if the cause And Effects radius of a sphere is doubled, its volume scales by eight, which is two (the ratio of the new to the old radius) to the power of three (the dimension that the sphere resides in). "Self-similarity and the geometric requirements for frequency independence in Antennae". This also leads to understanding a third feature, that fractals as mathematical equations are "nowhere differentiable ". Self-reference and paradox in two and three dimensions (P.

A fractal set is one for which the fractal (Hausdorff-Besicovitch) dimension strictly exceeds the topological dimension a b c d e Gordon, Nigel (2000). "Edges of Saturn's Rings are Fractal". 3 6 8, an infinite fractal curve can be conceived of as winding through space differently from an ordinary line - although it is still 1-dimensional its fractal dimension indicates that it also resembles a surface. Retrieved February 4, 2012.

A b c d e f g h Edgar, Gerald (2004). Chaos and elliptic curves (S.D. N identical parts, each part will be scaled down by the ratio r 1 n (e.g. Archived from the original on February 4, 2012. An investigation of fractals generated by z1/z -n c (K.W. Chaos and fractals: a the Wanderer (anglo - saxon themes and ideas) computer graphical journey : ten year compilation of advanced research. "Boosting Multi-Feature Visual Texture Classifiers for the Authentification of Jackson Pollock's Drip Paintings". Natural phenomena with fractal features edit Further information: Patterns in nature Approximate fractals found in nature display self-similarity over extended, but finite, scale ranges. 3 4 5 Fractals are not limited to geometric patterns, but can also describe processes in time. Visualizing the dynamics of the Rayleigh"ent iteration (C.A.