## Julia Set Fractal (2D)Written by Paul BourkeJune 2001 See also: Julia set of sin(z) Python generator: julia_set.py by Tim Meehan.
The Julia set is named after the French mathematician Gaston Julia who
investigated their properties circa 1915 and culminated in his famous
paper in 1918. While the Julia set is now associated with a simpler
polynomial, Julia was interested in the iterative properties of
a more general expression, namely z
The Julia set is now associated with those points z = x + iy
on the complex plane for which the series
z
Computing a Julia set by computer is straightforward, at least by
the brute force method presented here. The image is created by
mapping each pixel to a rectangular region of the complex plane.
Each pixel then represents the starting point for the series,
z The well known Mandelbrot set forms a kind of index into the Julia set. A Julia set is either connected or disconnected, values of c chosen from within the Mandelbrot set are connected while those from the outside of the Mandelbrot set are disconnected. The disconnected sets are often called "dust", they consist of individual points no matter what resolution they are viewed at. Another property of Julia sets relates to the various domains of c. If c is real then the Julia set is mirrored about the real axis. Other values of c with a non-zero imaginary component have 180 degree rotational symmetry. Example of sin-Mandelbrot by Tim Meehan |