The Mandelbrot set is based on iterations of the following complex polynomial:
Where z and c are a complex numbers. Starting with the value z = 0 + 0i, we apply the iteration repeatedly until a maximum number of iterations is reached or the value of z exceeds a specified maximum. For a given value of c, if the iteration remains stable (z doesn't increase above the maximum) the point is inside the Mandelbrot set and we color the position corresponding to c black. Otherwise, we color the point based on the number of iterations it took for the value to exceed the maximum.
In the following figure, the image of the Mandelbrot set is applied as a texture to a cube: