# The Ameyalli-Rule: Logical Universality in a 2D Cellular Automaton

@inproceedings{Soto2021TheAL, title={The Ameyalli-Rule: Logical Universality in a 2D Cellular Automaton}, author={Jos{\'e} Manuel G{\'o}mez Soto and A. Wuensche}, year={2021} }

We present a new spontaneously emergent glider-gun in a 2D Cellular Automaton and build the logical gates NOT, AND and OR required for logical universality. The Ameyalli-rule is not based on survival/birth logic but depends on 102 isotropic neighborhood groups making an iso-rule, which can drive an interactive input-frequency histogram for visualising iso-group activity and dependent functions for filtering and mutation. Neutral inputs relative to logical gates are identified which provide an… Expand

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SHOWING 1-10 OF 22 REFERENCES

The X-Rule: Universal Computation in a Non-Isotropic Life-Like Cellular Automaton

- Mathematics, Computer Science
- J. Cell. Autom.
- 2015

We present a new Life-like cellular automaton (CA) capable of logic universality -- the X-rule. The CA is 2D, binary, with a Moore neighborhood and $\lambda$ parameter similar to the game-of-Life,… Expand

X-Rule's Precursor is Also Logically Universal

- Mathematics, Physics
- J. Cell. Autom.
- 2017

It is shown that glider-guns, originally absent, have recently been discovered, as well as other complex structures from the Game-of-Life lexicon, and the logical gates required for universality in the logical sense are built. Expand

Computing in Spiral Rule Reaction-Diffusion Hexagonal Cellular Automaton

- Mathematics, Computer Science
- Complex Syst.
- 2006

It is demonstrated that the rich spatio-temporaldynamics of interacting traveling localizations and their generators can be used to implement computation, namely manipulation with signals, binary logical operations, multiple-value operations, and ﬁnite-state ma-chines. Expand

Growth and Decay in Life-Like Cellular Automata

- Computer Science, Physics
- Game of Life Cellular Automata
- 2010

This chapter discusses the mathematical systems of cellular automata, the fascinating patterns that have been discovered and engineered in Conway’s Game of Life, and of the possible existence of other cellular automaton rules with equally complex behavior to that of Life. Expand

Classifying cellular automata automatically: Finding gliders, filtering, and relating space-time patterns, attractor basins, and the Z parameter

- Computer Science
- Complex.
- 1999

The method allows the automatic “filtering” of CA space-time patterns to show up gliders and related emergent configurations more clearly and approximate correlations with global measures on convergence in attractor basins are approximate. Expand

Statistical mechanics of cellular automata

- Physics
- 1983

Cellular automata are used as simple mathematical models to investigate self-organization in statistical mechanics. A detailed analysis is given of ''elementary'' cellular automata consisting of a… Expand

A new kind of science

- Computer Science
- 2002

A New Kind of Science, written and published by Stephen Wolfram, is the outcome of the studies he conducted systematically upon cellular automata, a class of computer model which may be visualized as a set of memory locations, each containing one bit. Expand

Turing Universality of the Game of Life

- Mathematics, Computer Science
- Collision-Based Computing
- 2002

This chapter describes a Turing machine built from patterns in the Conway’s Game of Life cellular automaton. It outlines the architecture of the construction, the structure of its parts and explains… Expand

Mathematical games: the fantastic combinations of john conway's new solitaire game "life

- Computer Science
- 1970

In 1967 he discovered a new group-some call it "Conway's constellation"--that includes all but two of the then known sporadic groups, a breakthrough that has had exciting repercussions in both group theory and number theory. Expand

Post's Functional Completeness Theorem

- Computer Science, Mathematics
- Notre Dame J. Formal Log.
- 1990

A new proof is provided, in a style accessible to modern logicians and teachers of elementary logic, of Post's Functional Complete- ness Theorem, which states that the set of connectives {V,Λ,~} is functionally complete: any (2- valued) truth table can be constructed from them. Expand