Data for Selected Computer Graphics

Especially in your first investigations, it is useful to know where the interesting sections occur. Then you can test out your own programs there. Some of the more interesting Julia sets, together with their parameters in the Mandelbrot set, are collected together below.

In addition to the title picture for this Chapter, an ‘Atlas’ of the Mandelbrot set, we also give a table of the appropriate data for many of the pictures in this book. For layout reasons many of the original pictures have been cropped. Some data for interesting pictures may perhaps be missing: they come from the early days of our experiments, where there were omissions in our formulas or documentation.

Table 13-1 shows for each figure number the type of picture drawn, as this may not be clear from the caption. We use the following abbreviations:

G Gingerbread man (Mandelbrot set) or variation thereon

J Julia set, or variation thereon

C Set after Curry, Garnett, Sullivan

N1 Newton development of the equation f(x) = (x-1)*x* (x+1)

N3 Newton development of the equation f(x) = x3-1

N5 Newton development of the equation f(x) = x5-1

T Tomogram picture, see Chapter 6

F Feigenbaum diagram

* See text for further information

Near the (approximate) boundaries of the picture sections you will see the maximal number of iterations and the quantity that determines the spacing of the contour lines. The last two columns give the initial value for Mandelbrot sets, and the complex constant c for Julia sets.