The Collatz CoralPick any whole number. If it's even, halve it; if it's odd, triple it and add one. Repeat. The Collatz conjecture — unproven since 1937 — says you always crash down to 1. Here the path of every number up to a few thousand is drawn back from 1: a small left turn for each even step, a bigger right turn for each odd one. Numbers that share the tail of their journey share a branch, so the paths grow together into a coral. The journey: iterate n → n/2 or 3n+1 to reach 1, then replay each sequence in reverse as a turtle that turns by a fixed angle on even vs. odd steps.