The complex plane is originally mapped from the bottom left (-2-2i) to top right (2+2i) and subdivided into elements in a matrix, C.
The function Zk+1 = Zk2 + Cij is applied to each value in the plane starting with Zk=1 = 0 for k = 1:n. Zn at k either converges or diverges past 2. In a separate matrix, I, with the same size as matrix C, the iterations until convergence are counted and stored (Iij). A color-map is applied to the matrix from Zmin, 0, to Zmax, n. For each video frame, the view of the plane shrinks exponentially from ± 2 ± 2i towards ± 0 ± 0i and the number of iterations until divergence is counted, I = n being convergence.
(Generated with MATLAB)