{ "license": "CC0-1.0", "shader": { "id": "7h4vl4jd", "title": "Trefoil Cord", "license": "CC0-1.0", "provenance_type": "witnessed_generation", "made_with": "glslop", "status": "active", "compile_ok": true, "render_hash": "08344cb21d0a0000", "tags": [ "volumetric", "raymarch", "knot", "trefoil", "plasma", "braid", "loop" ], "parents": [ "mfupgrz0" ], "author": "zazi5inxhmgi", "author_name": "ufffd", "author_url": "/u/ufffd", "created_at": "2026-07-21T04:15:31.175Z", "poster_url": "/posters/7h4vl4jd.avif", "stats": { "slops": 2, "views": 188, "forks": 0 }, "self": "/api/v1/shaders/7h4vl4jd", "isf": "/*{\n \"DESCRIPTION\": \"A trefoil knot rendered as volumetric plasma, with a second wire snaking around it. The main cord is the exact zero-set of cos(3*phi - 2*a) on a torus, so the knot's three crossings are real geometry - the ray marcher resolves the over/under occlusion where the cord passes through itself. The cord is a hollow braided sleeve (two counter-wound filament families beating into moire, the guilloche trick in 3D) around an incandescent core, and a thin satellite strand spirals along its whole length, orbiting the cord as it travels. Integrated as glow x transmittance; hue runs along the knot, decoupled from density, so it stays a vivid 2-tone. HDR march, bloom and tone-map in a second pass. Seamless 12s loop.\",\n \"CREDIT\": \"glslop agent\",\n \"CATEGORIES\": [\"volumetric\", \"raymarch\", \"knot\", \"trefoil\", \"plasma\", \"loop\"],\n \"INPUTS\": [\n { \"NAME\": \"cordRadius\", \"TYPE\": \"float\", \"DEFAULT\": 0.145, \"MIN\": 0.07, \"MAX\": 0.28 },\n { \"NAME\": \"density\", \"TYPE\": \"float\", \"DEFAULT\": 1.0, \"MIN\": 0.3, \"MAX\": 2.2 },\n { \"NAME\": \"filaments\", \"TYPE\": \"float\", \"DEFAULT\": 1.0, \"MIN\": 0.0, \"MAX\": 2.0 },\n { \"NAME\": \"molten\", \"TYPE\": \"float\", \"DEFAULT\": 0.35, \"MIN\": 0.0, \"MAX\": 1.6 },\n { \"NAME\": \"satTurns\", \"TYPE\": \"long\", \"DEFAULT\": 5, \"MIN\": 0, \"MAX\": 60 },\n { \"NAME\": \"satOrbit\", \"TYPE\": \"float\", \"DEFAULT\": 1.55, \"MIN\": 0.8, \"MAX\": 3.0 },\n { \"NAME\": \"satWeight\", \"TYPE\": \"float\", \"DEFAULT\": 1.0, \"MIN\": 0.0, \"MAX\": 2.5 },\n { \"NAME\": \"satColor\", \"TYPE\": \"color\", \"DEFAULT\": [1.0, 0.66, 0.18, 1.0] },\n { \"NAME\": \"hueTravel\", \"TYPE\": \"float\", \"DEFAULT\": 1.0, \"MIN\": 0.0, \"MAX\": 3.0 },\n { \"NAME\": \"bloom\", \"TYPE\": \"float\", \"DEFAULT\": 1.0, \"MIN\": 0.0, \"MAX\": 2.5 },\n { \"NAME\": \"exposure\", \"TYPE\": \"float\", \"DEFAULT\": 1.0, \"MIN\": 0.4, \"MAX\": 2.5 },\n { \"NAME\": \"speed\", \"TYPE\": \"float\", \"DEFAULT\": 1.0, \"MIN\": 0.0, \"MAX\": 3.0 }\n ],\n \"PASSES\": [\n { \"TARGET\": \"scene\", \"FLOAT\": true },\n { }\n ]\n}*/\n\n#define TAU 6.28318530718\n#define STEPS 112\nconst float PERIOD = 12.0;\n\nconst float RING = 1.00; // torus centre-circle radius\nconst float ROFF = 0.40; // how far the cord sits from that circle\n\n// NB: mat2 is COLUMN-major, so this constructor rotates by -a. Signs below assume that.\nmat2 rot(float a){ float c = cos(a), s = sin(a); return mat2(c, -s, s, c); }\n\n// shortest signed distance between two angles (keeps everything single-valued)\nfloat wrapAng(float x){ return atan(sin(x), cos(x)); }\n\nfloat wobble(vec3 p, float th){\n vec3 q = p + vec3(cos(th), sin(th), cos(th)) * 0.30;\n float f = sin(q.x * 3.1) * sin(q.y * 3.7) * sin(q.z * 2.9);\n f += 0.5 * sin(q.x * 6.7 + q.z * 2.1) * sin(q.y * 7.3);\n return f * 0.667;\n}\n\n// Trefoil density field.\n// a = angle around the ring, phi = angle around the tube.\n// The (3,2) torus knot is the set where cos(3*phi - 2*a) is maximal; the SIGNED angular\n// error to it, scaled by ROFF, gives a usable distance to the cord.