Although procedural generation is popular among game developers, academic research on the topic has primarily focused on new applications, with some research into empirical analysis. In this paper we relate theoretical work in information theory to the generation of content for games. We prove that there is a relationship between the Kolomogorov complexity of the most complex artifact a generator can produce, and the size of that generator's possibility space. In doing so, we identify the limiting relationship between the knowledge encoded in a generator, the density of its output space, and the intricacy of the artifacts it produces. We relate our result to the experience of expert procedural generator designers, and illustrate it with some examples.

翻译：尽管程序化生成在游戏开发者中广受欢迎，但学术界对该主题的研究主要集中于新应用领域，仅有部分研究涉及实证分析。本文我们将信息论的理论成果与游戏内容生成联系起来。我们证明，生成器能产生的最复杂工件的柯尔莫哥洛夫复杂度与该生成器可能性空间的大小之间存在关联。通过这一证明，我们识别出生成器中编码的知识、其输出空间密度与所生成工件复杂度之间的约束关系。我们将这一结论与程序化生成设计专家的经验相联系，并通过实例加以说明。