Still testing things out:

https://www.facebook.com/chris.thomasson.31/videos/777159090228253

On Saturday, September 17, 2022 at 4:06:08 PM UTC-4, Chris M. Thomasson wrote:
> Still testing things out:
>
> https://www.facebook.com/chris.thomasson.31/videos/777159090228253

Neat!
Looks like repeating multiple patterns all having there discrete starting and ending points that
and just repeats the pattern.
Or does it terminate at the ending point?
Nice work.

On 9/17/2022 5:26 PM, Dan joyce wrote:
> On Saturday, September 17, 2022 at 4:06:08 PM UTC-4, Chris M. Thomasson wrote:
>> Still testing things out:
>>
>> https://www.facebook.com/chris.thomasson.31/videos/777159090228253
>
> Neat!
> Looks like repeating multiple patterns all having there discrete starting and ending points that
> and just repeats the pattern.
> Or does it terminate at the ending point?

It does terminate. I am simply using n points of a circle to generate
Julia sets. So, it interpolates points from an angle [0...pi2], applies
a radius, and creates Julia sets from the cos(angle) + sin(angle)i
complex points that are generated.

> Nice work.

Basically, it's a spirograph of "special" Julia set points that fall
under a minimum distance from origin 0+0i during iteration. This can be
called, an orbit trap. During iteration of a point I find the minimum
distance it orbits go from origin. Then, if this minimum distance falls
below a certain epsilon, it gets plotted. Fwiw, here is another
animation that uses said points that fall under said condition in a
vector field:

https://www.facebook.com/chris.thomasson.31/videos/469954025022800

We can have fun with this, and it works for basically all escape time
fractals. Here is one using a Mandelbrot instead of a Julia set:

https://fractalforums.org/gallery/1612-090922223236.png

On 9/17/2022 1:05 PM, Chris M. Thomasson wrote:
> Still testing things out:
>
> https://www.facebook.com/chris.thomasson.31/videos/777159090228253

Check this out:

https://www.facebook.com/chris.thomasson.31/videos/829242224916610

;^)

On Sunday, September 18, 2022 at 4:12:13 AM UTC-4, Chris M. Thomasson wrote:
> On 9/17/2022 1:05 PM, Chris M. Thomasson wrote:
> > Still testing things out:
> >
> > https://www.facebook.com/chris.thomasson.31/videos/777159090228253
> Check this out:
>
> https://www.facebook.com/chris.thomasson.31/videos/829242224916610
>
> ;^)

Intriguing imaginary math art.

Dan

On 9/18/2022 8:24 AM, Dan joyce wrote:
> On Sunday, September 18, 2022 at 4:12:13 AM UTC-4, Chris M. Thomasson wrote:
>> On 9/17/2022 1:05 PM, Chris M. Thomasson wrote:
>>> Still testing things out:
>>>
>>> https://www.facebook.com/chris.thomasson.31/videos/777159090228253
>> Check this out:
>>
>> https://www.facebook.com/chris.thomasson.31/videos/829242224916610
>>
>> ;^)
>
> Intriguing imaginary math art.

;^D

Actually, its real math that I program myself. ;^)

On Sunday, September 18, 2022 at 5:21:33 PM UTC-4, Chris M. Thomasson wrote:
> On 9/18/2022 8:24 AM, Dan joyce wrote:
> > On Sunday, September 18, 2022 at 4:12:13 AM UTC-4, Chris M. Thomasson wrote:
> >> On 9/17/2022 1:05 PM, Chris M. Thomasson wrote:
> >>> Still testing things out:
> >>>
> >>> https://www.facebook.com/chris.thomasson.31/videos/777159090228253
> >> Check this out:
> >>
> >> https://www.facebook.com/chris.thomasson.31/videos/829242224916610
> >>
> >> ;^)
> >
> > Intriguing imaginary math art.
> ;^D
>
> Actually, its real math that I program myself. ;^)

So you don't use imaginary polar coordinates in your algorithms?
All Cartesian coordinate system 2d?