\n// Outputs: arc = continuous coordinate along the cord (drives hue)\n// core = incandescent filament down the cord's axis\n// sat = the satellite wire spiralling around the cord\nfloat knot(vec3 p, float th, out float arc, out float core, out float sat){\n float a = atan(p.z, p.x);\n vec2 cs = vec2(length(p.xz) - RING, p.y);\n float rad = length(cs);\n float phi = atan(cs.y, cs.x);\n\n float serr = wrapAng(3.0 * phi - 2.0 * a) / 3.0;\n\n // local frame on the cord: distance from its axis, and psi = angle AROUND the cord\n vec2 local = vec2(rad - ROFF, ROFF * serr);\n float dist = length(local);\n float psi = atan(local.y, local.x);\n\n float w = wobble(p * 2.4, th);\n float r = cordRadius * (1.0 + 0.18 * w);\n\n // HOLLOW sleeve, not a solid tube: density lives in a thin shell so the far wall\n // shows through the near wall — that overlap is what makes the moire.\n float shell = smoothstep(r, r * 0.72, dist) * smoothstep(r * 0.30, r * 0.60, dist);\n\n // TWO counter-wound filament families braided over the sleeve; where they cross they\n // beat against each other into large-scale moire (the guilloche trick, in 3D).\n float f1 = 0.5 + 0.5 * sin( 7.0 * psi + 21.0 * a + w * 1.1);\n float f2 = 0.5 + 0.5 * sin(-7.0 * psi + 26.0 * a - w * 1.1);\n float lace = pow(f1, 14.0) + pow(f2, 14.0);\n lace += 1.4 * pow(f1, 14.0) * pow(f2, 14.0); // bright nodes at the crossings\n\n // rhythm: bright passages travelling the cord so it breathes instead of being\n // uniformly busy (integer harmonic of a -> loop-safe)\n float rhythm = 0.55 + 0.45 * sin(2.0 * a - th);\n\n arc = (2.0 * a + 3.0 * phi) / TAU; // continuous coord along the cord\n\n // incandescent filament down the cord's axis: hot core inside coloured gas\n core = smoothstep(r * 0.22, r * 0.01, dist) * rhythm;\n\n // SATELLITE: a thin wire orbiting the cord at radius satOrbit*r, advancing satTurns\n // times along the knot and drifting one whole turn per loop (both integer -> loop-safe).\n float orbitR = r * satOrbit;\n float dpsi = wrapAng(psi - (float(satTurns) * a + th));\n float dsat = length(vec2(dist - orbitR, orbitR * dpsi));\n sat = smoothstep(r * 0.21, r * 0.015, dsat);\n sat *= 0.75 + 0.25 * sin(9.0 * a - 2.0 * th); // it glows unevenly as it travels\n\n return shell * mix(0.45, lace, filaments * 0.85) * rhythm;\n}\n\nvec3 pal(float t){\n return mix(vec3(0.00, 0.45, 0.90), vec3(1.00, 0.10, 0.38), 0.5 + 0.5 * cos(TAU * t));\n}\n\nvoid main(){\n float ph = fract(TIME * speed / PERIOD);\n float th = TAU * ph;\n\n if (PASSINDEX == 0){\n vec2 uv = (gl_FragCoord.xy - 0.5 * RENDERSIZE.xy) / RENDERSIZE.y;\n\n vec3 ro = vec3(0.0, 4.60, 4.60); // camera OUTSIDE the volume\n vec3 rd = normalize(vec3(uv, -1.95));\n rd.yz = rot(0.785) * rd.yz; // aim down at the knot\n ro.xz = rot(th) * ro.xz; // one full turn per loop\n rd.xz = rot(th) * rd.xz;\n\n float dt = 0.030;\n float t = 4.9;\n vec3 col = vec3(0.0);\n float trans = 1.0;\n\n for (int i = 0; i < STEPS; i++){\n vec3 p = ro + rd * t;\n float arc, core, sat;\n float sheath = knot(p, th, arc, core, sat) * density;\n float d = sheath + core * density * 0.55 + sat * satWeight * density * 0.85;\n\n if (d > 0.002){\n float hueArg = (atan(p.z, p.x) / TAU) * hueTravel + 0.06 * arc + ph;\n vec3 emit = pal(hueArg);\n emit += vec3(1.0, 0.84, 0.56) * core * 4.0; // incandescent core\n emit += vec3(1.0, 0.42, 0.10) * pow(sheath, 2.0) * molten * 3.0; // molten hot spots\n emit += satColor.rgb * sat * satWeight * 2.4; // satellite wire\n\n col += emit * d * trans * dt * 15.0 * exp(-0.26 * (t - 4.9));\n trans *= exp(-d * dt * 24.0);\n if (trans < 0.01) break;\n }\n t += dt;\n if (t > 8.4) break;\n }\n\n col += vec3(0.030, 0.018, 0.060) * exp(-length(uv) * 3.2);\n gl_FragColor = vec4(max(col, 0.0), 1.0);\n\n } else {\n vec2 uv = isf_FragNormCoord;\n vec3 c = IMG_THIS_PIXEL(scene).rgb;\n\n vec3 glow = vec3(0.0);\n for (int i = 0; i < 16; i++){\n float a = TAU * (float(i) + 0.5) / 16.0;\n vec2 dir = vec2(cos(a), sin(a));\n glow += max(IMG_NORM_PIXEL(scene, uv + dir * 0.013).rgb - 0.55, 0.0);\n glow += max(IMG_NORM_PIXEL(scene, uv + dir * 0.034).rgb - 0.55, 0.0) * 0.55;\n }\n glow /= 24.8;\n\n vec3 col = c + glow * bloom * 1.5;\n col *= exposure * 1.25;\n col = 1.0 - exp(-col); // soft knee at DISPLAY only\n col = pow(max(col, 0.0), vec3(0.92));\n gl_FragColor = vec4(col, 1.0);\n }\n}\n", "generator": { "model": "claude-opus-4-8", "provider": "anthropic", "prompt": null, "params": null } } }