Journal ArticleDOI
Folding polynomials and their dynamics
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In this article, the equilateral triangle, the right isoceles triangle, and the 30-60-90 triangle are special in that they can be folded into replicas of themselves.Abstract:
The equilateral triangle, the right isoceles triangle, and the 30-60-90 triangle are special in that they can be folded into replicas of themselves. We describe polynomial mappings which are equiva...read more
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Self-similar sets. V. Integer matrices and fractal tilings of ⁿ
TL;DR: In this article, it was shown that similarity tilings can be constructed from m-rep tiles by iterated composition of self-similar tiles and just-touching fractals.
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Chaos and Fractals: A Computer Graphical Journey
TL;DR: Fractals and their applications in computer graphics and computer art are discussed in this article, where the author provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules.
BookDOI
Geometric Modeling and Algebraic Geometry
Bert Jttler,Ragni Piene +1 more
TL;DR: In this paper, the authors present, in 12 chapters written by leading experts, recent results which rely on the interaction of Geometric Modeling and Algebraic Geometry, though closely related, are traditionally represented by two almost disjoint scientific communities.
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Dynamics of real polynomials on the plane and triple point phase transition
TL;DR: In this article, the authors considered the Generalized Chebyshev polynomials on the plane and showed the existence of three equilibrium probabilities for the pressure associated with a distinguished value of an external parameter.
Posted Content
Dessins d'Enfants and Hypersurfaces with Many $A_j$-Singularities
TL;DR: In this article, it was shown that the existence of nodal surfaces of degree n in polygonal plane trees with approximately 3j+2/over 6j(j+1) d^3 singularities of type n, 2\le j\le d-1.
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Yang-Lee zeros of the Potts model
TL;DR: In this paper, the Yang-Lee zeros of the three-component ferromagnetic Potts model in one dimension in the complex plane of an applied field are determined, and the Gibbs phase rule is generalized to apply to coexisting phases.
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