# Questions tagged [fractals]

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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### Who proved that the Mandelbrot set's Julia sets are locally connected?

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### Numerically Evaluate the limit of the solution of a functional equation

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### What is the geometric or dynamic meaning of a global attractor with an infinite fractal dimension?

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### Wavefront set of characteristic function of rough set

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### The Koch snow flake, Holder exponents of conformal mappings

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### Does fractallity depend on the Riemannian metric?

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### Hausdorff dimension and von Neumann dimension

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### Hausdorff outer measure is finite if $\sum_{j = 1}^m |f(x_i)-f(x_{i-1})|^s \le c$ [closed]

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### Bounds on the Hausdorff dimension for an IFS satisfying the OSC

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### Covering lemmas in Hochman's ''On self-similar sets with overlaps and inverse theorems for entropy''

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### Fourier coeffients of Cantor measure

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### Pointless characterization relating between a fractal and its code space

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### Evaluating this limit in Fourier analysis

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### Box dimension as the critical value of the fractal content

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### Formal justification of the Chaos game in the Sierpinski triangle

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### Box dimension of the graph of an increasing function

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### Failure of Falconer distance problem in one dimension

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### Quasilinear elliptic problem on fractal domain

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### Set with modified lower box counting dimension strictly less than Hausdorff dimension

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### Has this self-similar sequence the ratio $(\sqrt2+1)^2$?

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### Why do weak and L metric topology for measures coincide?

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### Is the Mandelbrot set weakly self-similar?

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### Lipschitz property of holonomies fails when stable leaves $W^s(x)$ inside the leaves $W^{ss}(x)$

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### continuity entropy with respect gibbs measures

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### Is each Peano continuum a topological fractal?

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### How many two-dimensional space filling Hilbert-like curves are there?

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### Limit of homeomorphisms from square to square

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### Is the function Point -> Julia set “injective”?

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### Laplacians and Renormalization

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### Running most of the time in a connected set

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### Intersections of Sierpinski carpets with lines

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### Examples of probability measures with `fake' decay

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### Hausdorff dimension of the graph of an increasing function

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### On the convergence problem of box counting for the Rössler attractor

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### algebraic structure of fractals

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### density of fractal measures

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### Is it known that MLC is sufficient to prove the density of hyperbolic conjecture of rational maps (or not)

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### Fractal covering of a plane with complex-base numeral systems - is periodicity necessary?

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### Cardinality of fractal without CH? [closed]

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### Causal fermion systems fromm fractal geometry

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### Diffeomorphisms preserving “nice” smooth functions

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### Equi-Hölder embeddings of compact metric spaces of finite packing dimension into $\ell_2$

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### Rössler attractor, Convergence of box counting to estimate the fractal dimension

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### Fractal homological algebra

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### Hausdorff dimension of $X\times X$

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### Complexity of the Mandelbrot set on rationals

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### Relationship between the Hurst exponent and the alpha parameter

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### Literature on the total variation of fractal graphs/fractal Brownian motion?

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### ♢ ⧫ ⬠: the fourth kind of Penrose tiling?

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