Irrational speeds of configurations growth in generalized Pascal triangles (Q1210304)

In the introduction the author asks for properties that a one-dimensional cellular automaton should have to simulate waves caused by throwing coins into a \((1-D)\) water-reservoir. A natural condition, as suggested by the author, is that, for a bounded initial configuration, the length of the support grows in linear time and with a speed independent of the initial conditions. The author then introduces generalized Pascal's triangles which give rise to irrational speeds, which are effectively constructed. For this purpose pleasant number-theoretical ideas enter the picture.