Deterministic rendering of self-affine fractals

Most literature on fractals defined by self-affine systems (SASs) assume that Monte Carlo methods will be used for rendering the attractor. These are so inefficient as to be unsuitable for use in decompressing fractally coded images. The authors introduce a deterministic algorithm, minimum point plotting (MPP), which is optimal in the number of pixels plotted on a graphics screen without requiring an auxiliary frame store. Its efficiency in rendering simple test fractals on a sequential computer is compared to the Monte Carlo method. A generalization of the algorithm, called the Generation Game (G² ), is readily shown to be a variant of the previously described image transformation algorithm (ITA), using different initial conditions. MPP is superior to ITA for sequential machines, and G² is at worst equivalent for parallel applications. A further generalization of G² is the constant mass algorithm (CMA), which can be used to render colour and grey scale images, and comparisons of CMA with Monte Carlo methods are also given