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Results tagged with fractals
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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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sequences with a fractal dimension
This is inspired by the self-similarity of the celebrated Golay-Rudin-Shapiro sequence, more exactly, of its alternating partial sums. (This latter one is oeis 020990). The pictures show the 550 first …
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Angles and proportions occurring in L-system fractals
This is about properties of certain fractals defined by Lindenmayer systems, a.k.a. L-systems. … Unlike “classical” fractals like Julia sets or the Mandelbrot set (the name “set” says it all), these fractals are not defined by calculus, but rather geometically, by iterating certain drawing procedures …
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Has this self-similar sequence the ratio $(\sqrt2+1)^2$?
This is inspired by a math.SE question, where an infinite sequence of pairwise distinct natural numbers $a_1=1, a_2, a_3, ...$ has been defined as follows:
$a_n$ is the smallest number such that $s_n: …
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Is there an L-system for aperiodic tilings of the plane with the "hat" monotile?
(In a precise sense, we are of course not talking about the fractals themselves, rather about the iterations approximating them. …
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