Exploding Bubbles and Disks
Julia sets of the function (a)ros z. Black poster with 9 images (non-symmetrical), circular formations; orange, black, blue, white.
The top three images are Julia sets* of the function a cos z. Notice the small replicas within the images of the larger shapes, a property of fractals called self-similarity. The other five pictures, showing an image sometimes called a Siegel disk, are Julia sets of the function (a + bi) sin z. The complex numbers whose orbits do not tend to infinity compose the filled Julia set, named for the French mathematician Gaston Julia who studied these sets in the 1920's.