One Fourier Bin

analytical · neon · twelve laws · under keeper eris

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analytical

A pure 3-cycle wave on 32 samples puts its Fourier energy in bin 3 and bin 29, and nowhere else.

LIT x[n] = cos(2π · 3 · n / 32). The page sums the 32-point discrete Fourier transform directly (not a fast algorithm). Bins 3 and 29, the mirror pair, hold the energy. Every other bin is under 10⁻⁶. Parseval's relation for this normalization is checked: Σ x² = (1/N) Σ |X|².

AMBER Fourier's 1822 analytical theory is the ancestor. Cooley and Tukey, 1965, is the fast algorithm. This page uses the definition, which is short at N = 32.

MODEL Bars are the bin energies. The ribbon is the 3-cycle wave. Bin 29 is the same wave seen from the other end of a real transform.

Sources AMBER

  1. Discrete Fourier transform (reference)

LIT on load: the identity is recomputed (it throws on mismatch), the training target scores 1, 200 rounds improve the shared sketch, the workspace loop logs 5 entries, and the OBJ and SVG exports match the sketch.

Gallery of kept sketches:

Workspace improvement loop MODEL

  1. Measure: every 40 rounds, record the acceptance rate, the current score and how many rounds since the last improvement.
  2. Try next: if the score has been flat for 40 rounds, widen the mutation step. If acceptance is under 15%, shrink it; over 45%, widen it. Otherwise keep it.
  3. Log back: append {entry, round, measured, tried, step} to the workspace log (it is in the export JSON and the list below).
  4. Repeat: re-check the identity before claiming it. The seal stays write-if-missing.

Live workspace log:

    Shared board MODEL

    localStorage key mayhem-twelve-laws-board. Each page writes its best shared reward.

      Attempt board MODEL

        ← Euler's Count · Twelve Laws · Hamilton's Quarter Turn → · ERIS

        Background wash: AMBER MODEL a field seeded from this page's seal. The viewport is a deep colour, not black, over a vivid page.

        proving…

        Seal sha256(name|slug|blurb): b0d13cbc7f66b6b104069207ffdd152196759d9a9abb064534600d68d0b73d1b