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...moving the middle third of a [[line segment]] on each iteration. It is a [[fractal]] with a [[Hausdorff dimension]] of [[Natural logarithm|ln]](2)/ln(3), whic

In [[mathematics]], in the study of [[fractal]]s, a '''Hutchinson operator''' is a collection of functions on an underlyi

...= Chaos theory, Asimov's foundations and robots, and Herbert's Dune : the fractal aesthetic of epic science fiction

...of mathematical concepts, featuring [[curve]]s, [[symmetry]], [[chaos]], [[fractal]]s, [[Moiré pattern]]s, [[kinematics]] and [[simulation]]s

...n Ness proposed the name '''fractional noise''' (sometimes since called '''fractal noise''') to emphasise that the exponent of the spectrum could take non-int

3. Jacob Gagnon, "Columns of the Ocean", "Fractal of the Sea", "Sphere-Duo", 3-D Digital Artwork for an Art Exhibition in Lon

*Fractal dimension

...t. However, it would not make sense to give the [[Sierpiński triangle]] [[fractal]] a dimension of 2, since it does not fully occupy the 2-dimensional realm. ...nature are not strictly classical smooth bodies, but best approximated as fractal sets, i.e. subsets of '''R'''^''N'' whose Hausdorff dimension is

| title = Fractal dimension in human cortical surface: multiple regression analysis with cort

...are, who suggest that there may be self-similarity that is not necessaruly fractal.

...has a complicated boundary, which defines a [[fractal]] called a [[Newton fractal]].

...for earthquake sizes, or scaling relationships such as those observed in [[fractal]]s, [[1/f noise]] and [[allometric law|allometric scaling laws]] in living

this allows to apply a function some "fractal number'' of times. For summation and multiplication, loginal is easy to exp

...nt may be self-similar in a way that can be exploited statistically; see [[Fractal]] for a specific type of self-similarity.

...[Hausdorff measure]] which is a refinement of the Lebesgue measure to some fractal sets.

...<math>L</math> and <math>L^*</math>. Function is quasi-periodic; the same fractal structure reproduces again and again at the translation of argument with qu ...z)>1~,~ 1<|\Im(z)|<2</math>. In these regions, the function slogr show the fractal behavior.

Aside from his musical interests, Ligeti expressed fondness for the [[fractal geometry]] of [[Benoît Mandelbrot]], and the writings of [[Lewis Carroll]]

118. Mandelbrot, B.B. 1982. The Fractal Nature of Geometry. W.H. Freedman and Company. 139. Palmer, M.W. 1992. The coexistence of species in fractal landscapes. American Naturalist, 139, p. 375-397.

...cialist, the first thing you need to know (and you look for) is: what is a fractal? Same for [[pseudoscience]] in my view. ...entitled e.g. "Introduction" (this is at least what I'm trying to do in [[Fractal]]). Proportions may depend heavily on the topic. For example, in the presen

## [[Fractal]]