Most stromatolites are built by photosynthetic organisms, for which sunlight is a driving factor. We examine stromatolite morphogenesis with modelling that incorporates the growth rate of cyanobacteria (the dominant stromatolite-builder today, and presumably through much of the past), as a function of the amount of irradiance received. This function is known to be non-monotonic, with a maximum beyond which growth rate decreases. We define optimal irradiance as that which generates maximal growth, and we find fundamentally different morphologies are predicted under suboptimal and superoptimal direct irradiance. When the direct irradiance is suboptimal, narrow widely spaced columns are predicted, with sharp apices resembling conical stromatolites. When it is superoptimal, broad, closely spaced, flattened domical forms appear. Such disparate morphologies could also occur as a result of other vector-flux-dependent growth factors (e.g. currents). A differential equation is developed that describes the rate of change of the radius of curvature R at the apex of a growing stromatolite column, allowing simple simulations of the time evolution of R for model stromatolites. The term photomorphism is proposed to describe the disparate morphologies that may arise due to the effects described here (and photomorphogenesis as the process). Model results appear to explain, at least qualitatively, the morphologies of a number of stromatolites. If stromatolites are encountered on Mars, our model suggests that they are quite likely to be conical in form, owing to likely suboptimal irradiance since Mars has always received less irradiance than Earth.