Does anyone know of any good resources on Kolmogorov complexity and fractals such as the Mandelbrot set? Or even on information theory and fractals?<p>For some reason reading this article is making me wonder about the difference between the information required to generate something like a mandelbrot, knowing the underlying rule, and the information required to represent it as it is, without following the rule. Or e.g., the difference between the information of the generating rule and the information implicitly represented through the time or number of operations needed to generate it.<p>It seems like there's some analogy between potential and kinetic energy, and kolmogorov complexity and something else, that I'm having trouble putting my finger on. Even if you have a simple generating algorithm that might be small in a kolmogorov complexity sense, if that algorithm entails a repeating something over a large number of operations, the resulting object would be complex, so there's an implied total complexity as well as an "generating" one.<p>Maybe this is some basic computational complexity concept but if so I'm not recalling this, or am being dense. E.g., I'm used to discussions of "compressibility" but not of the "generating representation information cost" versus "execution cost".