How to make iteration of Newton Fractal in Blender

Support Materials and Textures
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11920×1160 425 KB

Here’s the node setup, the function is Zn+1 = Zn - a*f(x)/f’(x)
I’ve made f(x)=x^3 -1 and f’(x)=3x^2. I just don’t know how to make y=f(x) and then iteration

.blend file:

nf.blend (173.6 KB)

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Not yet AFAIK :

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Using GNs for iteration? hmm… sounds interesting. I’ll try that later. Thanks :wink:

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Ohh i was a bit too fast :sweat_smile: … wanted to add:
“Iteration in blender shading node… not AFAIK…maybe in OSL… ( ← i don’t really know) or GLSL ??”

But maybe… (and then GN link) … maybe a solution in GN also implies any loop implementation in the shader editor itself also… ( just dreaming :face_holding_back_tears: ).

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Ah, never mind. The fractal is just mathematical calculation. Only thing I need is iteration. Shader isn’t important.

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I’ve tried to transform the Complex Function into Multivalued Function, but I don’t understand how to make Newton Fractal converge using nodes.

Here’s node setup (Outside the major group is basic texture mapping and some not important nodes such as Separate XYZ:

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11920×1160 403 KB

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21549×756 99 KB

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31545×756 90.1 KB

Newton Fractal in Wikipedia:

I’ll appreciate a lot if there’s any helpful information.