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### Author Topic:  Ultimate Anti-Buddhagram  (Read 240 times)

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#### claude ##### Ultimate Anti-Buddhagram
« on: November 21, 2019, 02:09:43 PM »
blog post: https://mathr.co.uk/blog/2019-11-20_ultimate_anti-buddhagram.html

implicit surface (4D) approximate distance estimate (no proof this is correct, but it seems to work)

Code: [Select]
float DE(vec2 c, vec2 z0){  vec2 z = z0;  vec2 dz = vec2(1.0, 0.0);  float de = 1.0 / 0.0;  for (int p = 1; p <= MaxPeriod; ++p)  {    dz = 2.0 * cMul(dz, z);    z = cSqr(z) + c;    de = min(de, max(length(z - z0), length(dz) - 1.0));  }  return 0.25 * de - Thickness;}
I think the 4D normal is $\left( \frac{\partial F}{\partial c} ; \frac{\partial F}{\partial z} \right)$ where $F(c, z) = f_c^p(z) - z$, choose the period p that minimizes the DE.

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