A computer simulation of evolution by natural selection must incorporate three processes: construction of morphology according to specified parameters, generation of descendants by random mutation of parameter values, and assessment of differential efficiency to allow the automated choice of a survivor. These processes are described with respect to a simple 2-dimensional dichotomous branching morphology. This structure may be relevant to some fossil graptolites and bryozoans. Simulated evolution using this model shows gradualism, punctuation, reversals, k and R type selection and other features claimed to occur in fossil lineages. These properties are explained in relation to the heterogeneities of morphospace. This simulation may be a valid model for real evolution: evolutionary mode, tempo and direction may often be the result of constraints inherent in the geometry of the organism.