Wolfram Research

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Mathematics

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General Topology EntityStore

Entity store representing definitions and theorems of point-set topology

Primitive Polynomials

Primitive polynomials for Galois field generation up to GF(2^1200), GF(3^660), GF(5^430), and GF(7^358)

Polyform Database

Data for some of the most popular polyforms

The Silver Game of Life Lexicon

Famous Game of Life configurations collected by Stephen A. Silver

Block Simulation Network of Elementary Cellular Automata

A network showing how one elementary cellular automaton can emulate another if its states contain only particular blocks

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

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}

Canonical Polyhedra

The canonical forms of polyhedra with 4 to 9 faces

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

Fields Medal Winners

Winners of the Fields Medal, 1936-2014

Theorem Network from Euclid's Elements

A graph of the theorems from Euclid's Elements and their logical dependencies

Minimal Inequivalent Square Tilings

A dataset of images and constraints for the minimal inequivalent square tilings, along with the allowed tiles that generate the tiling

Persistent Structures in Rule 110

The known families of persistent structures in the Rule 110 elementary cellular automaton

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

Proof of Wolfram's Axiom for Boolean Algebra

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

Solutions to Examples of Post’s Correspondence Problem

A dataset of instances and solutions (if they exist) for Post’s correspondence problem

Cover Image from A New Kind of Science

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

Linear Codes

Linear codes provide an optimal way for transmitting blocks of data over noisy channels

Mrs. Perkins's Quilts

Divide a square into a minimum number of integer-sided squares with a relatively prime subset

Repetition Periods for Elementary Cellular Automata

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

Australian Rules Football - 2018 Final Team Rankings

This dataset consists of the final team standing within the Australian Rules Football league for the 2018 season

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

Gliders in 2D Cellular Automata

A 2D cellular automaton glider compilation by David Eppstein