Kolmogorov complexity

$This image illustrates part of the Mandelbrot set fractal. Simply storing the 24-bit color of each pixel in this image would require 1.62 million bits; but a small computer program can reproduce these 1.62 million bits using the definition of the Mandelbrot set and the coordinates of the corners of the image. Thus, the Kolmogorov complexity of the raw file encoding this bitmap is much less than 1.62 million.$

In algorithmic information theory, the Kolmogorov complexity of an object, such as a piece of text, is a measure of the computational resources needed to specify the object.

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Berry paradox

Data compression