## Gliders of two velocities

A fourth demonstration shows gliders of two different velocities, which can be used to set up a remote still life whose reaction to further gliders gives it a life of its own.

Such constructions can be used to generate interesting patterns, but they also serve theoretical ends as well. For example, the binary counters establish the existence of structures with both exponentially long transients and exponentially long cycles. Since they still use several cells to establish the basic components and their spacings, they still do not reach theoretical maxima; but they do lie within certain factors of such maxima. When k becomes larger still, universal Turing machines can be programmed, but this probably requires a

kof at least6or8.

Harold V. McIntosh

E-mail:mcintosh@servidor.unam.mx