Julia fractal. Computer-generated dragon fractal derived from the Julia Set. Fractals are patterns that are formed by repeated subdivisions using some simple mathematical process. The large scale features of the pattern are repeated forever on an ever decreasing scale. The Julia Set is a class of shapes plotted from complex number coordinates. It was invented and studied during World War I by the French mathematicians Gaston Julia and Pierre Fatou. Fractals are used to model natural forms, such as snowflakes, and to study chaos theory.