The Open Set Condition and Neighbor Maps in Fractal Geometry
Neighbor maps are a new development in fractal geometry that can be used to determine if an iterated function system (IFS) obeys the open set condition (OSC). Neighbor maps also describe the topology of the fractal attractor. In this thesis, the de nition of the set of proper neighbor maps is generalised to any IFS comprising contractive similitudes. It is proven, an IFS of similitudes obeys the OSC if and only if the identity map is not in the closure of the set of proper neighbor maps. The...[Show more]
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