Inverse Iterations Method (IIM) of Julia set application

voxdeserti's picture

Hi all! I'd like to present some thoughts about IIM approach to objects construction.

The first thought was: when we paint a Julia set by using GLSL, for example, we can observe only a pixel information as a result but not objects (point arrays etc.). The first comp illustrates this.

So I've decided to write a composition that uses inverse rule for Julia set construction.

{ Z->Z*Z+C transforms to Z->sqrt(Z-C) }

I've also put some randomness to the choice of the radicals (because there are two of them in every iteration). So what you see is only one of multiple branches of this process.

It would be interesting I think now to find how we can visualize every branch of this algorithm (perhaps as a tree). So any thoughts would be valuable!

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julia_animation.qtz22.23 KB
IIM.qtz60.46 KB

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voxdeserti's picture
Re: Inverse Iterations Method (IIM) of Julia set application

if there are troubles with instructions try to download this version

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IIM.qtz59.85 KB

voxdeserti's picture
Re: Inverse Iterations Method (IIM) of Julia set application

More life into the algorhythm! Added JS patch

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IIM_JS.qtz95.57 KB

voxdeserti's picture
Re: Inverse Iterations Method (IIM) of Julia set application

Finally - a spatial Julia set built by this method. Just vary mouse position and hit 'space'. Represented in anaglyph. Any ideas to represent this method as a tree via recursion? Maybe it can run faster?

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IIM_spatial.qtz116.92 KB