4. Julia sets and the Mandelbrot set

‘Julia sets and Mandelbrot sets’ explores these frequently visualised fractal species. Complex numbers are imaginary numbers which involve the square root of -1. Plotting squared complex numbers on a plane will give a line which travels to either infinity or the origin. The boundary between these two types of behaviour is known as the Julia set. The simplest conformation of a Julia set is a circle, but other more complicated structures exist. The level of connectedness of a Julia set is determined by its position inside or outside the Mandelbrot set. The position of a Julia set in relation to the Mandelbrot set also determines its fractal dimension.