Journal of Statistical Physics, Vol. 42, Nos. 5/6, 1986. p. 809-821.
An automatic sequence is generated by a finite machine (automaton). These sequences can be periodic or not: in the latter case however, they are not random, but rather "quasicrystalline." We consider an lsing chain with variable interaction in a uniform external field, at zero temperature, and prove that, if this interaction is automatic, then the induced magnetic field is also automatic.