A growth model based on the arithmetic \(Z\)-game

DOI10.1016/j.chaos.2016.05.016zbMath1372.37027arXiv1511.04315OpenAlexW2213549537MaRDI QIDQ2410401

Cristian Cobeli, Alexandru Zaharescu, Mihai Prunescu

Publication date: 18 October 2017

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.04315

zbMATH Keywords

cellular automataself-similar processesgrowth modeldiscrete solitonsrecurrent sequencessandpiles\(Z\)-solitonsabsolute differencesdynamic lattice systemsgros sequenceruler sequence

Mathematics Subject Classification ID

Cellular automata (computational aspects) (68Q80) Dynamical aspects of cellular automata (37B15)

Cites Work

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• Scaling limits for internal aggregation models with multiple sources
• The Thue-Morse-Pascal double sequence and similar structures
• \(\mathbb F_p\)-affine recurrent \(n\)-dimensional sequences over \(\mathbb F_q\) are \(p\)-automatic
• Pattern formation in growing sandpiles with multiple sources or sinks
• On the identity of the sandpile group
• Patterns formed by addition of grains to only one site of an Abelian sandpile
• Internal DLA and the Stefan problem.
• Limiting shapes for deterministic centrally seeded growth models
• The Tower of Hanoi – Myths and Maths
• A game with divisors and absolute differences of exponents
• GAPS BETWEEN FRACTIONAL PARTS, AND ADDITIVE COMBINATORICS
• Limiting shapes for a non-abelian sandpile growth model and related cellular automata
• Iterated Absolute Values of Differences of Consecutive Primes
• A sandpile model for proportionate growth
• Proportionate growth in patterns formed in the rotor-router model
• Zaphod Beeblebrox's Brian and the Fifty-ninth Row of Pascal's Triangle
• Generalization of a theorem of Steinhaus
• Discrete analog computing with rotor-routers
• Gaps problems and frequencies of patches in cut and project sets
• RECURRENT TWO-DIMENSIONAL SEQUENCES GENERATED BY HOMOMORPHISMS OF FINITE ABELIAN p-GROUPS WITH PERIODIC INITIAL CONDITIONS
• Spherical asymptotics for the rotor-router model in $\mathbb{Z}^d$
• Explicit characterization of the identity configuration in an Abelian sandpile model
• Unsolved problems in number theory

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