Click on the picture to see a 640 x 480 pixel version.
We're revisiting the thin sparkly region to the left of the main body of the
M-set. This region, extending as far as the point -2, is sometimes referred
to as "The Utter West". The largest "flea" in this area, which was the main
subject of Region #5, is clearly visible toward the right-hand side of the
picture. This time, however, the surrounding colour contours have been
chosen to provide more detail.
You can see the relevant area indicated by a 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.
Now let's zoom in for a closer look into the left-hand end of the white box,
with double the magnification. (The large flea is now outside the right-hand
side of the box.)
You can see the relevant area indicated by a smaller 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.
As you can see, there is a lot of very obvious self-similarity going
on here.
Finally, we'll zoom in to 25 times the magnification of this view (or 50
times our orginal view, above) - still keeping over to the left-hand side,
including the point -2:
You can see the relevant area indicated by a very small white box -
not much more than a dot, really - 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.
If we were to continue to zoom in, we'd see essentially more of the same.
Having made the point - taking a leaf out of
Andrew Wiles's
book, I will stop here.
My home page
Preliminaries (Copyright, Safety)
Mandelbrot set: Region #24
"The Utter West"
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