>>> but won't, and if x goes 1, 0, 0, 0, 1, it shouldn't and doesn't.
>>>>
>>>> Some more outputs (which took 0.3 minutes; 2 minutes; and 4.3 minutes,
>>>> respectively, with >99% of the time being the computation of pi and the
>>>> other <1% walking the digits.
>>>>
>>>> Got pi to 10100111 digits, will process 10100100
>>>> Min Max Cross Zero Last @Orig
>>>> X: -5411 548 3493 1865 -2416 1 #54073
>>>> Y: -2953 7863 3308 1684 6714
>>>>
>>>> Got pi to 50000011 digits, will process 50000000
>>>> Min Max Cross Zero Last @Orig
>>>> X: -14627 548 3697 1943 -5764 1 #54073
>>>> Y: -4316 12484 6477 3362 -332
>>>>
>>>> Got pi to 100100009 digits, will process 100100000
>>>> Min Max Cross Zero Last @Orig
>>>> X: -14627 20240 7388 3841 -5522 1 #54073
>>>> Y: -33180 12484 6953 3590 -27829
>>> You can Shure bring out some fascinating stuff with your coding skills.
>>> Sadly to say I lost it on the cognitive skills needed for something
>>> like this.
>>> Nicely done!
>>> Pi's digits continue on --->oo but are bounded by x\y coordinates to
>>> never wander off in any
>>> direction --->oo on the Cartesians Coordinate plain.
>>> What's your thoughts on this?
>>
>> How can it not?  the central colored in square increases in size
>> or atleast the central outermost square increases in size -->oo
>>
>> I dont believe in RANDOM WALK HYPOTHESIS that he crosses 0,0
>> INF times.
>>
>> I think it forms a SKETCH that approaches INF-X -INF-X INF-Y -INF-Y
>> but it may be an INTERPRETATION of complete-infinity Vs
>> potential-infinity
>>
>> If you have billion step walks traced onto a picture would be interesting
>>
>
> Love the following on the following page:
>
> nonprimes = <3 5 7 9 15 17 25 ..>
>
> http://www.new-math.com/
>
> non prime means non prime right? Or, is that a typo?
>
> Any odd integer added to another odd integer is an even integer
>
> Is a number divisible by 2? Ring a bell?
>
>

After two, all primes are odd.

On Thursday, April 20, 2023 at 1:28:48 PM UTC+10, Chris M. Thomasson wrote:
> On 4/17/2023 5:58 PM, Graham Cooper wrote:
> > On Tuesday, April 18, 2023 at 9:42:33 AM UTC+10, Dan joyce wrote:
> >> On Monday, April 17, 2023 at 2:09:51 AM UTC-4, James Waldby wrote:
> >>> Dan joyce <danj...@gmail.com> wrote:
> >>>> Each digit of pi treated as an integer,
> >>>> Starting with 3 and x=0 and y=0.
> >>> [snip coordinates example]
> >>>>
> >>>> Repeat that order of directions with each digit of pi.
> >>>> What will be the x/y coordinates on the Cartesian coordinate plain
> >>>> after 1,000,000 digits of pi?
> >>>> How many times will it cross the x=0 axis and y=0 axis or where an
> >>>> actual digit of pi ends up on x=0 and y=0?
> >>>> Above the 10th and 11th digit of pi x=0 but y=-7 and y=-2 respectfully
> >>>>
> >>>> We know pi's digits --->oo but the Cartesian coordinate plain will not
> >>>> --->oo in any direction, in fact using the above method it will cross
> >>>> or land on the x=0 or y=0 --->oo.
> >>> ...
> >>>> When a zero or zeros like in pi are encountered it does not draw a line but uses only a direction change.
> >>> More clearly, it draws a line of length 0 for digit 0.
> >> Right.
> >>> Here are some stats for the million-digit case:
> >>> Min Max Cross Zero Last @Orig
> >>> X: -2076 439 1074 563 -1648 1 #54073
> >>> Y: -752 1842 753 388 -574
> >>>
> >>> In that output, you can see that X ranged from -2076 to 439, was zero
> >>> 563 times, crossed the Y axis at least 1074 times. The trace returned
> >>> to the (0,0) origin 1 time, at digit 54073, and ended at (-1648,-574)..
> >>>
> >>> Also Y ranged from -752 to 1842, was zero 388 times, and crossed the X
> >>> axis at least 753 times. Note, these cross counts are lower bounds.
> >>> If more than two zero locations occur in a row, my program may miss an
> >>> axis crossing. For example, if x goes -1, 0, 0, 1 the program will
> >>> correctly count one crossing, but if x goes -1, 0, 0, 0, 1, it should
> >>> but won't, and if x goes 1, 0, 0, 0, 1, it shouldn't and doesn't.
> >>>
> >>> Some more outputs (which took 0.3 minutes; 2 minutes; and 4.3 minutes,
> >>> respectively, with >99% of the time being the computation of pi and the
> >>> other <1% walking the digits.
> >>>
> >>> Got pi to 10100111 digits, will process 10100100
> >>> Min Max Cross Zero Last @Orig
> >>> X: -5411 548 3493 1865 -2416 1 #54073
> >>> Y: -2953 7863 3308 1684 6714
> >>>
> >>> Got pi to 50000011 digits, will process 50000000
> >>> Min Max Cross Zero Last @Orig
> >>> X: -14627 548 3697 1943 -5764 1 #54073
> >>> Y: -4316 12484 6477 3362 -332
> >>>
> >>> Got pi to 100100009 digits, will process 100100000
> >>> Min Max Cross Zero Last @Orig
> >>> X: -14627 20240 7388 3841 -5522 1 #54073
> >>> Y: -33180 12484 6953 3590 -27829
> >> You can Shure bring out some fascinating stuff with your coding skills..
> >> Sadly to say I lost it on the cognitive skills needed for something like this.
> >> Nicely done!
> >> Pi's digits continue on --->oo but are bounded by x\y coordinates to never wander off in any
> >> direction --->oo on the Cartesians Coordinate plain.
> >> What's your thoughts on this?
> >
> > How can it not? the central colored in square increases in size
> > or atleast the central outermost square increases in size -->oo
> >
> > I dont believe in RANDOM WALK HYPOTHESIS that he crosses 0,0
> > INF times.
> >
> > I think it forms a SKETCH that approaches INF-X -INF-X INF-Y -INF-Y
> > but it may be an INTERPRETATION of complete-infinity Vs potential-infinity
> >
> > If you have billion step walks traced onto a picture would be interesting
> >
> Love the following on the following page:
>
> nonprimes = <3 5 7 9 15 17 25 ..>

that sequence looks familiar ...

>
> http://www.new-math.com/

ahhh its my sequence

>
> non prime means non prime right? Or, is that a typo?
>
> Any odd integer added to another odd integer is an even integer

non-primes add to ALL even numbers 98% of simulations

zoom out click REFRESH 100 times to see how effective non-primes are
at satisfying the Goldbach Conjecture