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)
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)
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)
You can download and save a copy of the BASIC source-code for the 640 x 480
version by right-clicking
here.
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Mandelbrot set: Region #5
Click on the picture to see a 640 x 480 pixel version.
Click on the picture to see a 640 x 480 pixel version.
Click on the picture to see a 640 x 480 pixel version.
Click on the picture to see a 640 x 480 pixel version.
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Fractals #1: the Cantor and Mandelbrot sets