ar X iv : m at h / 03 12 31 4 v 1 [ m at h . PR ] 1 6 D ec 2 00 3 V - variable fractals and superfractals

Deterministic and random fractals, within the framework of Iterated Function Systems, have been used to model and study a wide range of phenomena across many areas of science and technology. However, for many applications deterministic fractals are locally too similar near distinct points while standard random fractals have too little local correlation. Random fractals are also slow and difficult to compute. These two major problems restricting further applications are solved here by the introduction of V -variable fractals and superfractals. AMS classification scheme numbers: 28A80, 60D05, 28A78 PACS numbers: 05.45.Df, 02.50.-r § To whom correspondence should be addressed. V -variable fractals and superfractals 2