Fractal Brownian Motion

fbm.frag

    float rand (vec2 st) {
        return fract(sin(dot(st.xy,
                             vec2(12.9898,78.233)))*
            43758.5453123);
    }

    float noise(vec2 p){
      vec2 ip = floor(p);
      vec2 u = fract(p);
      u = u*u*(3.0-2.0*u);

      float res = mix(
        mix(rand(ip),rand(ip+vec2(1.0,0.0)),u.x),
        mix(rand(ip+vec2(0.0,1.0)),rand(ip+vec2(1.0,1.0)),u.x),u.y);
      return res*res;
    }
  
    float fbm(vec2 x) {
      float v = 0.0;
      float a = 0.5;
      vec2 shift = vec2(100);
      // Rotate to reduce axial bias
        mat2 rot = mat2(cos(0.5), sin(0.5), -sin(0.5), cos(0.50));
      for (int i = 0; i < NUM_OCTAVES; ++i) {
        v += a * noise(x);
        x = rot * x * 2.0 + shift;
        a *= 0.5;
      }
      return v;
    }