Is there a universal image generator?

摘要

Synthetic pattern generation procedures have various applications, and a number of approaches (fractals, L-systems, etc.) have been devised. A fundamental underlying question is: will new pattern generation algorithms continue to be invented, or is there some “universal” algorithm that can generate all (and only) the perceptually distinguishable images, or even all members of a restricted class of patterns such as logos or letterforms? In fact there are many complete algorithms that can generate all possible images, but most images are random and not perceptually distinguishable. Counting arguments show that the percentage of distinguishable images that will be generated by such complete algorithms is vanishingly small. In this paper we observe that perceptually distinguishable images are compressible. Using this observation it is evident that algorithmic complexity provides an appropriate framework for discussing the question of a universal image generator. We propose a natural thesis for describing perceptually distinguishable images and argue its validity. Based on it, we show that there is no program that generates all (and only) these images. Although this is an abstract result, it may have importance for graphics and other fields that deal with compressible signals. In essence, new representations and pattern generation algorithms will continue to be developed; there is no feasible “super algorithm” that is capable of all things.