Journal ArticleDOI
Geometry of Binomial Coefficients
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This article is published in American Mathematical Monthly.The article was published on 1984-11-01. It has received 82 citations till now. The article focuses on the topics: Central binomial coefficient & Binomial distribution.read more
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Proceedings ArticleDOI
Algorithmic Self-Assembly of DNA
TL;DR: In this paper, the authors focus on molecular self-assembly, giving examples of engineered DNA tiles that crystallize into two-dimensional sheets, one-dimensional tubes and ribbons, and information-guided patterns such as a Sierpinski triangle and a binary counter.
Journal ArticleDOI
Random sequence generation by cellular automata
TL;DR: A 1-dimensional cellular automaton which generates random sequences is discussed, and an efficient random sequence generator based on them is suggested.
Book
Mathematics by experiment : plausible reasoning in the 21st century
TL;DR: Peters and Peters as discussed by the authors discuss the notion of normality as a stubborn question in the 21st century in Mathematics by Experiment: Plausible Reasoning in the Modern World, 2nd edition, 2008.
Journal ArticleDOI
Mellin transforms and asymptotics: digital sums
TL;DR: It is shown that such periodicity phenomena can be analyzed rather systematically using classical tools from analytic number theory, namely the Mellin—Perron formulae, which yields naturally the Fourier series involved in the expansions of a variety of digital sums related to number representation systems.
Book
The Tower of Hanoi – Myths and Maths
TL;DR: This is the first comprehensive monograph on the mathematical theory of the solitaire game The Tower of Hanoi which was invented in the 19th century by the French number theorist douard Lucas and contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs.
References
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Book
The Fractal Geometry of Nature
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Journal ArticleDOI
Statistical mechanics of cellular automata
TL;DR: Analysis is given of ''elementary'' cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to p definite rules involving the values of its nearest neighbors.
Universality and complexity in cellular automata
TL;DR: In this article, it was shown that all one-dimensional cellular automata fall into four distinct universality classes: limit points, limit cycles, chaotic attractors, and limit cycles.
Journal ArticleDOI
Universality and complexity in cellular automata
TL;DR: Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes, and one class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable.
Journal ArticleDOI
Algebraic properties of cellular automata
TL;DR: Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata, and the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities.