The process of adaptation occurs on two timescales. In the short term, natural selection merely sorts the variation already present in a population, whereas in the longer term genotypes quite different from any that were initially present evolve through the cumulation of new mutations. The first process is described by the mathematical theory of population genetics. However, this theory begins by defining a fixed set of genotypes and cannot provide a satisfactory analysis of the second process because it does not permit any genuinely new type to arise. The evolutionary outcome of selection acting on novel variation arising over long periods is therefore difficult to predict. The classical problem of this kind is whether 'replaying the tape of life' would invariably lead to the familiar organisms of the modern biota. Here we study the long-term behaviour of populations of autonomously replicating computer programs and find that the same type, introduced into the same simple environment, evolves on any given occasion along a unique trajectory towards one of many well-adapted end points.