Mathematics · Study 043
Collatz Coral
Seven thousand Collatz sequences drawn as overlapping paths that bend one way for even steps and the other for odd, forming a coral.
What you're looking at
Take a number. If it is even, halve it. If it is odd, triple it and add one. Repeat until you reach 1. Each number's journey is drawn in reverse from a shared root: an even step curls the line slightly one way and an odd step curls it the other. Numbers that merge onto the same path overlap, so the trunk is bright and the tips are faint.
The idea behind it
Lothar Collatz posed the question in 1937: does every starting number reach 1? Computers have checked far beyond a billion billion without finding an exception, and no one has proved it. The drawing shows the structure that makes the problem tantalising: vast numbers of paths funnel into a few shared routes.
Try this
Let it grow. Restart draws the same coral again, because nothing in it is random.
