Self-similar structures    The intriguing pattern on this
picture is a floor mosaic found  in the cathedral of Anagni
(Italy). The cathedral and the floor were constructed in the
year 1104 (information provided by Nicoletta Sala). It is a
spectacular early example of what is known in mathematics as an
iterative function system, a function that can be recursively
iterated (repeated) to create fractal-like structures. The most
important property of these functions is that they create self-
similar structures, i.e., structures with parts that have the
same form as the entire structure.  On the picture, you see that
the biggest triangles contain the next biggest triangles,
surrounded by three triangles of the same kind, containing the
next biggest triangle, etc. This process can be infinitely
repeated.   If you find such structures and ideas complicated,
just consider the following picture, which makes it all clear
(with thanks to BU's math department):    This picture shows how
the triangle patterns, so-called Si