An introductory article by Ralph Griswold on string rewriting systems and Lindenmayer systems (L-Systems) as a basis for pattern design. It defines strings, formal languages, seeds, rules and generations, and shows that L-Systems apply all rules in parallel. Worked examples include the Morse-Thue and Fibonacci string sequences, and the Fibonacci string is interpreted as a profile pattern. A short sidebar covers Aristid Lindenmayer, and an appendix has plates of L-system graphics (spirals, snowflake-like curves, branching plant forms). References point to related Griswold documents and to the L-system literature.