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ID: INPUT{id.yaml} Title: Hausdorff dimension of some fractals Definition: > This table lists the Hausdorff dimension $\text{dim}_H(F)$ CITE{Wiki} of certain fractals $F$. Parameters: F: title: fractal type: Symbolic Comments: comment-help-needed: > Readers are welcome to add more interesting examples. Formulas: Programs: References: McMullen: bib: > Curtis T. McMullen, "Hausdorff dimension and conformal dynamics III: Computation of dimension", 1997. url: > http://abel.math.harvard.edu/~ctm/papers/home/text/papers/dimIII/dimIII.pdf}, Links: Wiki: title: "Wikipedia: Hausdorff dimension" url: https://en.wikipedia.org/wiki/Hausdorff_dimension WikiList: title: "Wikipedia: List of fractals by Hausdorff dimension" url: https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension Similar tables: Keywords: - chaos theory Tags: - dynamical systems Data properties: type: R Display properties: number-header: $\text{dim}_H(F)$ Numbers: apollonian-gasket: param-latex: Apollonian gasket number: 1.305688 comment: > Value is only a heuristic estimate CITE{McMullen}, HREF{https://en.wikipedia.org/wiki/Apollonian_gasket} dragon-curve-boundary: param-latex: Dragon curve's boundary number: 1.523627086202492106277683935954216627284936383401193478138690909457921662895884106892664227464713942 comment: > Exact value: $2\log_2\lambda$, where $\lambda$ is the real solution of $\lambda^3-\lambda^2-2 = 0$. HREF{https://en.wikipedia.org/wiki/Dragon_curve} feigenbaum-attractor: param-latex: Feigenbaum attractor number: 3.5699456718709449018420051513864989367638369115148323781079755299213628875001367775263210342163 comment: > HREF{https://oeis.org/A098587}, HREF{https://en.wikipedia.org/wiki/Logistic_map} koch-curve: param-latex: Koch curve number: 1.261859507142914874199054228685521708599171280263760855741309887677370402761829610122345377098903491 comment: > Exact value: $\log_3(4)$, HREF{https://en.wikipedia.org/wiki/Koch_curve} sierpinski-triangle: param-latex: Sierpiński triangle number: 1.584962500721156181453738943947816508759814407692481060455752654541098227794358562522280474918088242 comment: > Exact value: $\log_2(3)$, HREF{https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle}

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