On Saturday, June 10, 2023 at 5:04:45 PM UTC-4, Dan joyce wrote:
> On Friday, June 9, 2023 at 12:55:26 PM UTC-4, Dan joyce wrote:
> > On Friday, June 9, 2023 at 9:18:00 AM UTC-4, Dan joyce wrote:
> > > On Friday, June 9, 2023 at 8:28:16 AM UTC-4, Dan joyce wrote:
> > > > On Thursday, June 8, 2023 at 8:20:35 PM UTC-4, James Waldby wrote:
> > > > > Dan joyce <danj...@gmail.com> wrote:
> > > > > > On Thursday, June 8, 2023 at 12:40:26???PM UTC-4, James Waldby wrote:
> > > > > >> Dan joyce <danj...@gmail.com> wrote:
> > > > > >> ...
> > > > > >> >>>>>> Draw an infinite square lattice without lifting the pencil. ...
> > > > > >> >>>>>> A much harder, and likely impossible drawing is where you make
> > > > > >> >>>>>> the grid without lifting the pencil and without retracing where
> > > > > >> >>>>>> you already been before.
> > > > > >> ...
> > > > > >> > So Chris how is it going.
> > > > > >> > You have seen the videos so what is your assessment?
> > > > > >> > The pencil never leaves the paper. Bogus or real?
> > > > > >> > I definitely believe it is real. The videos prove it.
> > > > > >> > It is surprising that some that are questioning it have run complex
> > > > > >> > algorithms that left me in the dust where I had no clue on how they
> > > > > >> > did it. I will send the largest square lattice ever produced where
> > > > > >> > it runs off the top and bottom of the screen. In which the old
> > > > > >> > algorithm would have used thousands of these directions R,U,D,L
> > > > > >> > where now it just uses a handful but in multiple times for
> > > > > >> > completing a large square lattice. Watch for the new video.
> > > > > >>
> > > > > >> Of course it's easy to make an indefinitely large drawing which "runs
> > > > > >> off the top and bottom of the screen" while enclosing lots and lots of
> > > > > >> squares. No question. However, the phrase "Draw an infinite square
> > > > > >> lattice" ought to imply a drawing, without lift or retrace, such that
> > > > > >> for any distance from the origin all the segments within that distance
> > > > > >> eventually get filled in. I proved (and Mike Terry also proved, in a
> > > > > >> simpler way) that's not possible in a one-way drawing that starts at
> > > > > >> the origin. As Mike also noted, if you allow adding lines at both
> > > > > >> ends of the trace it's easy to do. But a space-filling (without
> > > > > >> missing segments) single-ended trace without lift or retrace is not
> > > > > >> possible.
> > > > >
> > > > > > I never implied that. It was going out in certain steps ---->oo
> > > > > > LEAVING A PATH that later gets filled has always been what I have
> > > > > > been saying. I have mentioned that many times about going out and
> > > > > > leaving a path. Then on the return to the center of the square
> > > > > > lattice or the origin all gets filled in without crossing any lines
> > > > > > or retraces.
> > > > > Yes, I agree your method draws arbitrarily large square lattices of
> > > > > fixed sizes ok. But by no means does it do an "infinite lattice".
> > > > James, I agree. It just sounded more sexy as the infinite lattice
> > > > instead of a lattice that can --->oo.
> > > > I have always approched infinity, no pun intended, that way.
> > > I even stated in one of my post on this subject, not the exact wording, that
> > > suppose you wanted a huge square lattice --->oo and lets say in this case
> > > a square lattice with one hundread quaudrillion (10^17) cells on just one of its 4 sides
> > > that it is possible to draw that without lifting a pencil.
> > > I know it is wrong to put a number on --->oo but just saying how much bigger
> > > than one hundred quaudrillion cells on just one of its 4 sides of a square lattice
> > > could be. Even a square lattice with 10^303 (Centillion) cells on one of its sides.
> > > So I guess the name for this lattice, not as the infinite lattice, but (a square lattice--->oo)
> > > would be more appropriate.
> > Another thing I want to straigten out is, it is not really a square lattice more of a rectangle
> > but the closest to a square that you can possibly get. The top portion where it reverses and
> > comes back down the path does not need to protrude (stick above the border of the rectangle
> > drawn around the lattice.) I just need to shorten the last 2 lines going out to U-1 and L-1.
> > Then just adjust the return path length for that one side to D-1 and R-1.
> > Just by changing the last integer (n) in the first sequance to n-1.
> > Then change the first integer (n) in the second sequence to n-1.
> Then if you sdd another set of 4 pattern integers at the end of the first sequence then put the n-1 back to n+1 before you add the new set that actually breaks the pattern with the n-1 for the last number. The same for the second sequence adding 1 back to the starting number in that sequence before
> you add the new set of 3 unique pattern integers for that sequence + n-1as the first number.

It gets a little complex to maintain all the cells within one border when adding the next 4 integers to each
sequence for one more rotation in each sequence. If you follow the above instructions it works every time. So far 30 rotations have worked.
Or about 30^2=900 cells. So 4 directions for each completed cell = 3600 lines all done with a handful
of directions (R,U),L,D,R,D,R,U,L,U,L,D for the going out sequence, (R,U) only accessed once, and a simple R,D,L,D,L,U,R,U for the coming back in sequence. So 20 directions total and the pattern integers do the rest
wIth their 2 unique patterns for each of the 2 sequences.
Going out sequence for 9 rotations---
(1),2,1,3,2,4,3,5,4,6,5,7,6,8,7,9,8,10,9,11,10,12,11,13,12,14,13,15,14,16,15,17,16,18,17,19,17 ---(1) exicuted once.
The last number (17) should be 18 to maintain the pattern but to keep all cells within a border around
then 18-1 for this round and when 4 more numbers are added 17+1 to keep with the pattern.
Coming back in sequence.
17,17,17,16,16,15,15,14,14,13,13,12,12,11,11,10,10,9,9,8,8,7,7,6,6,5,5,4,4,3,3,2,2,1,1 The same goes for this sequence'
only it is the first number should be 18 but to maintain all cells within a border 18-1 then when you add 4 more numbers
for another rotation then 17+1 to keep with the pattern.
It is easy to construct an algorthm with the above info.

Happy coding