Hamilton's Quarter Turn

analytical · neon · twelve laws · under keeper eris

neon

{{ act || react || change }} · the sculpture

analytical

A unit quaternion turns a vector without changing its length, and a quarter turn about Y sends +X to -Z.

LIT q = cos(π/4) + sin(π/4) · j, a quarter turn about the Y axis. Sandwiching (1, 0, 0) by q sends it to (0, 0, −1). The length stays 1, and q itself has length 1. The algebra is in the check, written out with the cross-product form, not borrowed from the graphics library.

AMBER William Rowan Hamilton carved the quaternion rules on Broome Bridge in 1843. The right-hand rule used here matches the turn Three.js applies for a positive rotation about Y: local +X moves toward world −Z.

MODEL The gold needle is built along the parent's +X. The parent's yaw is the only turn. A ghost needle already sits at the quarter-turn pose, along −Z. On load the page also asks Three.js for the same turn and throws if the library disagrees.

Sources AMBER

  1. Quaternions and spatial rotation (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

        ← One Fourier Bin · Twelve Laws · The Halfway 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): d8e60f64c9e35e87834bbfe7f3f315dee403fc3c1a286d4d236b4bba679e0ecc