Abstract: A new technique of topological multi-scale analysis is
introduced. By performing a clustering recursively to build a
hierarchy, and analyzing the co-scale and intra-scale similarities, an
Iterated Function System can be extracted from any data set. The study
of fractals shows that this method is efficient to extract
self-similarities, and can find elegant solutions the inverse problem of
building fractals. The theoretical aspects and practical
implementations are discussed, together with examples of analyses of
simple fractals.