Complex numerals

Numbers written in a complex base. Choose a base $\beta$ among the Gaussian integers $\mathbb{Z}[i]$ or the Eisenstein integers $\mathbb{Z}[\omega]$ ($\omega = e^{2\pi i/3}$), and a set of digits. Every sum $\sum_k d_k \beta^k$ with at most $L$ places is then a point of the lattice. When the digits hold one number from each residue class mod $\beta$, those points are all different, and together they tile a fractal: base $-1 + i$ with digits $0$ and $1$ draws the twindragon.

A page draws these systems as a Show layer, LatticeTiles(RadixExpansions(ring, base, digits, places)). Its ./lattice entry is plain TypeScript with no engine. It holds the arithmetic, the layer, a handful of notable systems with their sources, and the favorites viewers sent to TheGrayCuber's imaginary-bases page. No heads are declared yet.

• Complex bases: the guide.

Pages

• Complex Bases

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• Source: packages/symbols/arithmetic/complex-numerals
• Depends on: numerals
• In development, also: config