The escape-time method was introduced to generate images of Julia and Mandelbrot sets, then applied to visualize attractors of iterated function systems. This paper extends it further to language-restricted iterated function systems (LRIFS's). They generalize the original definition of IFS's by providing means for restricting the sequences of applicable transformations. The resulting attractors include sets that cannot be generated using ordinary IFS's. The concepts of this paper are expressed using the terminology of formal languages and finite automata.Keywords: fractal, iterated function system, escape-time method, graphics algorithm, formal language, finite automaton.