Quadtree Flow

Nested rooms hold quarter-circle currents. Changing scales and orientations turn a recursive grid into a rhythmic architectural engraving.

Quadtree Flow: Nested rooms hold quarter-circle currents. Changing scales and orientations turn a recursive grid into a rhythmic architectural engraving.Quadtree Flow: Nested rooms hold quarter-circle currents. Changing scales and orientations turn a recursive grid into a rhythmic architectural engraving.

About this pattern

Raphael Finkel & Jon Bentley, quadtrees, 1974

Quadtree Flow, vector field, drawn by GART: Nested rooms hold quarter-circle currents. Changing scales and orientations turn a recursive grid into a rhythmic architectural engraving.
Quadtree Flow · CC BY 4.0

A quadtree recursively splits squares into four smaller rooms. Concentric currents originate at seeded corners and are clipped to each room. A gentle harmonic ripple bends the arcs as the animation loops.

Behind the mathematics

Raphael Finkelborn 1951

The quadtree, 1974

American computer scientist who with Jon Bentley introduced the quadtree in 1974: a square split into four, and each quarter split again wherever it is crowded.

Jon Bentleyborn 1953

The quadtree, 1974

American computer scientist and author of Programming Pearls, who with Raphael Finkel introduced the quadtree in 1974.