self similar branching pattern modeled silico using l systems principles ref name branching ref alt x px images fractals created fractal generating programs butterfly effect small change single variable unpredictable outcome ''iterated function systems ifs '' use fixed geometric replacement rules may stochastic deterministic ref name ifs ref eg koch snowflake cantor set haferman carpet sierpinski carpet sierpinski gasket peano curve harter heighway dragon curve square menger sponge ''strange attractors'' use iterations map solutions system initial value differential difference equations exhibit chaos eg see multifractal image
Formal science Mathematics Applied mathematics Dynamical systems Fractal geometry