Several protein properties embody symmetry of self-similarity. Symmetries observed in crystalline structures can be described with translations, rotations, and reflections; symmetry of self-similarity, on the other hand, manifests itself through scale invariance. Self-similar forms are composed of subunits that resemble the overall object. Many natural structures in nature - the branching trees, crinkly coastlines, mountain surfaces - demonstrate self-similarity. If the Hausdorff dimension of a self-similar object is found to be greater than its topological dimension, the object is called a fractal-object. What makes this information relevant in the field of Bioinformatics is the fact the several works of last three decades have established that proteins are fractal-objects.
Protein surfaces are fractal. Mass [4, 5], hydrophobicity and polarizability distribution of protein interior are fractal. Many other protein properties (main-chain connectivity profile, potential energy profile, dipole moment distribution etc. [6, and references therein]) - are fractal too. However, a computational resource that calculates fractal properties of protein interior and exterior - is (apparently) impossible to find.
ProtFract, the free online server, calculates the fractal dimension of many of the protein properties enlisted above.
 Mandelbrot, BB (1982). The Fractal Geometry of Nature, W.H. Freeman and Company.
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 Enright MB, Leitner DM (2005) Mass fractal dimension and the compactness of proteins. Phys Rev E 71:011912
 Banerji A, Ghosh I (2009) Revisiting the myths of protein interior: studying proteins with mass-fractal hydrophobicity-fractal and polarizability-fractal dimensions. PLoS One 4(10):e7361
 Banerji A, Ghosh I (2011) Fractal symmetry of protein interior: what have we learned? Cell. Mol. Life Sci. DOI 10.1007/s00018-011-0722-6