Fractal Tree

Branching trees are the classic introduction to self-similarity: the same simple rule — walk a segment, then fork into two smaller copies of yourself — repeated at ever-smaller scales produces the unmistakable silhouette of a tree, a fern, or a river delta. The branch angle and the length decay between generations are enough to move the shape from a sparse antenna to a dense canopy.

Here the rule is carried by pets. One walker starts at the bottom center heading straight up, painting each patch it crosses with its branch depth. When its segment runs out it hands position, heading, and a scaled-down length budget to two children turned left and right by the branch-angle slider, then dies. Children with no depth budget or sub-patch segments never spawn, so the population swells along the canopy and collapses to zero when the last leaf tip finishes — leaving a finished tree colored from brown trunk to green leaves.