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We consider a very simple Mealy machine (three states over a two-symbolalphabet), and derive some properties of the semigroup it generates. Inparticular, this is an infinite, finitely generated semigroup; we show that thegrowth function of its balls behaves asymptotically like n^2.4401..., wherethis constant is 1 + log(2)/log((1+sqrt(5))/2); that the semigroup satisfiesthe identity g^6=g^4; and that its lattice of two-sided ideals is a chain.Comment: 20 pages, 1 diagra

A MEALY MACHINE WITH POLYNOMIAL GROWTH OF IRRATIONAL DEGREE