The "Main Seahorse Valley Series"
from Bengt Månsson

The Large Seahorse Valley : The following series of images are succesive zooms into the largest (upper) seahorse valley of the Mandelbrot set, at -0.75. There are 18 images plus color variations and one "side-step", number 6a.

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 80000-640000. This much is required to resolve all details, although the number of iterations is much lower at most pixels. The total calculation time was several hundred hours even though I used a 200 MHz Pentium most of time. The last image demanded more than 200 hours by itself.

shv75_1 Magnification: 20000

Our journey starts at y-coordinates around 0.01, i e rather far down the valley. Notice the similarity between the shapes in the middle of picture and the buds on the cardioid to the right. A number of mini-MS:s are visible. These are better viewed in a high-resolution image. You can calculate it if you download the picture, load it into Fractint, and recalculate it with a disk/ram 'video' mode with 2048x1536 pixels.

shv75_2 Magnification: 400000

This is a section of a spiral in the preceding image. You can see a number of "bridges" and in high-resolution you can see, or at least guess, that there are small mini-MS:s at the centers of these bridges.

shv75_3.GIF Magnification: 4.65*10^6

A closer look at one of the bridges. An even closer look ...

shv75_4.GIF Magnification: 5.41*10^7

... reveals a mini-MS. We take ...

shv75_5.GIF Magnification: 2.22*10^8

... a closer look at it.

shv75_6.GIF Magnification: 4.43*10^9
shv75_6A.GIF Magnification: 1.14*10^10

A detail and a closer look, where you see several mini-MS:s. (Logarithmic palette.) The zoom-in continues from shv75_6.GIF, upper left part.

shv75_7.GIF shv75_7A.GIF Magnification: 8.87*10^10

(Logarithmic palette to the right.)

shv75_8.GIF shv75_8A.GIF Magnification: 1.77*10^12

Nice spirals! Zooming in at the center will probable not give anything, so ... (Logarithmic palette to the right.)

shv75_9.GIF shv75_9A.GIF Magnification: 3.55*10^13

... we zoom in on a section of the spiral to the right of the center. (Logarithmic palette to the right.)

shv75_10.GIF Magnification: 1.81*10^15

A bridge, where we look for a mini-MS. We will succed, but with much more effort than I first thought. In fact, the mini-MS is not found at the center but in a smaller bridge off the center. On our way down we will find fascinating new patterns.

shv75_11.GIF shv7511A.GIF Magnification: 3.41*10^15