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  1. mathematica-journal.com

    A morphism preserves the resulting angle if for any word , ; moreover, a morphism inverts the resulting angle if for any word , . The dense Fibonacci word is strongly linked to the Fibonacci word fractal because can generate a whole family of curves whose limit is the Fibonacci word fractal .
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  3. content.wolfram.com

    A morphism is a map h:S* Ø D* such that, for all x, yœS*, hHx yL=hHxLhHyL. There is a special class of words with many remarkable properties, the so-called Sturmian words. These words admit several equivalent definitions (see, e.g. [5], [8]). Definition 2 Let w œ Sw. Let PHw, nL, the complexity function of w, be the map that counts, for
  4. sciencedirect.com

    The word f can also be associated with a family of polyominoes which tile the plane by translation and are called Fibonacci snowflakes [4], [7].By polyomino we mean a finite union of unit lattice squares in the square lattice Z × Z whose boundary is a non-crossing closed path (see [18] for more on tilings and [9] for related problems). A path in the square lattice is a polygonal path made of ...
    Author:José L. Ramírez, Gustavo N. Rubiano, Rodrigo De CastroPublished:2014
  5. Fig.1:fractal curves generated by simple binary morphisms 1 De nitions 1.1 Morphisms and mirror morphisms In this paper, we will call "elementary morphisms", binary morphisms ˙such that, for any let-ter a, j˙(a)j<4. This includes the well known Fibonacci morphism and the Thue-Morse morphism. Let a morphism ˙de ned, for any letter a, by ˙(a ...
  6. academia.edu

    The Fibonaccci morphism, the most elementary non-trivial binary morphism, generates the infinite Fibonacci word Fractal through a simple drawing rule. We study, here, families of fractal curves associated with other simple binary morphisms. Among them the Sierpinsky triangle appears.
  7. A Generalization of the Fibonacci Word Fractal and the Fibonacci Snowflake Jos´e L. Ram´ırez ∗ †1, Gustavo N ... {0,1} is the morphism defined by σ(0) = 01 and σ(1) = 0. This morphism is called Fibonacci morphism. The name Fibonacci given to f is due to the fact that f is the limit sequence of the infinite sequence (fn)n=0 of ...
  8. semanticscholar.org

    The Fibonacci Word Fractal is a self-similar fractal curve based on the Fibonacci word through a simple and interesting drawing rule. This fractal reveals three types of patterns and a great number of self-similarities. We show a strong link with the Fibonacci numbers, prove several properties and conjecture others, we calculate its Hausdorff Dimension. Among various modes of construction, we ...
  9. Iterated function system, closed graph theorem, hyperbolic, fractal, morphism, conjugacy. A. Mundey 326 is a closed subspace of X Y. An alternate formulation—which is perhaps more relevant to our context—is that fWX!Yis continuous if and only if Gr.f/is itself a compact Hausdorff space. Applying a set-theoretic lens to functions—where f is
  10. match.stanford.edu

    rauzy_fractal_plot (n = None, exchange = False, eig = None, translate = None, prec = 53, colormap = 'hsv', opacity = None, plot_origin = None, plot_basis = False, point_size = None) #. Return a plot of the Rauzy fractal associated with a substitution. The substitution does not have to be irreducible. The usual definition of a Rauzy fractal requires that its dominant eigenvalue is a Pisot ...
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