A substitution system in which rules are used to operate on a string consisting of letters of a certain alphabet. String rewriting systems are also variously known as rewriting systems, reduction systems, or term rewriting systems. String rewriting is a particularly useful technique for generating successive iterations of certain types of fractals, such as the box fractal, Cantor dust, Cantor square fractal, and Sierpiński carpet.

# String Rewriting System

## See also

Rabbit Sequence, Substitution System## Explore with Wolfram|Alpha

## References

Peitgen, H.-O. and Saupe, D. (Eds.). "String Rewriting Systems." §C.1 in*The Science of Fractal Images.*New York: Springer-Verlag, pp. 273-275, 1988.Wagon, S. "Recursion via String Rewriting." §6.2 in

*Mathematica in Action.*New York: W. H. Freeman, pp. 190-196, 1991.

## Referenced on Wolfram|Alpha

String Rewriting System## Cite this as:

Weisstein, Eric W. "String Rewriting System."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/StringRewritingSystem.html