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// Created: Sun Nov 20 06:09:53 2016
#include "Progressive2D.frag"
#include "Complex.frag"
#info Rational Mandelbrot or Julia with Distance Estimation and Atom Domains
#group Mandelbrot
uniform int  Iterations; slider[10,200,5000]
uniform bool Julia; checkbox[false]
uniform float JuliaX; slider[-10,0,10]
uniform float JuliaY; slider[-10,0,10]

// dual complex numbers for automatic differentiation
vec4 mul(vec4 a, vec4 b) {
  return vec4(cMul(a.xy, b.xy), cMul(a.xy, b.zw) + cMul(a.zw, b.xy));
}
vec4 div(vec4 a, vec4 b) {
  return vec4(cDiv(a.xy, b.xy), cDiv(cMul(a.zw, b.xy) - cMul(a.xy, b.zw), cMul(b.xy, b.xy)));
}

// from http://gamedev.stackexchange.com/a/59808
vec3 hsv2rgb(vec3 c) {
  vec4 K = vec4(1.0, 2.0 / 3.0, 1.0 / 3.0, 3.0);
  vec3 p = abs(fract(c.xxx + K.xyz) * 6.0 - K.www);
  return c.z * mix(K.xxx, clamp(p - K.xxx, 0.0, 1.0), c.y);
}

vec3 color(vec2 p) {
  // critical point
/*
  vec2 z0 = vec2(0.0);
*/
  vec2 z0 = vec2(pow(0.009/2.0, 1.0/3.0), 0.0);

  // initialisation
  vec4 c = Julia ? vec4(JuliaX, JuliaY, 0.0, 0.0) : vec4(p, dFdx(p));
  vec4 z = Julia ? vec4(p, dFdx(p)) : vec4(z0, 1.0, 0.0);
  int i = 0;
  int j = 0;
  float minl = 1.0 / 0.0;

  // main loop
  for (i = 0; i < Iterations; i++) {
    // iteration formula
/*
    z = mul(z, z) + c;
*/
    z = mul(z, z) + div(vec4(0.009, 0.0, 0.0, 0.0), z) + c;

    // atom domains
    float l = dot(z.xy,z.xy);
    if (l < minl) {
      j = i;
      minl = l;
    }

    // bailout
    if (l > 1.0e10) break;
  }
  if (i == Iterations) return vec3(0.0, 0.0, 0.0);

  // distance estimator shading with atomain colour
  float r = length(z.xy);
  float dr = length(z.zw);
  float de = 2.0 * r * log2(r) / dr;
  return vec3(tanh(clamp(de, 0.0, 4.0))) * hsv2rgb(vec3(float(j) * 0.05, 0.5, 1.0));
}


#preset Default
Gamma = 2.08335
Brightness = 1
Contrast = 1
Saturation = 1
Center = 0.00018,-0.1439975
Zoom = 132
ToneMapping = 1
Exposure = 1
AARange = 2
AAExp = 1
GaussianAA = true
Iterations = 5000
JuliaX = -1.059908
JuliaY = -0.0460829
Julia = true
#endpreset