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| Seahorse Valley, With a Twist | ||||||
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| Description: A coiled exponential map around a nanobrot in Seahorse Valley. This one doesn't go very deep. An interesting fact about the exponential map: it shows us the outer shapes "as the target point sees them", and the target point often sees things in the shapes that later adorn the nanobrots one finds. In the Forks case, the outermost "fork" in the exponential map doesn't even look like a fork in the normal view, but like a propeller with two blades. But its tightly-packed cousins close to the microbrot next reached do look like forks. From the microbrot's perspective, according to the exponential map, so does the original. In this one, we get a linear-ish embedded Julia from near the spike of a microbrot. This embedded Julia has sections that look like fishhooks, and the whole thing looks like two fishhooks in the exponential map. Not only that, though, the microbrot itself looks like a fishhook from the perspective of the deeper nanobrot! Most of which is its spike, but the longer rising arm of it is bulked out by the body of the microbrot. We also see that from the perspective of a seahorse spiral, the next seahorse up the valley looks curved into the same convex-backed form seen alternating with ones that have concave backs along seahorse spirals. In a sense, the exponential map is telling us why that form occurs there, and nowhere else. Stats: Total Favorities: 1 View Who Favorited Filesize: 487.31kB Height: 1200 Width: 1200 Discussion Topic: View Topic Keywords: Mandelbrot Seahorse Valley deepzoom Posted by: Pauldelbrot  October 16, 2011, 10:56:41 AMRating:  by 2 members.Image Linking Codes
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Comments (2)  |
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DarkBeam
Global Moderator Fractal Senior  Posts: 2512 Fragments of the fractal -like the tip of it 
| November 17, 2011, 11:06:03 AM Great |
| Guest | October 16, 2011, 04:10:00 PM An interesting perspective. Thanks for adding the comment as reference. |
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