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...olume=399 | year=1985 | pages=243–275 | issue=1817 }}</ref> The [[Iterated function|iteration]] of the operator converges to a unique [[attractor]], which is t ...math>\{f_i : X \to X\ |\ 1\leq i \leq N\}</math> be an [[iterated function system]], or a [[Set (mathematics)|set]] of [[contraction mapping|contractions]] f ...

{{short description|Characterises an iterated function system whose attractor is close to a given set}} ...hematics]], the '''collage theorem''' characterises an [[iterated function system]] whose [[attractor]] is close, relative to the [[Hausdorff metric]], to a ...

{{Short description|Condition for fractals in math}} ...989| url-access=limited}}</ref> Specifically, given an [[iterated function system]] of [[contraction mapping| contractive mappings]] <math>\psi_1, \ldots, \p ...

[[File:Fibonacci curve L-system.png|thumb|L-system representation<ref>Ramírez, José L.; Rubiano, Gustavo N. (2014). "[https:// ...|eprint=1601.04786|title=Hausdorff Dimension of Generalized Fibonacci Word Fractals|last1=Hoffman|first1=Tyler|last2=Steinhurst|first2=Benjamin|class=math.MG|y ...

...where''.<ref name=Fractals>[https://books.google.com/books?id=oh7NoePgmOIC Fractals Everywhere], Boston, MA: Academic Press, 1993, {{ISBN|0-12-079062-9}}</ref> ...a second course was developed, called ''Fractal Measure Theory''.<ref name=Fractals /> Barnsley's work has been a source of inspiration to [[Graphics|graphic a ...

...6-04-21 |url=http://chicagogeekguy.com/exploring-abacaba/ |title=Exploring Fractals with ABACABA |work=Chicago Geek Guy |access-date=January 22, 2021 |language In order to [[iterated function system|generate]] the next sequence, first take the previous pattern, add the next ...

...oles. These poles of (the [[analytic continuation]] of) the geometric zeta function <math> \zeta_{\mathcal{L}} (s) </math> are then called '''complex dimension ==The geometric zeta function== ...

...e chaotic behavior of the [[iterated function system|iterated]] [[logistic function]], which exhibits the [[logistic map|Feigenbaum bifurcation]]. A paperback ...heory]]. He has contributed to the [[periodic solution]]s of [[Hamiltonian system]]s and particularly to the theory of [[Mark Krein|Kreĭn indices]] for linea ...

...l function]] of [[complex frequency]]; distributed forms are an irrational function. Another difference is that [[cascade connection|cascade-connected]] length === Fractals === ...

...fty</math>, called "infinity", is used to denote an unbounded [[limit of a function|limit]].<ref>{{harvnb|Taylor|1955|loc=p. 63}}</ref> The notation <math>x \r ...a limit, infinity can be also used as a value in the extended real number system. Points labeled <math>+\infty</math> and <math>-\infty</math> can be added ...