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Results tagged with fractals
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user 11332
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 iterations in the complex plane, or as strange attractors to continuous dynamical systems, (see Lorentz attractor).
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notable inductive proofs relating to fractals
Spectral decimation is an inductive process where the eigenvalues of a natural Laplacian on "nice" fractals is computed inductively. … The local definition of "nice" for this answer is either post-critically finite fractals or finitely ramified with a doubly transitive symmetry group fractals. …
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How to define a differential form on a fractal?
Alexander Teplyaev has been working on exactly this question this is a paper in which he and Michael Hinz show that the Navier-Stokes equation on a Sierpinski gasket is sensibly defined and that it h …
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Sierpinski Triangle and the Chaos Game
Because the iterated function system that defines the Sierpinski gasket is a contraction mapping in the metric space of non-empty compact subsets of $\mathbb{R}^{2}$ with the Sierpinski gasket as its …
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Fractal dimension of 1D set, what if logN vs log(e) is a polygonal chain?
The canonical reference for this material (at least with the people I hang out with) is Ken Falconer's Fractal Geometry Mathematical Foundations and Applications.
For most sets that are fully self-s …
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What are integration on fractal?
That being said, I still wish he had actually exhibited one of these fractals. …
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Fractal questions: Weierstraß-Mandelbrot
A quick, partial answer to your second question about the definition of fractals. …
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