The Existence Of Attractors Based On The IFS

Iterated function systems have been at the heart of fractal geometry almost from its origins. The existence of attractors based on the IFS are at the core of iterated function systems(IFS). The focus is on geometrically simple systems with finitely many maps, such as affine, projective and..Mobius IFS. We disscussed the existence of attractors from three aspects. Particular topics include the role of contractive functions on the existence of an attractor(of an IFS), chaos game orbits for approximating an attractor, The study of the existence of an attractor depending on the joint spectral radius. At the last, it introduce the fibres and addresses of attractors.This article conclude that contractivity is integral to the existence of an attractor for affine, M?bius, and many projective IFS, and provide their necessary and sufficient condition; in a proper complete metric space, chaos game orbit can yield an attractor when being a random orbit in particular cases, it can yield an attractor with probability one; in a complete metric space, chaos game orbit can yield an attractor when it is of a disjunctive sequence; the joint spectral radius plaies an important role for having an attractor, especially for the compact affine IFS.