NumberDB$^\beta$
Advanced search
Tags
Tables
Add numbers
Help
No match in database
Hausdorff dimension of some fractals
edit on github
·
preview edits
·
show history
·
long url
·
dynamical systems
Numbers
$F$
$\text{dim}_H(F)$
Apollonian gasket:
1.305688
Dragon curve's boundary:
1.523627086202492106277683935954216627284936383401193478138690909457921662895884106892664227464713942
Feigenbaum attractor:
3.5699456718709449018420051513864989367638369115148323781079755299213628875001367775263210342163
Koch curve:
1.261859507142914874199054228685521708599171280263760855741309887677370402761829610122345377098903491
Sierpiński triangle:
1.584962500721156181453738943947816508759814407692481060455752654541098227794358562522280474918088242
Definition
This table lists the Hausdorff dimension $\text{dim}_H(F)$
[2]
of certain fractals $F$.
Parameters
$F$
— fractal
Comments
(1)
Readers are welcome to add more interesting examples.
References
[1]
Curtis T. McMullen, "Hausdorff dimension and conformal dynamics III: Computation of dimension", 1997.
http://abel.math.harvard.edu/~ctm/papers/home/text/papers/dimIII/dimIII.pdf},
Links
[2]
Wikipedia: Hausdorff dimension
[3]
Wikipedia: List of fractals by Hausdorff dimension
Data properties
Entries are of type: real number
