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Author Topic: Mandelbrot Challenge  (Read 2695 times)
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decayer
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« on: August 17, 2011, 04:38:53 AM »

I have a challenging mathematical / computational pounding in my head a few weeks and would like to share with you.

It provided an image of a region of the Mandelbrot set with, say, 640 Î 480 pixels. Colorfull, very pretty.
Find inside the Mandelbrot set the same image, which equals precisely, pixel by pixel in the image provided. Of course, the solution would be the function values​​.
To ease the challenge would be provided the source code of the program that generated this image with the default values ​​of the function.

In my view would be like finding a grain of sand in the universe.
What would be the applicability of this? One-way function? Encryption? I do not know.

Daniel
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cKleinhuis
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« Reply #1 on: August 17, 2011, 12:55:19 PM »

i do not think this is possible ... you may find a mirrored copy of the current location on the opposite x-axis, but i believe
that self similarity means "similarity" and not self-equalness ... wink so, you would not find any copy of your current image, because the structures
get more complex when you zoom in, the shapes of the mandelbrots are all the same, but the "surroundings" are always kinda different ...

so, i think it is not possible sad

but you could make a challenge to find a image that you made, and give a region where to search for it....
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decayer
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« Reply #2 on: August 17, 2011, 01:54:49 PM »

i do not think this is possible ... you may find a mirrored copy of the current location on the opposite x-axis, but i believe
that self similarity means "similarity" and not self-equalness ... wink so, you would not find any copy of your current image, because the structures
get more complex when you zoom in, the shapes of the mandelbrots are all the same, but the "surroundings" are always kinda different ...

so, i think it is not possible sad

but you could make a challenge to find a image that you made, and give a region where to search for it....


Exactly, I think it's impossible to find it. Even taking into account the features like self similarity present in fractals.
That means something. Think of this picture as a unique identification in the world, or one-way function that can be used in cryptography.
I do not know, there must be something to do with it.
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