Fractals and iterated function systems

Due to the advent of the computer and the ability it gives us to perform operations rapidly, function iteration has become an intense area of research in mathematics and related fields. Fascinating and unexpected results are observed when functions are iterated with themselves a large number of times. Both purists and experimentalists are interested in these results and perform research in what could be dubbed iteration theory. Two subjects growing out of this research are chaos theory and fractal theory.