Wolfram code is a widely used[1] numbering system for one-dimensional cellular automaton rules, introduced by Stephen Wolfram in a 1983 paper[2] and popularized in his book A New Kind of Science.[3]
The code is based on the observation that a table specifying the new state of each cell in the automaton, as a function of the states in its neighborhood, may be interpreted as a k-digit number in the S-ary positional number system, where S is the number of states that each cell in the automaton may have, k = S2n + 1 is the number of neighborhood configurations, and n is the radius of the neighborhood. Thus, the Wolfram code for a particular rule is a number in the range from 0 to SS2n + 1 − 1, converted from S-ary to decimal notation. It may be calculated as follows:
List all the S2n + 1 possible state configurations of the neighbourhood of a given cell.
Interpreting each configuration as a number as described above, sort them in descending numerical order.
For each configuration, list the state which the given cell will have, according to this rule, on the next iteration.
Interpret the resulting list of states again as an S-ary number, and convert this number to decimal. The resulting decimal number is the Wolfram code.
The Wolfram code does not specify the size (nor shape) of the neighbourhood, nor the number of states — these are assumed to be known from context. When used on their own without such context, the codes are often assumed to refer to the class of elementary cellular automata, two-state one-dimensional cellular automata with a (contiguous) three-cell neighbourhood, which Wolfram extensively investigates in his book. Notable rules in this class include rule 30, rule 110, and rule 184. Rule 90 is also interesting because it creates Pascal's triangle modulo 2. A code of this type suffixed by an R, such as "Rule 37R", indicates a second-order cellular automaton with the same neighborhood structure.
While in a strict sense every Wolfram code in the valid range defines a different rule, some of these rules are isomorphic and usually considered equivalent. For example, rule 110 above is isomorphic with the rules 124, 137 and 193, which can be obtained from the original by left-right reflection and by renumbering the states. By convention, each such isomorphism class is represented by the rule with the lowest code number in it. A disadvantage of the Wolfram notation, and the use of decimal notation in particular, is that it makes such isomorphisms harder to see than some alternative notations. Despite this, it has become the de facto standard way of referring to one-dimensional cellular automata.
^Ceccherini-Silberstein, Tullio; Coornaert, Michel (2010). Cellular Automata and Groups. Springer. p. 28. doi:10.1007/978-3-642-14034-1. ISBN 978-3-642-14034-1. Retrieved 22 October 2022.
^Wolfram, Stephen (July 1983). "Statistical Mechanics of Cellular Automata". Reviews of Modern Physics. 55 (3): 601–644. Bibcode:1983RvMP...55..601W. doi:10.1103/RevModPhys.55.601.
^Wolfram, Stephen (May 14, 2002). A New Kind of Science. Wolfram Media, Inc. ISBN 1-57955-008-8.
Wolframcode is a widely used numbering system for one-dimensional cellular automaton rules, introduced by Stephen Wolfram in a 1983 paper and popularized...
Stephen Wolfram (/ˈwʊlfrəm/ WUUL-frəm; born 29 August 1959) is a British-American computer scientist, physicist, and businessman. He is known for his...
the kernel and the front end. The kernel interprets expressions (Wolfram Language code) and returns result expressions, which can then be displayed by...
binary number, this corresponds to the decimal value 110. This is the Wolframcode naming scheme. In 2004, Matthew Cook published a proof that Rule 110...
The Wolfram Language (/ˈwʊlfrəm/ WUUL-frəm) is a proprietary, general very high-level multi-paradigm programming language developed by Wolfram Research...
smallest Wolframcode which describes its rule set (as described below). The mirror image, complement, and mirror complement of Rule 30 have Wolframcodes 86...
Martin, Odlyzko & Wolfram (1984) call it "the simplest non-trivial cellular automaton", and it is described extensively in Stephen Wolfram's 2002 book A New...
features of the automaton's state with particles. The name of Rule 184 is a Wolframcode that defines the evolution of its states. The earliest research on Rule...
automata are generally referred to by their Wolframcode, a standard naming convention invented by Wolfram that gives each rule a number from 0 to 255...
Tungsten (also called wolfram) is a chemical element; it has symbol W and atomic number 74. Tungsten is a rare metal found naturally on Earth almost exclusively...
SequenceL Speakeasy Wolfram Mathematica (Wolfram language) X10 ZPL Aspect-oriented programming enables developers to add new functionality to code, known as "advice"...
223 possible elementary cellular automata. Stephen Wolfram proposed a scheme, known as the Wolframcode, to assign each rule a number from 0 to 255 which...
Festival of Code, the culmination of Young Rewired State 2012. Wolfram is also part of Flooved advisory board. On 10 June 2020, Wolfram released his...
The Code of Hammurabi is a Babylonian legal text composed during 1755–1750 BC. It is the longest, best-organized, and best-preserved legal text from the...
original on 2020-07-28. Retrieved 2020-07-28. "Gray Code" demonstration by Michael Schreiber, Wolfram Demonstrations Project (with Mathematica implementation)...
The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-sized) interactive programmes called Demonstrations, which...
pp. 300–301. Heather 1999, pp. 43–44. Wolfram 1988, pp. 24–25. Heather 1999, p. 75. Wolfram 1988, p. 24. Wolfram 1988, p. 387, fn57. Heather 1998, pp. 52–57...
Discussion Groups—Wolfram Community". community.wolfram.com. Retrieved 3 February 2017. Freeland SJ, Hurst LD (September 1998). "The genetic code is one in a...
Sybil Wolfram, 2014 [1989]. In-laws and Outlaws: Kinship and Marriage in England by Sybil Wolfram, 1987. Levy, Steven. "The Man Who Cracked The Code to Everything...
Kind of Science is a book by Stephen Wolfram, published by his company Wolfram Research under the imprint Wolfram Media in 2002. It contains an empirical...
interactivity. According to Stephen Wolfram: "The idea of a notebook is to have an interactive document that freely mixes code, results, graphics, text and everything...
Global Information