Planetary Disk

CD7e, this picture is an example of fractal art and design, and was made using Möbius transformations of the unit disk.

This is an image for a fine art print.

The functions used are Möbius automorphisms of the unit disk (also known as the Poincaré disk in non-Euclidean geometry) which are of the form M(z) = exp(iθ) × (z − a) / (az − 1), where exp(iθ) rotates anti-clockwise by an angle θ and the constant complex number “a” lies inside the unit disk. The order in which these functions are applied is restricted by the use of a directed graph in a similar way to that described here. See also the pictures K Disk, Planetary Disk 2 and Lunar Disk which were made using similar methods.