On 9/18/2022 2:42 PM, Dan joyce wrote:
> On Sunday, September 18, 2022 at 5:21:33 PM UTC-4, Chris M. Thomasson wrote:
>> On 9/18/2022 8:24 AM, Dan joyce wrote:
>>> On Sunday, September 18, 2022 at 4:12:13 AM UTC-4, Chris M. Thomasson wrote:
>>>> On 9/17/2022 1:05 PM, Chris M. Thomasson wrote:
>>>>> Still testing things out:
>>>>>
>>>>> https://www.facebook.com/chris.thomasson.31/videos/777159090228253
>>>> Check this out:
>>>>
>>>> https://www.facebook.com/chris.thomasson.31/videos/829242224916610
>>>>
>>>> ;^)
>>>
>>> Intriguing imaginary math art.
>> ;^D
>>
>> Actually, its real math that I program myself. ;^)
>
> So you don't use imaginary polar coordinates in your algorithms?

I generate points along the border of the unit circle using cos and sin
where cos is x axis and sin is y axis. These points are already
normalized around the origin at point (0, 0). So, we can easily scale
and/or move them to different origins.

> All Cartesian coordinate system 2d?

I convert the polar coordinates generated from the iterative circle
generation back into rectangular form to actually perform the fractal
iterations that use complex numbers, so, using 0 radians:

cos(0) + sin(0)i gets converted to point (1, 0), or 1+0i.

cos(pi/2) + sin(pi/2)i gets converted to point (0, 1), or 0+1i.

ect...

To scale the circle, to say, radius 1.42, I go, for example angle 0:

p = cos(0) + sin(0)i = (1, 0) = 1+0i

s = p * 1.42 = (1.42, 0) = 1.42+0i

I can set different origins, ect... Right now I am focusing on the
origin for Julia sets around point 0+0i.

Each generated point gets run through Julia set iterations that cull out
certain points that make it through the minimum distance orbit trap I
described in another post in this thread.

On Sunday, September 18, 2022 at 5:56:31 PM UTC-4, Chris M. Thomasson wrote:
> On 9/18/2022 2:42 PM, Dan joyce wrote:
> > On Sunday, September 18, 2022 at 5:21:33 PM UTC-4, Chris M. Thomasson wrote:
> >> On 9/18/2022 8:24 AM, Dan joyce wrote:
> >>> On Sunday, September 18, 2022 at 4:12:13 AM UTC-4, Chris M. Thomasson wrote:
> >>>> On 9/17/2022 1:05 PM, Chris M. Thomasson wrote:
> >>>>> Still testing things out:
> >>>>>
> >>>>> https://www.facebook.com/chris.thomasson.31/videos/777159090228253
> >>>> Check this out:
> >>>>
> >>>> https://www.facebook.com/chris.thomasson.31/videos/829242224916610
> >>>>
> >>>> ;^)
> >>>
> >>> Intriguing imaginary math art.
> >> ;^D
> >>
> >> Actually, its real math that I program myself. ;^)
> >
> > So you don't use imaginary polar coordinates in your algorithms?
> I generate points along the border of the unit circle using cos and sin
> where cos is x axis and sin is y axis. These points are already
> normalized around the origin at point (0, 0). So, we can easily scale
> and/or move them to different origins.
> > All Cartesian coordinate system 2d?
> I convert the polar coordinates generated from the iterative circle
> generation back into rectangular form to actually perform the fractal
> iterations that use complex numbers, so, using 0 radians:
>
> cos(0) + sin(0)i gets converted to point (1, 0), or 1+0i.
>
> cos(pi/2) + sin(pi/2)i gets converted to point (0, 1), or 0+1i.
>
> ect...
>
> To scale the circle, to say, radius 1.42, I go, for example angle 0:
>
> p = cos(0) + sin(0)i = (1, 0) = 1+0i
>
> s = p * 1.42 = (1.42, 0) = 1.42+0i
>
> I can set different origins, ect... Right now I am focusing on the
> origin for Julia sets around point 0+0i.
>
> Each generated point gets run through Julia set iterations that cull out
> certain points that make it through the minimum distance orbit trap I
> described in another post in this thread.

Thanks for the explanation.

Dan

>Still testing things out:
>
>https://www.facebook.com/chris.thomasson.31/videos/777159090228253

Very nice, like all your stuff !