Undecidable Problems in Fractal Geometry

Undecidable Problems in Fractal Geometry Simant Dube
Abstract
	In this paper, a relationship between the classical theory of computation and fractal geometry is established. Iterated function systems (IFS) are used as the tools to define fractals. It is shown that two questions about IFS are undecidable - to test if the attractor of a given IFS and a given line segment intersect and to test if a given IFS is totally disconnected. These results show that fractals are complex objects from a computational point of view.

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