According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." Presented here is a list of fractals, ordered by increasing Hausdorff dimension, to illustrate what it means for a fractal to have a low or a high dimension.
Deterministic fractals
Random and natural fractals
See also
Fractal dimension Hausdorff dimension Scale invariance
Notes and references
Further reading Mandelbrot, Benoît (1982). The Fractal Geometry of Nature. W.H. Freeman. ISBN 0-7167-1186-9. Peitgen, Heinz-Otto (1988). Saupe, Dietmar (ed.). The Science of Fractal Images. Springer Verlag. ISBN 0-387-96608-0. Barnsley, Michael F. (1 January 1993). Fractals Everywhere. Morgan Kaufmann. ISBN 0-12-079061-0. Sapoval, Bernard; Mandelbrot, Benoît B. (2001). Universalités et fractales: jeux d'enfant ou délits d'initié?. Flammarion-Champs. ISBN 2-08-081466-4.
External links The fractals on Mathworld Other fractals on Paul Bourke's website Soler's Gallery Fractals on mathcurve.com 1000fractales.free.fr - Project gathering fractals created with various software Fractals unleashed IFStile - software that computes the dimension of the boundary of self-affine tiles