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Results tagged with fractals
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user 36812
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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Iterated function system on the plane
Let $r_1, r_2, r_3$ be three nonnegative real numbers with $r_1^2+r_2^2+r_3^2 <1$. Can you find three similitudes $f_1,f_2,f_3$ on $\mathbb{R}^2$ with similarity ratios $r_1,r_2,r_3$ resp. and a nonem …
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Reference for the iterated function system of the Koch snowflake
For the boundary of the Koch snowflake, you can look at:
THE SNOWFLAKE CURVE AS AN ATTRACTOR OF AN ITERATED FUNCTION SYSTEM
Demir, B. Ozdemir, Y. Saltan, M.
Communications of the Korean Mathematical …
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