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Author Topic:  Cellular Coloring of Mandelbrot insides  (Read 2330 times)

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Offline C0ryMcG

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Re: Cellular Coloring of Mandelbrot insides
« Reply #45 on: February 14, 2020, 09:29:02 PM »
Ah, I should have read post 2 and 3 more carefully! It's making more sense to me now. I find the results are better for zoomed-in sections, since, with black borders, the highlights tend to sink into the border junctions in the main shapes and interrupt the illusion of shape a little bit. But on the edges, I now have nice balloon-like structures, just as I had hoped to!

One thing I noticed is that I had initially misread part of your formula, but gotten similar results... You highlight the cell edges with "min/min2", while I set mine up based on "min2 - min".
I suppose it's a similar idea either way. with yours, value approaches 1 when the distances are the same, and with mine, value approaches 0.

Anyway, here's an example of today's tinkering after your hint.

Offline C0ryMcG

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Re: Cellular Coloring of Mandelbrot insides
« Reply #46 on: February 14, 2020, 10:08:18 PM »
Update: I like your method better (min/min2) It does a much better job of scaling the intensity for areas that show higher-iteration details.

Offline hobold

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Re: Cellular Coloring of Mandelbrot insides
« Reply #47 on: February 15, 2020, 12:15:22 AM »
There is no right or wrong version. Dividing sort of scales wall thickness with cell size; while subtraction sort of sets a constant boundary thickness. Either may be more appropriate for any given image. I think of it as a design decision.

BTW, one welcome side effect of me being a bit vague (about computing final colors from the raw values) is that some of you might discover yet more interesting variants that would have never occurred to me.

Offline 3DickUlus

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Re: Cellular Coloring of Mandelbrot insides
« Reply #48 on: March 03, 2020, 12:39:26 AM »
Here's a Fragmentarium version...

the attached image @128 samples per pixel took about 00:01:15 to render  :thumbs:

Offline hobold

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Re: Cellular Coloring of Mandelbrot insides
« Reply #49 on: March 03, 2020, 07:52:07 AM »
Now let the trap position move and watch more hidden structure coming to light.

Offline 3DickUlus

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Re: Cellular Coloring of Mandelbrot insides
« Reply #50 on: March 04, 2020, 04:15:35 AM »
« Last Edit: March 04, 2020, 04:28:56 AM by 3DickUlus »

Offline hobold

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Re: Cellular Coloring of Mandelbrot insides
« Reply #51 on: March 09, 2020, 09:08:25 AM »
The example pictures with cobweb like cells inside the main cardioid got me thinking. Is it possible to make such webs simultaneously visible everywhere inside the Mandelbrot set? That would mean choosing an orbit trap position per pixel.

It may be kind of possible. Here's an experiment where I took the centroid of the entire orbit as the trap position for coloring.

I guess a more correct (less approximate) way of doing this would be to identify the attracting periodic cycle, and use the centroid of just the cycle's points. But even then I am not sure if the pattern could be spread beyond just the main cardioid. Outside colors are pretty much meaningless here.

Offline hobold

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Re: Cellular Coloring of Mandelbrot insides
« Reply #52 on: April 20, 2020, 02:37:15 PM »
Okay, returning to the construction site here, after some exploration over in the showcase thread.

Observations:
  • Minibrot innards need very specific trap positions (besides the origin) to retain any cell detail at deeper zoom magnifications.
  • Embedded Julias generally seem to result in nicer surrounding patterns than minibrots.
  • Shape stacking seems to be especially fruitful with these orbit trap cells. I guess that is because the resulting image then shows dynamics of each and every stacked shape; i.e. the set of "interesting" orbit trap regions seems to be the union of the interesting regions of each of the stacked shapes.
  • Shape stacking tends to make the images much more volatile with respect to small changes in orbit trap position.
  • Conversely, zooming alone does not necessarily cause the resulting images to be more sensitive to small changes in orbit trap position.
  • When shape stacking, there can be narrow orbit trap regions where the dynamics of more than one shape fight each other over the color cells. I believe my vinyl worms (over in the showcase) are a special case of this.

All of this is merely conjecture based solely on exploring the good ole' Mandelbrot formula. My judgement of what looks good or bad is purely subjective, of course.

Offline iRyanBell

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Re: Cellular Coloring of Mandelbrot insides
« Reply #53 on: June 14, 2020, 05:09:59 AM »
Really cool stuff. Here's a result of applying this orbit trap to a small Julia set.

Offline hobold

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Re: Cellular Coloring of Mandelbrot insides
« Reply #54 on: June 15, 2020, 01:49:27 AM »
Experimentation is welcome! Not that you needed my permission for that. :)