Nothing on this page is stored data. Every prime is tested, every trajectory computed, every digit of π generated — live, in your browser, while you watch.
In 1963, Stanisław Ulam was doodling in a boring meeting: he wrote the integers in a square spiral and circled the primes. They should look like static. Instead they organise into diagonal streaks — visible order in the primes that mathematics still cannot fully explain. Watch ~65,000 integers spiral out below; the bright points are prime.
Take any number. If it's even, halve it. If it's odd, triple it and add one. Repeat. Every number ever tested collapses to 1 — but no one has ever proved they all must. Paul Erdős said mathematics is "not ready for such problems". Below, hundreds of trajectories drawn as organic tendrils: each bends by its path of odd and even steps.
Here your browser computes the digits of π itself, with a spigot algorithm on big integers — then turns each digit into a compass direction and takes one step. If π's digits are truly patternless (nobody has proved that either), this walk should wander like a drunkard. It draws its own map as it computes.