Julia Filigree

Twin curls, branching islands and finely engraved edges emerge from a single complex number. Nested contours trace their changing silhouette.

Julia Filigree: Twin curls, branching islands and finely engraved edges emerge from a single complex number. Nested contours trace their changing silhouette.Julia Filigree: Twin curls, branching islands and finely engraved edges emerge from a single complex number. Nested contours trace their changing silhouette.

About this pattern

Gaston Julia and Pierre Fatou · quadratic complex dynamics

Julia Filigree, complex dynamics, drawn by GART: Twin curls, branching islands and finely engraved edges emerge from a single complex number. Nested contours trace their changing silhouette.
Julia Filigree · CC BY 4.0

Contours of the smooth escape-time field for z → z² + c. The two shape controls set the real and imaginary parts of c. Motion follows a small closed path around the chosen parameter; some settings cross between connected and disconnected Julia sets.

Behind the mathematics

Gaston Julia1893–1978

Complex iteration

Mathematician whose work on iterated rational functions helped establish complex dynamics and the fractal sets now named after him.

Pierre Fatou1878–1929

Complex dynamics

Mathematician who independently developed foundational results on iteration in the complex plane, alongside the work of Gaston Julia.