ABSTRACT
Pictured in Figure 2.1 are four fractal curves. What makes these shapes different from most of the curves we encountered in Chapter 1 is their amazing amount of fine detail. In fact, if we were to magnify a small region of a fractal curve, what we would typically see is the entire fractal in the large. In Chapter 1, we showed how to generate complex shapes like the rosette by applying iteration to repeat over and over again a simple sequence of turtle commands. Fractals, however, by their very nature cannot be generated simply by repeating even an arbitrarily complicated sequence of turtle commands. This observation is a consequence of the Looping Lemmas for Turtle Graphics.
