Fractals deal with special sets that exhibit complicated patterns in every scale. Fractal sets usually have a Hausdorff dimension different from its topological dimension. Examples include Julia sets, the Sierpinski triangle, the Cantor set. Fractals naturally appear in dynamical system, such as ...

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What are the fractal parameters?

There are so many fractal which are not uniquely characterize by some fractal parameters like Fractal dimension, Succolarity, Lacunarity, Morphological entropy. Can you suggest some fractal parameters ...
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Shortest Paths on fractals

How can one find shortest paths between 2 specified points on fractals, or (since I'm pretty sure this is quite complicated) make useful generalizations about them? Since the above question is broad, ...
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1answer
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Is there an nontrivial function whose 'period paralellograms' are Gosper Islands?

The Gosper island tiles the plane, so I'm curious if a nontrivial elliptic? function exists which would have a 'period gosper-island' instead of a period parallelogram. In this case, I'm using ...
11
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3answers
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Is there an intrinsic definition of fractal (i.e. not embedded in euclidean space)?

Long ago, manifolds were embedded subsets of euclidean space defined by polynomials. Later, using the gluing of open sets, people realized they could define manifolds intrinsically. And in certain ...
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2answers
375 views

Systematization of deterministic and stochastic integrals

With this question I try to build up a systematization of different kinds of integrals. The following table differentiates between deterministic and stochastic integrals, the summation processes ...
4
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4answers
622 views

Determining a lower bound on the Hausdorff dimension of a set

Does anyone know of a good method for finding a lower bound of the Hausdorff dimension of a set $G$? The only method I could find is to find an $\alpha$-Hölder function $f \colon G \to H$ then ...
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Self-similar matrices? [closed]

Does anyone know anything about self-similar (infinite) matrices, with more or less fractal(-like) structure and admitting meaningful matrix-algebra operations?