Lattice

点阵 Lattice

万物皆点集，交互即映射。
Everything here is a set of points. Every interaction is a map.

A design system for personal sites and WebGL pieces: formal mathematics, data, agent systems and games, each built up from its premises.

  • MOVE disturb the field
  • HOLD melt the points
  • LET GO recrystallise into the next set

定理之瀑 A waterfall of theorems

43 results of real analysis, from ZFC down to existence theorems for differential equations. Each stream falls from a premise into what it proves. Hover a result: what it needs, what it enables. Click to grow its proof.

    All 43 results, in dependency order

      A guided walk down the waterfall, one result per scroll step

      证明树 A proof grows

      A theorem is a seed. Its proof grows upward: every branch reaches for a premise, until the leaves are axioms. Lemmas used twice appear once; later uses are marked ↺.

      Hover a node to trace it down to the conclusion. Click it to grow its own tree. Drag to turn.

      证明树 · 连播 One proof per turn

      01

      Keep scrolling: the stand turns half a revolution, the old proof falls, the next one grows.

      器 The instruments

      The parts this site is made of. Each control keeps its native behaviour; its state is drawn as a set of dots that maps to the next state. Move the pointer over anything you can press: the cursor's points re-form around it.

      钮 Buttons

      Primary, accent, ghost and disabled. Pressing bursts the cursor's points outward.

      标 Tabs

      The indicator is a swarm. Change tabs and it pours across to the new one.

      相 Switches

      Off, the points drift free as a gas across the whole track. On, they converge and lock into a crystal. The same points, a different phase.

      晶 Progress

      Unfinished work is free-floating gas. Each newly finished part is built from it: the points converge, lock into the lattice with a flash, and stay. Indeterminate progress is a band of order sweeping through. The bar plays by itself; drag the slider to take over.

      Progress
      42

      字 Matrix type & loader

      5×7 matrix lettering whose dots reflow between strings. The loader is one Lorenz trajectory.

      043

      入 Text field

      A dotted rule that flows while you type and tightens in orange when something is wrong.

      Press Enter to check the format.

      令 Commands & messages

      ⌘K or Ctrl+K opens every action on the page. Messages arrive with a dot-matrix tag.

      元 Tokens

      Ink for points at rest, signal orange for what a thing needs and for action, ice blue for what it enables. Atkinson Hyperlegible Next for reading (labels sit at 12 px over moving points), Doto for the matrix, Noto Sans SC for Chinese.

      bg #07080b
      ink #ece7da
      dim #9d988c
      hot #ff5a1f
      hot-2 #7fd8ff

      Atkinson Hyperlegible Next — the reading voice, 17 / 1.6.

      DOTO 900 — THE MATRIX VOICE

      思源黑体 — 中文，与点阵并排。

      证毕 Q.E.D.

      This page is its own proof: every picture above is a set of points under one clock, and every relation in it is real. If you would like to build something from first principles together, write.

      Write to me Back to the axioms

      点阵 LATTICE 0.2 · an open design system · three.js, WebGL2, WebAudio · theorem data: undergraduate real analysis