Julia fractal. Computer-generated spiral fractal derived from the Julia Set. The Julia Set is a class of shapes plotted from complex number coordinates. Each point is assigned a colour depending upon its behaviour under a series of simple, but repeated, mathematical operations or mappings. The Julia Set was invented and studied during World War I by the French mathematicians Gaston Julia and Pierre Fatou. The better-known Mandelbrot Set arose as a result of attempts by the mathematician Benoit Mandelbrot to rationalize the massive variety of forms of the Julia Set.