Lesson 9 of 10 · Shader patterns

Chladni

Geometric vibration. The Chladni plate.

Ernst Chladni put sand on a metal plate and made it vibrate. The sand moved to the quiet spots and formed geometric patterns. Each frequency produces a different pattern.

Two waves multiply. Interference draws itself.

The formula is two sines multiplied: sin(n * p.x) * sin(m * p.y). The numbers n and m are the vibration modes, how many nodes in each direction. When you add two terms with n and m swapped, the classic patterns appear.

n and mWhole numbers that define the pattern identity. 2, 3 = complex circuit. 5, 7 = labyrinth. 8, 8 = symmetric grid. When n and m share no common factors, complexity is maximum.

TryChange 5. and 3. to 8., 8., perfect pattern. To 2., 3., few cells. To 7., 11., maximum complexity. Hint: add + T * 0.5 to both to make it mutate slowly.

The code

void main(){
  vec2 p = (2.*gl_FragCoord.xy - R) / min(R.x, R.y);
  float n = 5., m = 3.;
  float z = sin(n*3.14*p.x)*sin(m*3.14*p.y)
         + sin(m*3.14*p.x)*sin(n*3.14*p.y);
  float zx = sin(n*3.14*(p.x+.015))*sin(m*3.14*p.y)
           + sin(m*3.14*(p.x+.015))*sin(n*3.14*p.y);
  float zy = sin(n*3.14*p.x)*sin(m*3.14*(p.y-.02))
           + sin(m*3.14*p.x)*sin(n*3.14*(p.y-.02));
  float v = abs(z);
  float emboss = ((z-zx)+(z-zy))*.5;
  float hard = step(0.3, v);
  vec3 a = vec3(0.92, 0.9, 0.85);
  vec3 b = vec3(0.06, 0.04, 0.12);
  vec3 col = mix(b, a, hard);
  col += vec3(.2,.18,.12) * clamp(emboss,0.,1.) * hard;
  col -= vec3(.15,.12,.1) * clamp(-emboss,0.,1.);
  col *= .85 + .15 * exp(-length(p)*.4);
  gl_FragColor = vec4(col, 1.);
}