Looking for Mandelbrot Butterfly explorers and developers

  • 20 Replies
  • 300 Views

0 Members and 1 Guest are viewing this topic.

Offline JonathanD

  • *
  • Fractal Fanatic
  • ***
  • Posts: 36
  • Fractal Physics Guru
« Reply #15 on: February 02, 2020, 05:33:19 AM »
Note:

Setting the iterand to the value: bailout + 1 means it will kick out of the loop and assign a color, as though the butterfly wing or disc was one of the repeller sets (the color bands lining the edges of the set).  Obviously; if these color bands are not being displayed that method will not work, and the butterfly wings will not be colored in either.  However; it is possible to suppress the repeller sets lining the edge and display the butterfly parts, with a slight adjustment.

More later,

Jonathan
Jonathan J. Dickau

Offline gerrit

  • *
  • 3f
  • ******
  • Posts: 1928
« Reply #16 on: February 02, 2020, 05:40:27 AM »
Well what I tried was to replace \( z \) by \( z+\psi \) with \( \psi \) as Grassman variable (i.e., \( \psi^2=0 \), but \( \psi \neq 0 \)).

So we get the super iteration:
\( z+\psi \leftarrow z^2+2z\psi + c + \gamma \)
with \( \gamma \) the Grassmann component of the pixel.

Unfortunately this just amounts to
\( z \leftarrow z^2 +c\\
\psi \leftarrow 2z\psi + \gamma \)

so no non-trivial mixing of the Grassman variable and \( z \).

I don't quite get the relevance of G2 Lie algebra, perhaps the graded Lie-algebra's used in supersymmetry speculations in theoretical physics can be used?

Offline JonathanD

  • *
  • Fractal Fanatic
  • ***
  • Posts: 36
  • Fractal Physics Guru
« Reply #17 on: February 02, 2020, 07:40:32 AM »
You have cool ideas Gerrit...

And that substitution does sound interesting.  I got a package for NodeJS from Rick Lockyer for Octonion Maths, that I need to take more time to play with.  But now it's about time to catch some sleep.

More when there is time,

Jonathan

Offline JonathanD

  • *
  • Fractal Fanatic
  • ***
  • Posts: 36
  • Fractal Physics Guru
« Reply #18 on: February 04, 2020, 03:35:53 AM »
Look for my formula files...

Now in the Fractal software Downloads section.  Also copied below.  ZIP has instructions and CFM file for Chaos Pro.

Best,

JJD

Online C0ryMcG

  • *
  • Fractal Friend
  • **
  • Posts: 19
« Reply #19 on: February 10, 2020, 07:38:28 AM »
Hello! I read about your algorithm and became intrigued.
I have a little Javascript project that I'm intending to make as flexible as possible, and I used that to implement the method you described as a coloring model, rendering Only the butterfly. It resulted in some pretty interesting results, I think. I don't know if it'll help you with your ultimate goal of linking the Mandelbrot set to particle physics theory, but at least it looks nice!

I can share a code snippet if it's desired... but basically it looks at a list of points, and for the first set of points that declines in radius from center, it performs this:

colorIndex = d1 * Math.max(1/(d3 - d2),1/(d2 - d1));

Then it selects a color from a looping array (with some lerping to get nice in-betweens), and sends it to the screen.
Any thoughts?


Offline gerson

  • *
  • Fractal Furball
  • ***
  • Posts: 275
« Reply #20 on: February 10, 2020, 02:39:20 PM »
Thanks for sharing the formulas. Liked very much.


xx
Announcing FracTest: a Mandelbrot zoomer for explorers.

Started by AtticusLake on Other

0 Replies
287 Views
Last post January 11, 2018, 01:27:19 PM
by AtticusLake
xx
Introducing the Mandelbrot Butterfly Safari

Started by JonathanD on Meet & Greet

0 Replies
47 Views
Last post February 01, 2020, 02:47:24 AM
by JonathanD
clip
The Mandelbrot Butterfly is a Spectral Manifold

Started by JonathanD on Share a fractal

0 Replies
57 Views
Last post February 01, 2020, 06:31:34 PM
by JonathanD
clip
Does the Mandelbrot Butterfly show us associative regions of M in higher-d?

Started by JonathanD on Fractal Mathematics And New Theories

1 Replies
57 Views
Last post February 03, 2020, 09:50:46 PM
by JonathanD
clip
Formula files for Mandelbrot Butterfly family figures on Chaos Pro

Started by JonathanD on Downloads

1 Replies
99 Views
Last post February 05, 2020, 06:31:41 AM
by JonathanD