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- 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. Specifically, given an iterated function system of contractive mappings ψi, the open set condition requires that there exists a nonempty, open set V satisfying two conditions: 1.
* 2.
* Each is pairwise disjoint. Introduced in 1946 by P.A.P Moran, the open set condition is used to compute the dimensions of certain self-similar fractals, notably the Sierpinski Gasket. It is also used to simplify computation of the packing measure. An equivalent statement of the open set condition is to require that the s-dimensional Hausdorff measure of the set is greater than zero. (en)
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- 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. Specifically, given an iterated function system of contractive mappings ψi, the open set condition requires that there exists a nonempty, open set V satisfying two conditions: 1.
* 2.
* Each is pairwise disjoint. An equivalent statement of the open set condition is to require that the s-dimensional Hausdorff measure of the set is greater than zero. (en)
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