Exercises for Chaos Under Control

Chapter 7: A Quick Tour of the Mandelbrot Set

6.[C] Use MICRO to develop your own chart of the antenna patterns of buds attached to the body of the Mandelbrot Set. In the next section, we shall find a method of organizing these patterns. For now, try to find a pattern yourself.

7.[C] Using MICRO, go exploring around the body of the Mandelbrot Set, describing the features you find. Now go exploring around the head of the Mandelbrot Set. Compare the features around the head to those around the body.

8.[C] Using MICRO, compare the features around a midget with those around the body.

9.[C] We know for a point selected in the body of the M Set, repeatedly applying the Mandelbrot map produces a sequence of points converging to a fixed point. Use ORBIT to investigate the structure of this sequence. Specifically, take points in the body but near 3, 4, and 5-cycle buds. What pattern do you see?

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