Abstract : As Barnsley, Demko and others have shown, one effective method for producing fractal shapes (in any number of dimensions) is with Iterated Function Systems (IFSs), using the 'Chaos Game' algorithm (or some deterministic algorithm). This approach has been used for producing naturalistic shapes, finding interpolants to given data and fractal approximations of given functions, and even for visualizing arbitrary discrete sequences. Indeed, any contractive IFS will give an attractor (usually of fractal dimension); thus it is possible to generate IFSs at random to explore the graphical possibilities, as is done in some educational software. Similarly, because the attractor depends continuously on the parameters in the IFS, a small data sets from any source could be encoded as IFSs for visualization
['David Canright']
Estimating the spatial extent of attractors of iterated function systems