Re: Rotation Bifurcation...

On 3/30/2024 9:18 AM, Volney wrote:

On 3/29/2024 8:24 PM, Chris M. Thomasson wrote:

A strange bifurcation algorithm from an older iterated function system of mine:
>
https://youtu.be/XKhS_nklCkE
>
My pseudo code is in the description:
>
______________
// px_mutation interpolates from -4...4 across each frame; 1440 here.
>
render frames:
_________
// angle interpolates from 0...pi2 across iterations
// px = py = 0
>
// Iteration:
px = sin(angle * px_mutation);
py = cos(angle * py);
______________
>
Anybody should be able to reproduce it on their end. Right?
>
It's all 2d, but has a 3d vibe! Nice.
>
Any thoughts?

 It looks like a fractal version of an optical illusion of whether a cylinder (with the fractal on it) is rotating in one direction or the other.

Notice the alpha blend where we can see through the illusion of a 2d plane looking 3d even with a completely 2d IFS? I did some simple 3d volumetric protrusions of it. Well, it looks like some sort of strange helix curve. px_mutation going from -4...4 across the frames (1440) here is the main animation driver, so to speak. when px_mutation hits zero, the plane is on edge where we can see a thin vertical line. In the volumetric we can see how its a plane because we can move the camera around it. You can see this moment right around this time:
https://youtu.be/XKhS_nklCkE?t=29