An IteratedFunctionSystem (IFS) {X:f1,f2,...,fN} on a TopologicalSpace X is given by a finite set of continuous maps fi:X->X (i=1,2,...,N). If X is a CompleteMetricSpace and the maps fi are all contracting, then the IFS is said to be hyperbolic.
A hyperbolic IFS induces a ContractingMap on the CompleteMetricSpace HX of all non-empty compact subsets of X with a unique fixed point called the attractor of the IFS.
For graphical applications, X is usually the plane R
2, fi are contracting affine transformations, and the attractor is a ["Fractal"].