Zooming further with Bengt in
The "Seahorse Valley"

Bengt Månsson in Sweden continues his deepzooming explorations. The following images constitute a series of zooms into the Mandelbrot set, in the largest "sea-horse valley" of the main mini-MS, at around -1.76.

The succesive zooms are from an area around or near the centre of the previous image with one exception, indicated below. Total magnification is given for each image. Magnification is, of course, with respect to the entire Mandelbrot set or, more precisely, a region in the complex c-plane with max(Re c) - min(Re c) = 8/3 , max(Im c) - min(Im c) = 2 . Maximum number of iterations is set to 30000 for all images, although this is unnecessarily high in some cases.

MIN3_1.GIF
min3_1 Image:
Magnification: 1.29*10^4

The black regions to the left and to the right indicate that we are in a valley.

MIN3_2.GIF
min3_2 Image:
Magnification: 6.32*10^5

See remark after the next image.

MIN3_3.GIF
min3_3 Image:
Magnification: 1.26*10^7

This and the previous image show the Julia set resembling shapes that are often found in the "beads" on sprouts in the valleys of the Mandelbrot set. Notice the rich inner structure, from which details are chosen in the following images.

MIN3_4.GIF
min3_4 Image:
Magnification: 1.04*10^8

If you look at this image in full size you will notice the enormous amount of details to be explored. However, I choose the central part, which ...

MIN3_5.GIF
min3_5 Image:
Magnification: 2.07*10^9

... again shows a wealth of details. The almost square form is intriguing!

MIN3_6.GIF
min3_6 Image:
Magnification: 4.14*10^10

Wow! Is this a Flying Saucer or what? The small rectangle somewhat to the right and upwards from the center shows the region covered by the next image.

MIN3_7.GIF
min3_7 Image:
Magnification: 8.29*10^11

MIN3_8.GIF
min3_8 Image:
Magnification: 1.66*10^13

MIN3_9.GIF
min3_9 Image:
Magnification: 3.31*10^14

MIN3_10.GIF
min3_10 Image:
Magnification: 6.63*10^15

Strange structure. Something similar was earlier found in my "cou"-series, and ...

MIN3_11.GIF
min3_11 Image:
Magnification: 5.16*10^18

... the same goes for this one. One more Flying Saucer?

MIN3_12.GIF
min3_12 Image:
Magnification: 2.06*10^21

Of course we finish the image series with another mini-MS!

Finally I recalculated MIN3_6.GIF with the maximum number of iterations as low as 500, producing this ugly image:

LOWRES_6.GIF
lowres_6 Image:
Magnification: 2.06*10^21

Details have vanished, of course, but that is not all. The resulting image could at first sight be taken for something quite else since the outer parts of the large, black region makes it look a little like the Mandelbrot set of the iteration z^9 + c --> z .

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