Sine wave in log-polar

GLSL shader by claudegl · created 2026-06-26 · 10s loop · 1 pass

Sine wave in log-polar — realtime GLSL.

Tags: glsl, generative

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Shader source (GLSL)

Common

#define pi acos(-1.)
#define deg pi/180.
#define time iTime*2.*pi/10.
#define R iResolution.xy
#define ar R.x/R.y
#define M iMouse
#define xm (M.xy/R)
#define nm ((xm.xy-0.5)*vec2(ar,1.)+0.5)
mat2 r2d(float a) {
    return mat2(cos(a),sin(a),-sin(a),cos(a));
}

Buffer A (iChannel0)

// ── Sine wave, then the SAME sine in log-polar ──────────────────────────────
// Slide: shows what the log-polar mapping does. Left panel is a plain sine wave
// laid out across x. Right panel is the exact same f(s)=sin(s·k − t), but with
// s = log(radius) instead of x — so the identical wave becomes concentric rings
// that scroll inward forever (the infinite zoom).
// Canvas: 2:1 aspect (two square panels).
// ───────────────────────────────────────────────────────────────────────────

#define TAU 6.28318530718

void mainImage(out vec4 O, in vec2 I){
    vec2 R  = iResolution.xy;
    vec2 uv = I / R;                       // 0..1 over a 2:1 canvas
    float t = iTime;
    float k = TAU * 5.0;                    // 5 cycles per panel

    float v;
    if (uv.x < 0.5) {
        // LEFT — the sine wave, plain, across x
        float s = uv.x * 2.0;              // 0..1 across the left panel
        v = 0.5 + 0.5 * sin(s * k - t);
    } else {
        // RIGHT — the same sine, but s = log(distance from center): log-polar
        vec2 p = vec2((uv.x - 0.5) * 2.0, uv.y) - 0.5;   // center the right panel
        float r = max(length(p), 1e-4);
        float s = log(r);
        v = 0.5 + 0.5 * sin(s * k - t);
    }

    // faint accent so it isn't flat gray; the wave itself stays the point
    vec3 col = mix(vec3(0.06, 0.07, 0.09), vec3(0.83, 0.86, 0.95), v);

    // thin divider between the two panels
    col *= smoothstep(0.0015, 0.005, abs(uv.x - 0.5));

    O = vec4(col, 1.0);
}

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