Instantly Getting the Fractal Equation of Any Image

phiaera

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« on: March 08, 2012, 08:30:23 PM »

I have been wondering for awhile now on how to instantly find the fractal equation of any digital image.

Colors of Infinity by Arthur Clarke goes in a bit on it, but it doesn't tell the viewer how to do it.

<a href="http://www.youtube.com/v/AjdogjBxfco&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/AjdogjBxfco&rel=1&fs=1&hd=1</a>

(Starts from around 2:10)

Anyone have any ideas?


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hobold

Fractal Bachius

Posts: 573

Re: Instantly Getting the Fractal Equation of Any Image

« Reply #1 on: March 08, 2012, 10:03:59 PM »

Quote from: phiaera on March 08, 2012, 08:30:23 PM

I have been wondering for awhile now on how to instantly find the fractal equation of any digital image.
Anyone have any ideas?

Fractal compression is a promise that could not be kept for exactly this reason. No one has managed to develop a general algorithm that could always find good iterated function mappings for any image.

Don't get me wrong. Some fractal CODECs were eventually developed and productized. But they could not consistently beat other compression methods in terms of compression rate, perceived image quality, speed, and memory footprint. So the other compression methods won and fractal compression fell out of favour. Even as a research topic it is pretty much dead today.


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cKleinhuis

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Fractal Senior

Posts: 7044

formerly known as 'Trifox'

Re: Instantly Getting the Fractal Equation of Any Image

« Reply #2 on: March 08, 2012, 11:00:45 PM »

i think barnsley was it who stated, that any picture can be described via an iterated function ... but dont forget, this takes actually MORE data to store, than the bitmap data itself,
basically you would need an ifs function for each pixel, guaranteeing that the pixel color is met, and worst of it, break up the iteration after the first pixel has been hit ... this is what he means with describing any image with an ifs function ,... it is clearly possible, but it has no inherent compression included sad


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divide and conquer - iterate and rule - chaos is No random!

phiaera

Guest

Re: Instantly Getting the Fractal Equation of Any Image

« Reply #3 on: March 08, 2012, 11:35:05 PM »

I actually wasn't too concerned about its applications for image compression. When I first saw the documentary, I thought that the idea that any image can be described as a fractal equation is an interesting concept as it would have huge applications in my idea of developing an instant "beautifying" technique in image editing:

1) Take an image and find its interated function
2) Altering the function in specific ways and basing it upon phi, 1.618...

Can anyone can point me to a link or specific chapter in a book that goes in depth about Barnsley's idea described in the video?


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