Tools, APP Software Used etc.

C++ and Python custom code

Description

julia_fractal_2000_inverted_quadric_small

This unique object is a julia fractal based on quaternions. a very fine 3d grid is evaluated for each point with an ietrativ formula.

depending on the result, it defines a surface.

Usually these object are showing a fixed number of iterations, this one shows simulaneously the effec of different iterations.

low iteration count give a smooth surface while high number gives lot of detail.

Millions of triangles are generated from the grid, and must be simplfiied, I use some python libraries for that.

Code

some code

C/C++

vec4 qsqr(vec4 &a) { // square a quaternion
  return vec4(a.x * a.x - a.y * a.y - a.z * a.z - a.w * a.w, 2.0 * a.x * a.y,
              2.0 * a.x * a.z, 2.0 * a.x * a.w);
}

inline float criticalLoop(vec4 in, vec4 c, int iter) {
  vec4 z = in;
  float bailout = 4.0;
  float md2 = 0.0;
  float mz2 = dot(z, z);
  for (int i = 0; i < iter; ++i) {
    md2 = 4.0 * mz2;
    z = qsqr(z) + c;
    mz2 = dot(z, 
      z);
    if (mz2 > bailout)
      break;
  }
  mz2 *= .38;
 return 0.25 * sqrt(mz2 / md2) * log(mz2);
}

CAD-Custom parts and enclosures

C-CN7W703158A_C-CN6W703158A_julia_fractal_2000_inverted_quadric_small

C-CN7W703158A_C-CN6W703158A_julia_fractal_2000_inverted_quadric_small.stl

Jul 07,2026

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julia_fractal_2000_inverted_quadric_small

a unique fractal sculpture

Published: Jul 07,2026

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