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Mathematics

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Proof of Wolfram's Axiom for Boolean Algebra

Steps in an automated proof of the correctness of Wolfram’s Axiom

General Topology EntityStore

Entity store representing definitions and theorems of point-set topology

Persistent Structures in the Code 357 Cellular Automaton

A collection of the persistent structures in the k=3, r=1 totalistic code 357 cellular automaton

Cunningham Number Factorizations

Numbers of the form b^n-1 and b^n+1 are factored for small prime bases b={2,3,5,7}

Persistent Structures in the Code 20 Cellular Automaton

The known persistent structures in the k=2, r=2 totalistic code 20 cellular automaton

Block Simulation Network of Elementary Cellular Automata

This shows how one elementary cellular automaton rule can emulate other rules if its states consist only of particular blocks. Only the 88 inequivalent elementary rules are included.

The Silver Game of Life Lexicon

Famous Game of Life configurations collected by Stephen A. Silver

Repetition Periods for Elementary Cellular Automata

A collection of rules and their repetition periods as a function of size

NKS Cover Image

The cellular automaton evolution shown on the cover of Stephen Wolfram’s “A New Kind of Science”

Famous 2D Cellular Automata

Well-known 2D cellular automata are listed, such as Conway’s Game of Life

Three-Color Cellular Automaton Rules that Double Their Input

A list of rules for k=3 cellular automata that eventually double a block of gray input cells

A Million Bits of the Center Column of the Rule 30 Cellular Automaton

The center column of the rule 30 center automaton over a million steps of evolution

Published Papers Per Year on Cellular Automata

A time series of the number of papers published on cellular automata by year from 1974 through 2015

Persistent Structures in the Code 1329 Cellular Automaton

A collection of the persistent structures in the k=3, r=1 totalistic code 1329 cellular automaton