This region is a blow-up of part of the main "heart-shaped" part of the
M-set within the cleft between that and the largest more-or-less circular
part to its left, below the horizontal axis.
You can see the relevant area indicated by a 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.
It's quite attractive in its own right; but we can do better by refining the
way the colours are allocated:
You can download and save a copy of the BASIC source-code for the 640 x 480
version by right-clicking
here.
If you read through this program, you'll see that I've arranged for the ten
"ribbon" colours to cycle, by using the MOD function. This is the first
example of the technique in these pages. In this case, using MOD 20, the
effect is to divide by 20 keeping only the remainder, and using that to
determine the colour. This is the standard method used for most of the
following graphics in this collection. It works well, and looks good!
One more adjustment - a slight blow-up of the actual spiral, as indicated by
the white rectangle:
- and here's the result:
You can download and save a copy of the BASIC source-code for the 640 x 480
version by right-clicking
here.
Incidentally:
When the Mandelbrot set burst into the public consciousness in the
middle-to-late 1980's, it could be seen in all kinds of situations. At one
stage, it was possible to buy wrapping paper featuring exquisite Mandelbrot
graphics. Also, it appeared in some rock videos. A classic example: "Stand
Up for Your Love Rights" by Yazz (1988) included some zooms of parts of
the M-set which are very similar to the graphics in this and the next
three pages (Regions #9, #10, and #11). By the way, the video also
features some short animated glimpses of the
Koch snowflake curve
(a close relative of the Cantor Set), and even a very brief
glimpse - just before the end - of the butterfly-shaped
Lorenz Attractor!
Well worth a look if you can find a copy.
UPDATE, 31st October 2010:
After a long time searching, I've finally found that video on YouTube.
It's the 12" version of the song, which runs for seven and a quarter
minutes. I must say that it's not really my kind of music; with rare
exceptions, I was never a disco fan! I could see some merit in
songs like the Bee Gees'
"Jive Talkin'"
and
"Stayin' Alive"
- even, perhaps,
"Night Fever"
- but to my mind, most disco (including this song, I'm afraid) was little
more than musical fluff. The fractal animations are a saving grace, in
this case! If you'd like to view the video,
here's
the link.
My home page
Preliminaries (Copyright, Safety)
Mandelbrot set: Region #8
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.
Return to
Fractals #1: the Cantor and Mandelbrot sets