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Results tagged with fractals
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user 3621
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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Fractal dimension of scaling limits of discrete structures
Let $S$ be the set of positive integers whose base-three expansion contains only the digits 0 and 2. The discrete set $S$ in a sense has (negative) fractal dimension $(\log 1/2)/(\log 3)$, since if yo …
- 19.7k
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Spirals in Apollonian circle-packings
Given mutually (externally) tangent circles $C_1,C_2,C_3$,
let $C_n$ be the unique circle externally tangent to
$C_{n-1}$, $C_{n-2}$, and $C_{n-3}$ for $n \geq 4$.
Let $P_{\infty}$ be the point toward …
- 19.7k
6
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Isotropy of Apollonian disk-packing
Is there any sense in which the "epsilon-tail" of an Apollonian disk-packing (by which I mean the union of the disks of radius less than epsilon) exhibits more and more statistical isotropy as epsilon …
- 19.7k