Hausdorff dimension in graph directed constructions

@article{Mauldin1988HausdorffDI,
  title={Hausdorff dimension in graph directed constructions},
  author={R. Daniel Mauldin and S. C. Williams},
  journal={Transactions of the American Mathematical Society},
  year={1988},
  volume={309},
  pages={811-829}
}
We introduce the notion of geometric constructions in Rm governed by a directed graph G and by similarity ratios which are labelled with the edges of this graph. For each such construction, we calculate a number a which is the Hausdorff dimension of the object constructed from a realization of the construction. The measure of the object with respect to fl"* is always positive and <r-finite. Whether the ^""-measure of the object is finite depends on the order structure of the strongly connected… 
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