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Chapter 3:
Fractal Encoding of Grayscale Images
Abstract
An image such as the fractal fern of the previous chapter can be reproduced with a relatively simple iterated function system (IFS) because this type of image has the property of global self-similarity. That is, the entire image is made up of smaller copies of itself, or parts of itself. If one zooms in on this type of image, it will display the same level of detail, regardless of the resolution scale. Also, this type of image is a binary image, that is, each of its pixels can be represented with either a 1 or a 0. Real-world images do not exhibit the type of global self-similarity present in the IFS images of the previous chapter. Moreover, real-world images are not binary, but rather each pixel belongs to a range of values (grayscale) or a vector of values (color). If we are going to represent such an image as the attractor of an iterated system, then clearly we need a more general system than the IFS's of the previous chapter. This chapter examines the development and implementation of such a system that can be used for the fractal encoding of general grayscale images.
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CHAPTER 3
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