Cellular Coloring of Mandelbrot insides

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Offline gerson

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« Reply #15 on: January 10, 2020, 10:20:10 PM »
Better and better.

Offline hobold

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« Reply #16 on: January 11, 2020, 02:20:47 AM »
First impressions in motion.

http://vectorizer.org/3doodle/CellularZoom001.mp4


(Edit: hosted on a humble little virtual server. Because of bandwidth limitations, you will probably need to download and play from local disk.)
« Last Edit: January 11, 2020, 07:52:21 PM by hobold »

Offline 3DickUlus

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« Reply #17 on: January 11, 2020, 07:46:24 PM »
Fantastic  :thumbs:

The site that hosts your mp4 doesn't stream very well :(

The forum will show the preview image for vids posted on vimeo or Utoob if you use the BBC code [youtube]<link to file>[/youtube]  or [vimeo]<link to file>[/vimeo]
Fragmentarium is not a toy, it is a very versatile tool that can be used to make toys ;)

https://en.wikibooks.org/wiki/Fractals/fragmentarium

Offline gerrit

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« Reply #18 on: January 11, 2020, 09:03:12 PM »
First impressions in motion.

http://vectorizer.org/3doodle/CellularZoom001.mp4


(Edit: hosted on a humble little virtual server. Because of bandwidth limitations, you will probably need to download and play from local disk.)
Very nice. Streams perfectly smooth from that server for me here.

Offline hobold

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« Reply #19 on: January 12, 2020, 08:56:29 PM »
I realize that I forgot one detail that I did for the old "Christmas style" images. That is, the ones with purely the "halo" valuess and without the pronounced cell boundaries.

For these images, I saved the whole picture in an array. After filling each entry with "halo" values from the code fragment at the start of this forum thread, I did a min/max scan over the whole array. Then I re-scaled the range to [0.0 .. 1.0] again; i.e. the minimum got mapped to zero, and the maximum to one. This was necessary to prevent small cells being drowned out by large ones.

Sorry that I have overlooked this, it's not exactly a minor detail. :-/

This is not an issue for the "bounds" values.

Offline hobold

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« Reply #20 on: January 14, 2020, 10:58:17 PM »
The opposite of action packed.

Here is a slow survey, so to speak, with the orbit trap position following some sort of Lissajous path. It also loops back on itself after eight and a half minutes.

http://vectorizer.org/3doodle/FireflyMandala502.mp4

(Thanks to not much happening, compression ratio is fairly high. File size is roughly the same as the previous animation.)

Offline gerrit

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« Reply #21 on: January 15, 2020, 01:12:31 AM »
Very pretty.

Offline mclarekin

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« Reply #22 on: January 15, 2020, 09:59:14 AM »
beautiful O0

Offline gerson

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« Reply #23 on: January 15, 2020, 09:54:05 PM »
Amazing videos, congratulations.

Offline 3DickUlus

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« Reply #24 on: January 15, 2020, 10:34:50 PM »
That one streams nicely here :thumbs: smooth, hypnotic.

Offline gerrit

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« Reply #25 on: January 15, 2020, 11:00:46 PM »
Spiral near cusp of M-set, very shallow, using the d_min/d_min_next coloring.

Offline hobold

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« Reply #26 on: January 16, 2020, 12:07:24 AM »
It's a sunflower! I am glad to see others exploring on their own.

Offline gerrit

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« Reply #27 on: January 16, 2020, 06:59:13 AM »
Here's Julia set of (z^2+i)/(z^2-2).

Offline hobold

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« Reply #28 on: January 16, 2020, 09:45:30 AM »
Still trying to find more structure. When one looks at how the orbit arrives at the minimum distance from the orbit trap, e.g. the number of steps before the minimum was reached, then the boundaries of large cells continue across the smaller cells.

It's just the two lines with the new variable "decIter" below:

Code: [Select]
  double Re = Cx;
  double Im = Cy;
  double Re2 = Re*Re;
  double Im2 = Im*Im;
  int iter = 1;   // start with iteration 1 to avoid (0, 0)
  int mIter = iter;  // remember iteration of closest approach
  int decIter = 0;  // remember how often min distance did decrease
  double magnitude = Re2 + Im2;

  // distance to orbit trap
  double trap = (Re - TrapX)*(Re - TrapX) + (Im - TrapY)*(Im - TrapY);
  double min = trap;  // closest distance
  double min2 = 10000.0*min;  // 2nd closest distance

  while (((magnitude) < 10000.0) && (iter <= maxIter)) {
    Im = 2.0*Re*Im + Cy;
    Re = Re2 - Im2 + Cx;
    Re2 = Re*Re;
    Im2 = Im*Im;
    magnitude = Re2 + Im2;
    ++iter;

    // squared distance to orbit trap
    trap = (Re - TrapX)*(Re - TrapX) + (Im - TrapY)*(Im - TrapY);

    // sort current distance into our "list" of closest and 2nd closest
    if (trap < min) {
      min2 = min;
      min = trap;
      mIter = iter;
      ++decIter;  // number of steps to reach minimum distance
    } else if (trap < min2) {
      min2 = trap;
    }
  }

And then I use "mIter + decIter" as some sort of index into the color palette.

Offline hobold

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« Reply #29 on: January 17, 2020, 01:37:03 AM »
... aaaand here is the latter in another slow survey. Not a spectacular find.

http://vectorizer.org/3doodle/MinimumDescent530.mp4

The new subdivision boundaries rarely make a big visible difference.