# A strongly universal cellular automaton in the dodecagrid with five states

@article{Margenstern2021ASU, title={A strongly universal cellular automaton in the dodecagrid with five states}, author={Maurice Margenstern}, journal={ArXiv}, year={2021}, volume={abs/2104.01561} }

In this paper, we prove that there is a strongly universal cellular automaton in the dodecagrid, the tesselation {5, 3, 4} of the hyperbolic 3D space, with five states which is rotation invariant. This improves a previous paper of the author where the automaton required ten states.

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SHOWING 1-10 OF 12 REFERENCES

A strongly universal cellular automaton on the heptagrid with seven states

- Computer Science
- J. Cell. Autom.
- 2021

In this paper, we prove that there is a strongly universal cellular automaton on the heptagrid with seven states which is rotation invariant. This improves a previous paper of the author where the… Expand

A Weakly Universal Cellular Automaton in the Heptagrid of the Hyperbolic Plane

- Computer Science, Mathematics
- Complex Syst.
- 2018

A weakly universal cellular automaton in the heptagrid is constructed which is not rotation invariant but which is truly planar, and under these conditions, cannot be improved for the tessellations. Expand

A Weakly Universal Cellular Automaton in the Pentagrid with Five States

- Physics, Computer Science
- Computing with New Resources
- 2014

A cellular automaton on the pentagrid which is planar, weakly universal and which have five states only is constructed, which much improves the best result which was with nine states. Expand

A Weakly Universal Cellular Automaton on the Heptagrid with Three States

- Computer Science, Physics
- 2014 Second International Symposium on Computing and Networking
- 2014

This paper improves previous results giving the construction of a weakly universal cellular automaton on the heptagrid with three states only using the railway circuit model, to which several important changes are given. Expand

A universal cellular automaton in the hyperbolic plane

- Computer Science
- Theor. Comput. Sci.
- 2003

The paper gives the construction of a universal CA with 22 states in the regular rectangular pentagonal grid of the hyperbolic plane. The CA implements a railway circuit which simulates a register… Expand

A New Universal Cellular Automaton on the Pentagrid

- Computer Science, Mathematics
- Parallel Process. Lett.
- 2008

This paper significantly improves a result of the first author, and lowers the number of states for a weakly universal cellular automaton down to 9. Expand

An Upper Bound on the Number of States for a Strongly Universal Hyperbolic Cellular Automaton on the Pentagrid

- Computer Science, Mathematics
- JAC
- 2010

It is proved that there is a hyperbolic cellular automaton which is rotation invariant and whose halting problem is undecidable and which has 9~states. Expand

Small Universal Cellular Automata in Hyperbolic Spaces: A Collection of Jewels

- Mathematics
- 2013

Why hyperbolic geometry?.- Cellular automata and the railway model.- Inthepentagrid.- In the heptagrid.- In the tilings.- In the dodecagrid.- Strongly universal hyperbolic cellular automata.- The… Expand

Computation Finite And Infinite Machines

- Computer Science
- 2016

There are very few individuals today who doubt that the computer and its relatives are developing rapidly in capability and complexity, and that these machines are destined to play important (though not as yet fully understood) roles in society's future. Expand

A weakly universal cellular automaton in the hyperbolic 3D space with three states

- Mathematics, Computer Science
- 2010

In this paper, we significantly improve a previous result by the same author showing the existence of a weakly universal cellular automaton with five states living in the hyperbolic 3D-space. Here,… Expand