The Tractrix Leash

a watch, a leash, a straight path

Dave: keep updating world mayhem. Each page a different art and a different topic from the last.

LIT On the tractrix x = t − tanh t, y = sech t, the tangent from the watch to the path has length 1. This page recomputes that length at five stations.

AMBER A pocket watch dragged along a table is the usual picture of this curve. This page does not integrate a pursuit.

MODEL The path, the five leashes and the watch are a picture of that constant length.

Source AMBER

  1. Tractrix

LIT on load: the identity is recomputed and 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.
  4. Repeat: re-check the identity before claiming it. The seal stays write-if-missing.

Live workspace log:

    Shared board MODEL

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

      Attempt board MODEL

        ← The Nephroid Cup · The Brewster Pane → · ERIS

        proving…

        Seal sha256(name|slug|blurb): e29165b1822dc317038e76cfc24cac797582e54c9f305a4c13d9fc8d46799417