Take any positive whole number — any size at all. If it is even, halve it; if it is odd, triple it and add one. Then repeat. Every number ever tested eventually collapses to 1, and remarkably, no one has been able to prove that it always must.

The explorer below traces a single orbit, coloring each step by its remainder mod 3 and marking the moment the path lands on a power of 2 — after which it simply free-falls to 1.