Cellular Automata in Hyperbolic Spaces

Margenstern, Maurice

doi:10.1007/978-3-319-33924-5_14

Cited by 15 publications

(4 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This general scenario is described in detail in [4,7]. Here, we simply give the guidelines in order to introduce the changes which are specific to this implementation.…”

Section: The Scenario Of Our Simulationmentioning

confidence: 99%

“…We present the rules according to the same order as we presented the implementation in Subsection 3.0. 3 The rules are rotation invariant. This means that if we perform a circular permutation on the neighbours of a cell, this does not change the new state.…”

Section: The Rulesmentioning

confidence: 99%

“…It also introduce new constructions which significantly improve the scenario used in the previous papers. The reader is referred to [3,4,7] for an introduction to hyperbolic geometry turned to the implementation of cellular automata in this context. A short introduction can also be found in [2].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Weakly Universal Cellular Automaton on the Heptagrid with Three States

Margenstern

2014

2014 Second International Symposium on Computing and Networking

Self Cite

View full text Add to dashboard Cite

show abstract

“…This general scenario is described in detail in [4,7]. Here, we simply give the guidelines in order to introduce the changes which are specific to this implementation.…”

Section: The Scenario Of Our Simulationmentioning

confidence: 99%

Section: The Rulesmentioning

confidence: 99%

See 1 more Smart Citation

A Weakly Universal Cellular Automaton on the Heptagrid with Three States

Margenstern

2014

2014 Second International Symposium on Computing and Networking

Self Cite

View full text Add to dashboard Cite

show abstract

“…We give a tile assembly system that is capable of simulating a very wide class of tile systems, including itself. Our notion of simulation is inspired by, but somewhat stronger than, intrinsic universality in cellular automata [2,7,[14][15][16]. In our construction a simulated tile assembly system is encoded in a seed assembly of the simulating system.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic Universality in Self-Assembly

Doty¹,

Lutz²,

Patitz³

et al. 2015

Encyclopedia of Algorithms

View full text Add to dashboard Cite

We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is capable of simulating a very wide class of tile systems, including itself. Specifically, we give a tile set that simulates the assembly of any tile assembly system in a class of systems that we call locally consistent: each tile binds with exactly the strength needed to stay attached, and that there are no glue mismatches between tiles in any produced assembly.Our construction is reminiscent of the studies of intrinsic universality of cellular automata by Ollinger and others, in the sense that our simulation of a tile system T by a tile system U represents each tile in an assembly produced by T by a c × c block of tiles in U , where c is a constant depending on T but not on the size of the assembly T produces (which may in fact be infinite). Also, our construction improves on earlier simulations of tile assembly systems by other tile assembly systems (in particular, those of Soloveichik and Winfree, and of Demaine et al.) in that we simulate the actual process of self-assembly, not just the end result, as in Soloveichik and Winfree's construction, and we do not discriminate against infinite structures. Both previous results simulate only temperature 1 systems, whereas our construction simulates tile assembly systems operating at temperature 2.

show abstract

A Spherical XOR Gate Implemented in the Game of Life

Ventrella¹

2010

Game of Life Cellular Automata

View full text Add to dashboard Cite

Cellular Automata in Hyperbolic Spaces

Cited by 15 publications

References 24 publications

A Weakly Universal Cellular Automaton on the Heptagrid with Three States

A Weakly Universal Cellular Automaton on the Heptagrid with Three States

Intrinsic Universality in Self-Assembly

A Spherical XOR Gate Implemented in the Game of Life

Contact Info

Product

Resources

About