''fractal sets''
...or set and the non-differentiable curve obtained by von Koch. Typically, a fractal is self-similar in a deterministic or a stochastic way. D. Sullivan introdu
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is the fractal dimension of $X$. It has also been called the capacity, the Mandelbrot dime
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// recursive procedure, draws the fractal within the rectangle [x0,x1]×[y0,y1]
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has a [[Fractal dimension|fractal dimension]] and may be termed a fractal (cf. [[Fractals|Fractals]]). D. Sullivan has given an exhaustive classifica
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...s properties of signals, functions and images, such as discontinuities and fractal structures. They have been termed a mathematical microscope. In addition, w
...D> <TD valign="top"> M. Holschneider, "On the wavelet transformation of fractal objects" ''J. Stat. Phys.'' , '''50''' (1988) pp. 963–993</TD></TR><TR
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real ratio=horn_end.z/(-horn_start.y); // fractal levels ratio
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...rs). In a non-linear dynamical system, the domain of attraction can have a fractal boundary. Furthermore, certain particular solutions need not be included in
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...iński carpet, or "tapis de Sierpiński" — belongs to the toolkit of every fractal geometer. It adorns many articles and books on the subject and is frequentl
...s common value, $\log(3)/\log(2)\approx 1.58$, is often referred to as the fractal dimension of $G$. Here, $2$ is the reciprocal of the contraction ratio and
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...atics, such as potential theory ([[#References|[a3]]]), harmonic analysis, fractal geometry ([[#References|[a6]]]), functional analysis, the theory of nonline
.../td></tr><tr><td valign="top">[a6]</td> <td valign="top"> K. Falconer, "Fractal geometry" , Wiley (1990)</td></tr><tr><td valign="top">[a7]</td> <td valig
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...butions in the physical and engineering sciences" , '''1: Distribution and fractal calculus, integral transforms and wavelets''' , Birkhäuser (1997) pp. 19
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...[[#References|[a1]]] for a general approach; [[#References|[a3]]] for the fractal aspect; [[#References|[a11]]] for the special case of small convex bodies o
...><TR><TD valign="top">[a3]</TD> <TD valign="top"> B.B. Mandelbrot, "The fractal geometry of nature" , Freeman (1982)</TD></TR><TR><TD valign="top">[a4]</T
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...lows), it allows one to study geometric and number-theoretic problems like fractal dimensions, Diophantine approximations and recurrence.
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|valign="top"|{{Ref|Fa}}|| K. J. Falconer, "The geometry of fractal sets". Cambridge Tracts in Mathematics, 85. Cambridge University Press, Ca
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.../TD> <TD valign="top"> J.S. Geronimo, D.P. Hardin, P.R. Massopust, "Fractal functions and wavelet expansions based on several scaling functions" ''J.
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...period-doubling, intermittency, quasi-periodicity, frequency locking, and fractal torus [[#References|[a1]]], [[#References|[a2]]], [[#References|[a3]]], [[#
dimensional fractal surface with a strong transverse packing of the sheets of the attractor. Th
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|valign="top"|{{Ref|Fa}}|| K.J. Falconer, "The geometry of fractal sets" , Cambridge Univ. Press (1985) {{MR|0867284}} {{ZBL|0587.28004}}
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...</td></tr><tr><td valign="top">[a3]</td> <td valign="top"> L. Nottale, "Fractal space-time and microphysics" , World Sci. (1993)</td></tr><tr><td valign="
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....I. Grigorchuk, "On the spectrum of Hecke type operators related to some fractal groups" (to appear)</td></tr><tr><td valign="top">[a3]</td> <td valign="to
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..."Attractors for the Bénard problem: existence and physical bounds on their fractal dimension" ''Nonlinear Anal. Theory Methods Appl.'' , '''11''' (1987) pp
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of a strange attractor is a fractal number related to the [[Hausdorff dimension|Hausdorff dimension]]. J.L. Kap
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