Deterministic Abelian Sandpile Models and Patterns

  • Guglielmo Paoletti

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Guglielmo Paoletti
    Pages 1-8
  3. Guglielmo Paoletti
    Pages 9-35
  4. Guglielmo Paoletti
    Pages 37-56
  5. Guglielmo Paoletti
    Pages 57-78
  6. Guglielmo Paoletti
    Pages 79-123
  7. Guglielmo Paoletti
    Pages 125-127
  8. Back Matter
    Pages 129-163

About this book

Introduction

The model investigated in this work, a particular cellular automaton with stochastic evolution, was introduced as the simplest case of self-organized-criticality, that is, a dynamical system which shows algebraic long-range correlations without any tuning of parameters.  
The author derives exact results which are potentially also interesting outside the area of critical phenomena. Exact means also site-by-site and not only ensemble average or coarse graining. Very complex and amazingly beautiful periodic patterns are often generated by the dynamics involved, especially in deterministic protocols in which the sand is added at chosen sites.
For example, the author studies the appearance of allometric structures, that is, patterns which grow in the same way in their whole body, and not only near their boundaries, as commonly occurs. The local conservation laws which govern the evolution of these patterns are also presented.
This work has already attracted interest, not only in non-equilibrium statistical mechanics, but also in mathematics, both in probability and in combinatorics. There are also interesting connections with number theory. Lastly, it also poses new questions about an old subject. As such, it will be of interest to computer practitioners, demonstrating the simplicity with which charming patterns can be obtained, as well as to researchers working in many other areas.

Keywords

Abelian Sandpile Model Algebraic Structure Cellular Automata Computer Art Pattern Formation Plane Tesselation Sierpinski Fractal Structure

Authors and affiliations

  • Guglielmo Paoletti
    • 1
  1. 1.LIP6 - (Université Paris 6) UPMCPARIS CEDEX 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-01204-9
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-01203-2
  • Online ISBN 978-3-319-01204-9
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
  • About this book
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