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new article taking some material from Hausdorff dimension - Open Set Condition is studied in its own right and is now tied to other measures and conditions. |
Adding short description: "Condition for self-similar fractals" (Shortdesc helper) |
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{{Short description|Condition for self-similar fractals}}
In [[fractal geometry]], the '''open set condition''' ('''OSC''') is a commonly imposed condition on self-similar fractals. In some sense, the condition imposes restrictions on the overlap in a fractal construction.<ref>{{cite journal |last1=Bandt |first1=Christoph |last2= Viet Hung |first2= Nguyen |last3 = Rao |first3 = Hui | title=On the Open Set Condition for Self-Similar Fractals | journal=Proceedings of the American Mathematical Society | volume=134 | year=2006 | pages=1369–74 | issue=5 | url=http://www.jstor.org/stable/4097989| url-access=limited}}</ref> Specifically, given an [[iterated function system]] of [[contraction mapping| contractive mappings]] ψ<sub>''i''</sub>, the open set condition requires that there exists a nonempty, open set S satisfying two conditions:
#<math> \bigcup_{i=1}^m\psi_i (V) \subseteq V, </math>
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