Diamond-square algorithm

This algorithm can be used to generate realistic-looking landscapes, and different implementations are used in computer graphics software such as Terragen.

[4] In this variant the weights on the neighboring points are obtained by solving a small linear system motivated by estimation theory, rather than being fixed.

The Lewis algorithm also allows the synthesis of non-fractal heightmaps such as rolling hills or ocean waves.

Similar results can be efficiently obtained with Fourier synthesis,[5] although the possibility of adaptive refinement is lost.

The diamond-square algorithm and its refinements are reviewed in Peitgen and Saupe's book "The Science of Fractal Images".