Mandelbrot Set: Region #8

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Mandelbrot set: Region #8

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

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:


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.

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:


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.

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 realtive 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.

Return to Fractals #1: the Cantor and Mandelbrot sets

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