Spectral Noise

1/f^β synthesised in the frequency domain.

patterns.spectral · v1 · renderer canvas

Brown · β = 2.00 · slope -2.00 · 7 colours

The spectrum of a random walk. Soft, rolling, cloud-like: each step is small and the errors accumulate. Built by filling a 1024×1024 complex spectrum with Gaussian coefficients scaled by f^(-β/2), then inverse-transforming and taking the real part — 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-β) rather than f^(1-β). 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.

[data-canvas-stage] { display: none; }

Drawn in the browser

This generator does not send you an image. The server sends a short description of one — the parameters below, plus a 32-byte key — and the drawing is done here, from the same byte stream the server would have used. That needs JavaScript, so with it switched off there is nothing to show.

The description itself is still public: /api/v1/g/patterns.spectral returns it, and the maths is in resources/js.

Brown · β = 2.00 · slope -2.00 · 7 colours

Controls · from schema()

Width

200 2048

Height

200 2048

Colour of noise

-2.5 4

The exponent itself. 0 is white, 1 pink, 2 brown, −1 blue. Only read when the preset is Custom.

Contrast

0.6 4

Where the palette's ends are pinned, in standard deviations. A spectral field is Gaussian, so it has tails rather than bounds — stretching to the extremes would leave the whole picture in the middle third of the ramp.

Zoom

1 12

Magnifies the same field. At 1 you see every octave the raster can hold, which for pink noise is mostly grain; wind it up and the low frequencies take over. A 1/f field is scale-free, so this is a real zoom and not a blur.

Colour

Palette size

2 12

Banding

Quantise into flat bands. On a brown field this draws something very close to a contour map, because that is what a brown field is.

Entropy source

Picking a source changes the story on the receipt, never the quality: anything below class A is mixed with the OS CSPRNG before it reaches you. This result actually came from Bitcoin Proof-of-Work.

seed token SMT1DABK718ZGT9CH6R22ZKC0M

Re-render keeps this token. Generate replaces it. That is the whole idea.

Burned into the corner before the file is written, so the image keeps its provenance wherever it ends up:

entropy in

16 bytes

stream used

4 bytes

rejections

duration

72 µs

palette

beta

spectral slope

-2

colour name

brown

audio twin

audio.noise

Seed receipt

Class B · Public beacon cached

Bitcoin block 973,812 — 19 leading zeros of proof-of-work, found about ten minutes ago.

Published openly — anyone can look this value up after the fact.

source: Bitcoin Proof-of-Work
observed: 2026-10-30T11:13:18+00:00
latency: 0ms
mixed with: csprng — always

https://mempool.space/block/00000000000000000001437feed9aae961c1ad1a4747d5b76de354fe6846c2cf ↗

Permalink

The token is the seed, so this link recomputes the result rather than looking it up. No database, and it works for as long as v1 does.

This page and /api/v1/g/patterns.spectral run the same code. There is no private endpoint.

Spectral Noise

Result

Measurements

Seed receipt

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