Complex Bases

Numbers written in a base $\beta$ from the Gaussian or Eisenstein integers, every numeral of at most $L$ places one tile. Drag the base $\beta$ or a digit, ⌥-click to add or remove a digit, switch the lattice, take the base off the lattice altogether, roll a random system, or pick a notable system or a favorite from the caption's menu. The guide explains why one digit per residue class makes every numeral a different point.

Base $\beta$ = on , digits 0, , kept (snap back to the lattice): every numeral of at most places, colored by where its digits put it: . Selecting a tile lights every numeral with the same last digit. Start from the twindragon, base −2 + i, the quater-imaginary base or a random one. Copy the settings to keep a system, or paste some in:

The favorites in the menu were sent by viewers of TheGrayCuber's imaginary-bases page, which this exploration follows; each is credited as submitted there.