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Lesson 1 – Page 6:


    When you zoom directly into the centers of spirals – the two-armed or multi-armed spirals in Figure 16, for example – you will continue to find similar spiral structure, infinitely. No new structures will be revealed.

    To find structures that are different, you have to look for midgets, which occur in the intersecting structure between spirals. It is the occurrence of these midgets that effects change in spiral structure. If you'll look back at Figure 16, you'll notice that the midget is located at the intersection of the two large multi-arm spirals. But that midget then begets additional structure – two medium and four smaller spiral systems (Figure 17).

    After a bit more zooming, I found this midget near the midget in Figure 17. Where the midget in Figure 17 spawned two large, two medium and four small spiral systems, this one has four that are equally-sized. The midget isn't visible yet, but I know it is there at the intersection of the four spiral systems. The intersection appears to contain a circular shape. If we zoom into it...

Figure 18: Midget with 4 spiral arms

... we find our midget. This one has spawned 16 spiral arms of approximately the same size and shape in the inner ring and 32 spiral arms of different sizes and connections in the outer ring. This is just one example of the hidden treasures awaiting your exploration. There is an infinity of midgets in the Mandelbrot set, so it's quite possible that you'll find one that has never been seen before!

Figure 19: Midget with 16 spiral arms

    Because it takes more iterations to tell if a pixel is an inside or an outside point, the more deeply one zooms in, the more slowly the image will render. You will also need to watch for unwanted inside areas. The centers of spirals should always be filled with structure, not inside points – so the only turquoise you want to see as you zoom are the midgets. If you have other-shaped areas of turquoise, or if the coastlines of the midgets appear smooth, increase the Maximum Iterations setting on the Fractal tab.

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