{"generator":"patterns.spectral","version":1,"value":{"algorithm":"spectral","width":900,"height":600,"beta":2,"zoom":1,"contrast":2.5,"contours":false,"palette":["#000004","#310c5e","#71207b","#b53975","#e9666a","#feaf7b","#fcfdbf"],"seed":1584563028},"display":"Brown \u00b7 \u03b2 = 2.00 \u00b7 slope -2.00 \u00b7 7 colours","meta":{"palette":["#000004","#310c5e","#71207b","#b53975","#e9666a","#feaf7b","#fcfdbf"],"beta":2,"spectral_slope":-2,"colour_name":"brown","audio_twin":"audio.noise","note":"The spectrum of a random walk. Soft, rolling, cloud-like: each step is small and the errors accumulate. Built by filling a 1024\u00d71024 complex spectrum with Gaussian coefficients scaled by f^(-\u03b2\/2), then inverse-transforming and taking the real part \u2014 the same shaping audio.noise applies across audible frequency. One thing the shared name hides: a plane holds more modes at high frequency than a line does, about f of them per unit f, so the power in an octave goes as f^(2-\u03b2) rather than f^(1-\u03b2). The exponent that puts equal power in every octave is therefore 2 here where it is 1 in audio, which is why brown is the default and why pink reads as grain rather than as weather.","stream_bytes_used":4,"rejections":0,"entropy_in_bytes":16,"duration_us":72},"receipt":{"source":"csprng","source_label":"Operating System CSPRNG","class":"A","class_label":"Cryptographic","caveat":null,"narrative":"Drawn from the kernel entropy pool on the server that rendered this page. (The source you picked was unreachable, so we fell back to the kernel.)","proof_url":null,"reference":null,"observed_at":"2026-10-30T12:19:16+00:00","degraded":true,"mixed_with_csprng":false,"latency_ms":1507,"cached":false},"seed":{"token":"Y1MCWF2E72EJZ64P4BX9Q85BDR","permalink":"https:\/\/randomly.cluxnei.dev\/r\/Y1MCWF2E72EJZ64P4BX9Q85BDR?g=patterns.spectral&v=1&p=eyJiZXRhIjoxLCJjb2xvdXJzIjo3LCJjb250b3VycyI6ZmFsc2UsImNvbnRyYXN0IjoyLjUsImhlaWdodCI6NjAwLCJwYWxldHRlIjoibWFnbWEiLCJwcmVzZXQiOiJicm93biIsIndpZHRoIjo5MDAsInpvb20iOjF9&s=csprng"},"render_key":"dc086e5a604d331f31f49137e90239e67e9968d9a4da545a1602fab8f916f88a","uses_entropy":true,"reproducible":true}