The Incompressibility of Randomness
It is a known fact that an image of random black and white pixels, called “noise”, cannot be compressed due to its random nature. This also relates to information content, as in the following: “…the picture containing the most information would be a picture of completely random pixels… If the dots in the image have no correlation to their neighbors, there is no regularity to compress…” (p.97, The Pattern On The Stone).
Compression requires regularity. We can also speak of complexity, as in this formulation of Kolmogorov complexity of a pattern of bits: “The amount of information in a pattern of bits is equal to the length of the smallest computer program capable of generating those bits.” (p.99, Idem).
Therefore, we can speak of the incompressibility of randomness: “…many mathematicians use this property of incompressibility as a definition of randomness…” (p. 100, Idem).
The montage above starts with an image made up purely of random black and white pixels. It is a bitonal image, meaning pixels can only take on two values, 0 or 1, black or white. As we move towards the images on the right, a “pixelization” process is performed on the underlying image, essentially making the noise less complex, and therefore less random. That means that the images to the right of the “noise image” will require fewer bits to encode.
This is because some regularity is being added, through the simplification process. Naturally, the description length can be shorter. So pure noise is incompressible due to its randomness.
If you had a computer program that could generate “all possible images”, i.e. “all possible pixel configurations”, the vast majority of these images will be noise-like. Also, the set of perceptually distinguishable images will a tiny subset of the space of all possible images.
Noise is your friend. Noise is ubiquitous in nature. Noise has high information content.
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