Dendritic morphology constrains brain activity, as it determines first which neuronal circuits are possible and second which dendritic computations can be performed over a neuron's inputs. It is known that a range of chemical cues can influence the final shape of dendrites during development. Here, we investigate the extent to which self-referential influences, cues generated by the neuron itself, might influence morphology. To this end, we developed a phenomenological model and algorithm to generate virtual morphologies, which are then compared to experimentally reconstructed morphologies. In the model, branching probability follows a Galton-Watson process, while the geometry is determined by "homotypic forces" exerting influence on the direction of random growth in a constrained space. We model three such homotypic forces, namely an inertial force based on membrane stiffness, a soma-oriented tropism, and a force of self-avoidance, as directional biases in the growth algorithm. With computer simulations we explored how each bias shapes neuronal morphologies. We show that based on these principles, we can generate realistic morphologies of several distinct neuronal types. We discuss the extent to which homotypic forces might influence real dendritic morphologies, and speculate about the influence of other environmental cues on neuronal shape and circuitry.