The binomial number system represents numbers as (a, b, c) where every number is the sum C(a, 1) + C(b, 2) + C(c, 3).

Positional number systems typically have a integer base, but irrational and even complex bases are possible. The golden ratio was the first irrational base.

Knuth defines the twindragon fractal to be the set of complex numbers that are "fractions" in base 1-i. Implemented in Python code.