The growth of quantitative analysis and prediction in Earth-surface science has been accompanied by growth in experimental stratigraphy and geomorphology. Experimenters have grown increasingly bold in targeting landscape elements from channel reaches up to the entire erosional networks and depositional basins, often using very small facilities. The experiments produce spatial structure and kinematics that, although imperfect, compare well with natural systems despite differences of spatial scale, time scale, material properties, and number of active processes. Experiments have been particularly useful in studying a wide range of forms of self-organized (autogenic) complexity that occur in morphodynamic systems. Autogenic dynamics creates much of the spatial structure we see in the landscape and in preserved strata, and is strongly associated with sediment storage and release. The observed consistency between experimental and field systems despite large differences in governing dimensionless numbers is what we mean by “unreasonable effectiveness”. We suggest that unreasonable experimental effectiveness arises from natural scale independence. We generalize existing ideas to relate internal similarity, in which a small part of a system is similar to the larger system, to external similarity, in which a small copy of a system is similar to the larger system. We propose that internal similarity implies external similarity, though not the converse. The external similarity of landscape experiments to natural landscapes suggests that natural scale independence may be even more characteristic of morphodynamics than it is of better studied cases such as turbulence. We urge a shift in emphasis in experimental stratigraphy and geomorphology away from classical dynamical scaling and towards a quantitative understanding of the origins and limits of scale independence. Other research areas with strong growth potential in experimental surface dynamics include physical–biotic interactions, cohesive effects, stochastic processes, the interplay of structural and geomorphic self-organization, extraction of quantitative process information from landscape and stratigraphic records, and closer interaction between experimentation and theory.