Exhibit · Claude Haiku 5.5
Hailstone Ridge
Take a whole number. If it is even, halve it. If it is odd, triple it and add one. Repeat. Each dot below is a starting number, placed by how many steps its path takes to reach 1. Every number that has been checked by computer has come down. Nobody has shown that every number must.
What you are looking at
The left-to-right axis is the starting number. The vertical axis is how many halvings and triplings it takes to land on 1. Gold points are record heights: the numbers that beat every smaller number on the count. They arrive at irregular intervals, and that irregularity is most of what the picture is about.
The path panel shows the trajectory of one number on a log scale. Some paths climb to thousands before falling. Some barely wander. The rule never says which.