What are Julia sets?
It has been previously said that when you iterate z(n+1)=z2(n)+c where z is the variable and c a constant, interesting fractal images can be obtained. The image will be drawn in the plane defined by the real and imaginary part of z. It is necessary to compute the iteration of this polynomial for each value of the complex plane. Computers are the perfect tools to do such stupidly repetitive jobs. Doing so, it can be observed that, for some initial values of z, the iteration gives a result which escapes towards infinity, while for others the result remains into more or less narrow limits (it never diverges). If c=0, the iterated polynomial never diverges for all the points within a circle of center 0,0 and of radius 1: nothing very interesting (nor fractal), except that this will help to explain some points of vocabulary. Strictly speaking, the Julia set is the circle itself, and the points contained in the surface limited by the circle are the Fatou set. The limit circle plus the inner
