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Substitution System

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A substitution system is a map that applies rules to transform the elements of one sequence into a new sequence. For example, the substitution system {1->0,0->11} would take 10->011->1100->001111->11110000->....

The geometric counterpart replaces tiles by configurations of tiles, producing a substitution tiling when the replacements fit together and can be iterated (Frank 2008).

See also

Golden Ratio, Multiway System, Sequential Substitution System, String Rewriting System, Substitution Tiling, Tag System, Thue Constant, Thue-Morse Sequence

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References

Frank, N. P. "A Primer of Substitution Tilings of the Euclidean Plane." Expo. Math. 26, 295-326, 2008. https://doi.org/10.1016/j.exmath.2008.02.001.Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, pp. 82-92, 2002.

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Substitution System

Cite this as:

Weisstein, Eric W. "Substitution System." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SubstitutionSystem.html

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