NP problems are tractable in the space of cellular automata in the hyperbolic plane
Theoretical Computer Science
A new kind of science
A universal cellular automaton in the hyperbolic plane
Theoretical Computer Science
The domino problem of the hyperbolic plane is undecidable
Theoretical Computer Science
A Universal Cellular Automaton on the Ternary Heptagrid
Electronic Notes in Theoretical Computer Science (ENTCS)
Surprising Areas in the Quest for Small Universal Devices
Electronic Notes in Theoretical Computer Science (ENTCS)
Small Semi-Weakly Universal Turing Machines
Fundamenta Informaticae - Machines, Computations and Universality, Part I
Cellular automata and combinatoric tilings in hyperbolic spaces: a survey
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
Towards the frontier between decidability and undecidability for hyperbolic cellular automata
RP'10 Proceedings of the 4th international conference on Reachability problems
An algorithmic approach to tilings of hyperbolic spaces: 10 years later
CMC'10 Proceedings of the 11th international conference on Membrane computing
A new weakly universal cellular automaton in the 3D hyperbolic space with two states
RP'11 Proceedings of the 5th international conference on Reachability problems
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
Ten years of weakly universal cellular automata in the hyperbolic plane
ICCCI'12 Proceedings of the 4th international conference on Computational Collective Intelligence: technologies and applications - Volume Part I
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In this paper, we construct a new weakly universal cellular automaton on the ternary heptagrid. This significantly improves the previous result, obtained by the same author in the same grid with six states. This time, the number of states is four. This is the best result up to date for cellular automata in the hyperbolic plane, with true planar motions.