  We propose a new simple construction of an aperiodic tile set based on
self-referential (fixed point) argument. People often say about some discovery
that it appeared "ahead of time", meaning that it could be fully understood
only in the context of ideas developed later. For the topic of this note, the
construction of an aperiodic tile set based on the fixed-point
(self-referential) approach, the situation is exactly the opposite. It should
have been found in 1960s when the question about aperiodic tile sets was first
asked: all the tools were quite standard and widely used at that time. However,
the history had chosen a different path and many nice geometric ad hoc
constructions were developed instead (by Berger, Robinson, Penrose, Ammann and
many others. In this note we try to correct this error and present a
construction that should have been discovered first but seemed to be unnoticed
for more that forty years.

Logic in Computer Science;Discrete Mathematics;Combinatorics