Mandelbrot set: Region #5

Click on the picture to see a 640 x 480 pixel version.

On the left of the main body of the Mandelbrot set is a thin sparkle of colour indicating that there are some points even here that belong to the M-set. There are some "mini-Madelbrots" ("fleas"?) among them. Here, we concentrate on the largest such "flea".

It's tempting to think that these bits are separated from the main body.
However, this is not true: mathematicians John H. Hubbard, of Cornell
University, and Adrian Douady, of the University of Paris, who were
responsible for naming the set after Dr. Mandelbrot, proved that the M-set
is *connected* - that is, any part of it is connected to any other
part.

You can see the relevant area indicated by a *very* small white box in
the following picture:

You can download and save a copy of the BASIC source-code for the 640 x 480 version by right-clicking here.

Actually, there are two obvious "fleas" here. We'll zoom in on the larger one:

Mandelbrot set: Region #5 (zoom A)

Click on the picture to see a 640 x 480 pixel version.

You can download and save a copy of the BASIC source-code for the 640 x 480 version by right-clicking here.

As you can see, the colour scheme here is similar to the one I used in Region #4, "Winter in Mand-land" (although with one less colour).

I added the tenth colour back in, changed some colour codes, amd zoomed in closer:

Mandelbrot set: Region #5 (zoom B)

Click on the picture to see a 640 x 480 pixel version.

You can download and save a copy of the BASIC source-code for the 640 x 480 version by right-clicking here.

At this point, I had unwittingly set up what would become the basis of the colour-schemes to be used in all the rest of the graphics in this collection except for the final two: "traditional" black for the M-set itself; then four colours for what I would later come to think of as the "aura"; white for the "demarcation" or "buffer zone" colour; and finally up to ten colours for what I'd eventually call "ribbons". (I'll go into more detail in a following page.)

In the final graphic for this region, we have a full complement of 16 colours for the first time. In particular, note that I've changed the colours for the aura. Closest to the M-set is yellow; then light red, light green, and light blue. This seems to suggest a gradual cooling-off as we move out from the "black-body radiation" of the M-set itself.

Mandelbrot set: Region #5 (zoom B variation)

Click on the picture to see a 640 x 480 pixel version.

Return to Fractals #1: the Cantor and Mandelbrot sets

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