Reductionism, an approach to understanding that attempts to explain a complex phenomenon in terms of the functioning of its constituent elements, is the overwhelmingly dominant strategy of physics and many other sciences. In philosophy it is often closely associated with materialism and determinism. However, the rather counter-intuitive behavior of certain cellular automata strongly suggests that there is a limit to the explanatory power of reductionism. In particular, an artificial computational "world" which is perfectly reductionist by construction cannot be fully understood via reductionism. The talk will include animations, theorems and speculations.