• Corpus ID: 202661056

# The Variant-Rule Another Logically Universal Rule

@article{Soto2020TheVA,
title={The Variant-Rule Another Logically Universal Rule},
author={Jos{\'e} Manuel G{\'o}mez Soto and Andrew Wuensche},
journal={J. Cell. Autom.},
year={2020},
volume={15},
pages={147-173}
}
• Published 18 September 2019
• Physics
• J. Cell. Autom.
The Variant-rule derives from the Precursor-rule by interchanging two classes of its 28 isotropic mappings. Although this small mutation conserves most glider types and stable blocks, glider-gun engines are changed, as are most large scale pattern behaviors, illustrating both the robustness and fragility of evolution. We demonstrate these newly discovered structures and dynamics, and utilising two different glider types, build the logical gates required for universality in the logical sence.
1 Citations
Isotropic Cellular Automata: the DDLab iso-rule Paradigm
• Computer Science
J. Cell. Autom.
• 2021
A novel paradigm, the iso-rule, a concise expression for isotropic CA by the output table for each isotropics neighborhood group is presented, allowing an efficient method of navigating and exploring iso- rule-space.

## References

SHOWING 1-10 OF 22 REFERENCES
X-Rule's Precursor is Also Logically Universal
• Computer Science
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.
The X-Rule: Universal Computation in a Non-Isotropic Life-Like Cellular Automaton
• Physics
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,
Glider Dynamics in 3-Value Hexagonal Cellular Automata: The Beehive Rule
It is shown how analogous complex rules can be found, firstly by mutating a complex rule to produce a family of related complex rules, and secondly by classifying rule-space by inputentropy variance.
Growth and Decay in Life-Like Cellular Automata
• D. Eppstein
• Computer Science
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.
Post's Functional Completeness Theorem
• Philosophy, 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.
The two-valued iterative systems of mathematical logic
*Frontmatter, pg. i*CONTENTS, pg. vi*INTRODUCTION, pg. 1*Part I. PRELIMINARIES, pg. 10*PART II. DERIVATION OP CLOSED SYSTEMS, pg. 43*PART III. CO-ORDINATION AND APPLICATION, pg. 96*BIBLIOGRAPHY, pg.
Winning Ways for Your Mathematical Plays
• Art
• 1982
In the quarter of a century since three mathematicians and game theorists collaborated to create Winning Ways for Your Mathematical Plays, the book has become the definitive work on the subject of
Mathematical games: the fantastic combinations of john conway's new solitaire game "life
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.