Dragons, Seahorses, and Elephants. Oh my!

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Offline Duncan C

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« on: August 16, 2019, 03:19:31 AM »
The Mandelbrot set fractal has been widely explored. The different shapes found in the set have some common nicknames
Seahorses:
Dragons:
Elephants:

Then there's minibrots, and lots of other "visual themes". You can also find shapes that look like the Julia sets from a given region in the Mandelbrot set plots for that region.

Furthermore, as you explore you can see different visual themes at a couple of different scales in the same image. Take, for example, this image:

https://pbase.com/image/169637456.jpg

At the largest scale, it's a Dragon (or double spiral) shape. However, if you look at smaller shapes, they have a distinct seahorse shape to them. This image is taken from the "Dragon" region of a "minibrot" in a "Seahorse spiral".

Has anybody used machine learning to build a model that recognizes these different visual themes in Mandelbrot set and Julia set fractals? It would be an interesting project.

Offline marcm200

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« Reply #1 on: August 16, 2019, 08:26:49 AM »
Has anybody used machine learning to build a model that recognizes these different visual themes in Mandelbrot set and Julia set fractals? It would be an interesting project.
Not directly machine learning, but guided evolution: https://fractalforums.org/fractal-mathematics-and-new-theories/28/genetic-algorithms-to-search-the-mandelbrot-set/2886

Do you have in mind an approach with zero starting knowledge, hence the machine should find what type of visual shapes there are (partitioning the search space) ? Or an image-recognition type with manual, humanly pre-sorted shape presentation and then doing an automatic zoom to find new locations?


Offline Duncan C

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« Reply #2 on: August 17, 2019, 02:47:35 AM »
I think both approaches would be interesting. If you were to teach it different images to look for it would have a basis in our terms and images.

If, on the other hand, you had it operate purely self-directed it would decide which patterns were self-similar.


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