This page features an area of the M-set not yet discussed in these pages.
However, you may find some striking similarities with Region #4. We
shouldn't be too surprised; after all, the M-set is a fractal, and
self-similarity is to be expected.
Here's a graphic showing where we are with relation to the M-set as a whole:
You can download and save a copy of the BASIC source-code for the 640 x 480
version by right-clicking
here.
Here's an initial blow-up of the area. We'll need to zoom in again;
the small white box indicates the area of our ultimate interest, as shown
above:
You can click on the picture to see a 640 x 480 pixel version, without the
white box. Also, you can download and save a copy of the BASIC source-code
for the 640 x 480 version by right-clicking
here.
The first step in the investigation of the region within the white box was
to modify the program to show more detailed colour contours:
You can download and save a copy of the BASIC source-code for the 640 x 480
version by right-clicking
here.
A further modification to install a white buffer zone:
You can download and save a copy of the BASIC source-code for the 640 x 480
version by right-clicking
here.
Next, another modification to bring the aura into prominence:
You can download and save a copy of the BASIC source-code for the 640 x 480
version by right-clicking
here.
A final modification to expand the aura further and add more detail,
allowing the constituent colour contours to be seen clearly:
You can download and save a copy of the BASIC source-code for the 640 x 480
version by right-clicking
here.
I then used a DOS graphics editor to make adjustments to the colours,
starting with the ribbons...
... and then, finally, the aura in shades of grey:
Who says you can't do high-quality graphics in an old-fashioned DOS-based
environment?
UPDATE, 17th April 2006
OOPS
Oh dear - I feel very silly. Months after originally producing this page,
I've just realized that Region #19 looks like part of Region #4
precisely because it is part of Region #4, after all!
Scroll back up to the graphic about a quarter of the way down this page
which shows where Region #19 is. That graphic contains Region #4 - and
Region #19 is simply a blow-up of the end of the right-most of that tree's
four main branches! How embarrassing...
Never mind - it can all just stay as it is. I can't be bothered making big
changes to these pages to disguise the fact. Anyway, it all serves to
emphasize the point about self-similarity, so there's no harm done!
My home page
Preliminaries (Copyright, Safety)
Mandelbrot set: Region #19
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.
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