  In the context of abstract geometrical computation, computing with colored
line segments, we study the possibility of having an accumulation with small
signal machines, ie, signal machines having only a very limited number of
distinct speeds. The cases of 2 and 4 speeds are trivial: we provide a proof
that no machine can produce an accumulation in the case of 2 speeds and exhibit
an accumulation with 4 speeds. The main result is the twofold case of 3 speeds.
On the one hand, we prove that accumulations cannot happen when all ratios
between speeds and all ratios between initial distances are rational. On the
other hand, we provide examples of an accumulation in the case of an irrational
ratio between 2 speeds and in the case of an irrational ratio between two
distances in the initial configuration. This dichotomy is explained by the
presence of a phenomenon computing Euclid's algorithm (gcd): it stops if and
only if its input is commensurate (ie, of rational ratio).
