A new weakly universal cellular automaton in the 3D hyperbolic space with two states
Maurice Margenstern
TL;DR
This paper introduces a weakly universal, rotation-invariant cellular automaton with only two states in 3D hyperbolic space, utilizing a novel railway circuit implementation in the dodecagrid for true 3D computation.
Contribution
It presents the first weakly universal cellular automaton in 3D hyperbolic space with minimal states and a new railway circuit design for 3D cellular automata.
Findings
Constructed a 2-state weakly universal cellular automaton in 3D hyperbolic space
Implemented a novel railway circuit in the dodecagrid
Achieved rotation invariance in the automaton design
Abstract
In this paper, we show a construction of a weakly universal cellular automaton in the 3D hyperbolic space with two states. The cellular automaton is rotation invariant and, moreover, based on a new implementation of a railway circuit in the dodecagrid,the construction is a truly 3D-one.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCellular Automata and Applications · DNA and Biological Computing · Algorithms and Data Compression