Mandelbrot Set: Region #19

Mad Teddy's web-pages


Mandelbrot set: Region #19

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

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:


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.

A further modification to install a white buffer zone:


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.

Next, another modification to bring the aura into prominence:


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.

A final modification to expand the aura further and add more detail, allowing the constituent colour contours to be seen clearly:


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.

I then used a DOS graphics editor to make adjustments to the colours, starting with the ribbons...


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

... and then, finally, the aura in shades of grey:


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

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!

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