SF/09 · Seed 86

Sevenfold

Plane waves overlap into a pattern that never repeats.

Waves from evenly spaced directions sum to a quasicrystal: ordered and rotationally symmetric, but never periodic. The seed sets the symmetry, from five-fold to nine-fold.

Palette · Paper / indigo / signal
Interaction · Pointer turns and tightens the lattice · press to send a phase front
Runtime · WebGL2 / fragment shader

Seed 86

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Time 6.00 s

Fragment shaderGLSL ES 3.00

#version 300 es
precision highp float;

uniform vec2 u_resolution;
uniform float u_time;
uniform vec2 u_pointer;   // 0–1, eased; drifts by itself while nobody is pointing
uniform vec3 u_click;     // xy = last press (0–1), z = seconds since that press
uniform float u_seed;
out vec4 outColor;

// Integer hash: a given seed renders the same work on every GPU.
uint hashu(uint x) {
    x ^= x >> 16; x *= 0x7feb352dU;
    x ^= x >> 15; x *= 0x846ca68bU;
    x ^= x >> 16;
    return x;
}

float seeded(uint k) {
    return float(hashu(uint(u_seed) * 0x9e3779b9U + k)) / 4294967295.0;
}

vec2 toField(vec2 q) {
    return (2.0 * q - 1.0) * u_resolution / min(u_resolution.x, u_resolution.y);
}

float dither(vec2 p) {
    return (fract(52.9829189 * fract(dot(p, vec2(0.06711056, 0.00583715)))) - 0.5) / 255.0;
}

#define PI 3.14159265359

void main() {
    vec2 uv = toField(gl_FragCoord.xy / u_resolution.xy);
    float symmetry = 5.0 + floor(seeded(1u) * 5.0);
    float density = 12.0 + 6.0 * seeded(2u) + 6.0 * u_pointer.y;
    float t = u_time * 0.35;
    // A press sends a phase front outward through the lattice.
    float age = u_click.z;
    float front = exp(-age) * exp(-pow((length(uv - toField(u_click.xy)) - 0.9 * age) * 6.0, 2.0));
    float field = 0.0;
    for (int i = 0; i < 9; i++) {
        if (float(i) >= symmetry) break;
        float a = float(i) * PI / symmetry + 0.25 * (u_pointer.x - 0.5);
        field += cos(dot(uv, vec2(cos(a), sin(a))) * density + t + 2.0 * front);
    }
    field /= symmetry;
    float bands = abs(fract(field * 3.0 + 0.5) - 0.5);
    float ink = 1.0 - smoothstep(0.04, 0.12, bands);
    float bloom = smoothstep(0.15, 0.9, field);

int pick = int(floor(seeded(3u) * 3.0));
    vec3 paper = vec3(0.94, 0.92, 0.86), indigo = vec3(0.07, 0.09, 0.22), signal = vec3(0.89, 0.25, 0.11);
    if (pick == 1) { paper = vec3(0.03, 0.04, 0.06); indigo = vec3(0.86, 0.80, 0.62); signal = vec3(0.10, 0.62, 0.70); }
    if (pick == 2) { paper = vec3(0.90, 0.93, 0.90); indigo = vec3(0.05, 0.20, 0.16); signal = vec3(0.96, 0.66, 0.10); }

vec3 color = mix(paper, indigo, ink * 0.92);
    color = mix(color, signal, bloom * (1.0 - ink) * 0.85);
    color *= 1.0 - 0.18 * smoothstep(0.9, 1.7, length(uv));
    outColor = vec4(color + dither(gl_FragCoord.xy), 1.0);
}

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The source above is the complete fragment shader. Changes remain in this tab unless you take them to the playground. Download the original GLSL.