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Convergent smooth iterationNon Affine IFSDeep Menger Sponge
Non Affine IFS
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Description: This image shows how pruning the IFS tree based on #hits can improve the rendering.

The black and blue are the standard inside and outside of the Julia for z^2-0.76016+flip(0.06998).

The red is the complete 2 transform IFS for the same Julia Set rendered using the deterministic method to depth 24 and it took around 28 seconds to render.

The white is the same IFS also using the deterministic method but this time the IFS tree is pruned by stopping branches when #hits for a new point reaches 50. In this case the maximum depth allowed was 100000. Rendering this took just 2.5 seconds !

This just goes to show how pruning based on #hits can improve rendering non-affine IFS.
However the method does have the drawback that all the IFS needs to be on-screen (or at least on #hits buffer) and as you can see even going down to a depth of 100000 does not render a complete image (note that increasing the max. hits for pruning simply made the #hits values more uneven and increased the rendering time).

Total Favorities: 0 View Who Favorited
Filesize: 142.02kB
Height: 480 Width: 640
Keywords: non-affine ifs julia fractal digital algorithmic ultrafractal 
Posted by: David Makin September 19, 2009, 12:41:30 AM

Rating: *** by 1 members.

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