Gobal Order Or

usually is a Fibonacci number)? Is it possible to program locally connected computers in such a way that the network is still functional if a small fraction of the nodes is corrupted? Is it possible for a big team of people (or ants), each trying to reach private goals, to behave reasonably? These questions range from theology to "political science" and are rather difficult. In mathematics the most prominent example of this kind is the so-called Berger theorem on aperiodic tilings (exact statement below). It was proved by Berger in 1966 [1]. 1 In 1971 the proof was simplified by Robinson [7], who invented the well-known "Robinson tiles" that can tile the entire plane but only in an aperiodic way (Fig. 1). Since then many similar constructions have been invented (see, e.g., [3, 6]); some other proofs were based on different ideas (e.g., [4]). However, we did not manage to fmd a publication which provides a short but complete proof of the theorem: Robinson tiles look simple, but when you Fig. 1. The Robinson tiles [reflections and rotations are allowed].