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Results tagged with fractals
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user 500793
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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The graph of the fractal sets
Could you please provide me with the graph of the fractal set produced by the given following IFS?
Consider an IFS $\{\phi_i, i=1,...,9\}$ on ${X}=[0, \infty) \times[0,1]$ defined as follows
$$
\phi_i …
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Sets of Hausdorff measures zero
Let $H^g$ be the Hausdorff measure with respect to gauge function $g$.
I need to construct an example of a set E for which:
$H^g(E)=0$ for $g(r)=r^s$, $s>0$
and
$0<H^g(E)<+\infty$ for $g(r)=2^{-(log(1 …
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Fractal sets and dimensions
Can we construct two sets $E$ and $F$ meeting the following criteria
$\dim_H(E) = \dim_H(F) = \dim_H(E ∩ F)$
$\dim_P(E), \dim_P(F)$, and $\dim_P(E ∩ F)$ are distinct?
Here $\dim_H$ denotes the Ha …
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