Julia Sets

A Julia set is usually written where is an entire function (a function that is complex-differentiable at every point in the complex plane), usually a polynomial. Then is the boundary of the set of points that diverge to infinity upon iteration of the formula.

A common family of polynomials used is . And as can be inferred from the formula, gives results closely related to the mandelbrot set.

In fact the Mandelbrot set can be defined as the set of all values of c such that the Julia Set for the previous formula is connected. Also for small enough neighbourhoods of c, the Julia set appears identical to the Mandelbrot set as can be seen from the image below