Voronoi and Worley (cellular) noise

Worley noise/cellular noise

Worley noise, or cellular noise, is a distance value pattern where every pixel gets a value based on the distance to the closest point from a defined set. This creates a pattern like the one above.

vec2 random(vec2 uv) {
	return vec2(fract(sin(dot(uv.xy,
		vec2(12.9898,78.233))) * 43758.5453123));
}

float worley(vec2 uv, float columns, float rows) {
	
	vec2 index_uv = floor(vec2(uv.x * columns, uv.y * rows));
	vec2 fract_uv = fract(vec2(uv.x * columns, uv.y * rows));
	
	float minimum_dist = 1.0;  
	
	for (int y= -1; y <= 1; y++) {
		for (int x= -1; x <= 1; x++) {
			vec2 neighbor = vec2(float(x),float(y));
			vec2 point = random(index_uv + neighbor);
			
			vec2 diff = neighbor + point - fract_uv;
			float dist = length(diff);
			minimum_dist = min(minimum_dist, dist);
		}
	}
	
	return minimum_dist;
}

void fragment() {
	float worley = worley(UV, 3.0, 5.0);
	COLOR = vec4(vec3(worley), 1.0);
}

If you want the pattern to move you can add this to the loop. You will have to pass TIME from the fragment function. Play around with the different values for different results.

...
vec2 point = random(index_uv + neighbor);
float speed = 4.5;
point = vec2( cos(time * point.x * speed), sin(time * point.y * speed) ) * 0.5 + 0.5;
...

Voronoi diagram

With the Worley noise as a base, we can make a Voronoi diagram. Instead of the fading distance value, each “cell” gets its own defined value.

vec2 voronoi(vec2 uv, float columns, float rows) {
	
	vec2 index_uv = floor(vec2(uv.x * columns, uv.y * rows));
	vec2 fract_uv = fract(vec2(uv.x * columns, uv.y * rows));
	
	float minimum_dist = 1.0;  
	vec2 minimum_point;

	for (int y= -1; y <= 1; y++) {
		for (int x= -1; x <= 1; x++) {
			vec2 neighbor = vec2(float(x),float(y));
			vec2 point = random(index_uv + neighbor);

			vec2 diff = neighbor + point - fract_uv;
			float dist = length(diff);
			
			if(dist < minimum_dist) {
				minimum_dist = dist;
				minimum_point = point;
			}
		}
	}
	return minimum_point;
}
void fragment() {
	vec3 voronoi = vec3(voronoi(UV, 10.0, 5.0).r);
	COLOR = vec4(voronoi, 1.0);
}

This code is converted from The Book of Shaders article on Cellular Noise, where you can read more about how Voronoi diagrams and Worley noise (cellular noise) works.