Fractal image scaling

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Good evening!

Liquid scaling is beautiful technology, but differs from fractal scaling pretty much. 
The fractal image scaling is based upon an Fractal compression algorythm and a functional analisys.
In the fractal compression algorythm we propose that our image is fixed point of contractive affine transformations. Such system of the affine transformations is called Iterated function system (IFS). We build the IFS based upon our image. Then, to get our image we should take any starting point (any image for example) and apply the IFS many times. As the result we get our image. That's interesting, that the IFS don't know about image resolution, and we can take an big resolution image as the starting point. This way of image scaling is noted by Stephen Welstead in his book "Fractal and Wavelet Image Compression Techniques" (Chapter 3, 3.6. Resolution independence).

If it is not good approach, could you offer me another task related to image processing research field?

Regards, Alexander Beloborodov.
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