1d0=?
Round 0 draws the fundamental sequence of ε0 (1, ω, ωω, …). Every interval wider than 4 px is then subdivided by fundamental sequences (limit) or by splitting off natural numbers (successor), for at most 6 rounds, with each round's ticks drawn shorter. Labels above show the important ordinals; the triangle below marks the sampled random number.

How to use

This page rolls a random ordinal between 0 and the maximum ordinal m, and displays 1d(m)=α.

Max Ordinal is written in Cantor normal form, e.g. ω^ω·2+ω·3+5, ω^ω^ω, ω·2+1 or 5. w may be used instead of ω, parentheses are allowed in exponents such as ω^(ω+1), and the exponents must be strictly decreasing (so ω+ω^2 is invalid).

Ratio (p) controls the distribution: a higher ratio makes large ordinals more likely. The Ratio is also the geometric-distribution parameter used to assign a sub-interval of [0,1) to every ordinal below ε0, so that each roll is a uniform random number in [0, pos(m)).