Morphogenesis allows millions of cells to self-organize into intricate structures with a wide variety of functional shapes during embryonic development. This process emerges from local interactions of cells under the control of gene circuits that are identical in every cell, robust to intrinsic noise, and adaptable to changing environments. Constructing human technology with these properties presents an important opportunity in swarm robotic applications ranging from construction to exploration. Morphogenesis in nature may use two different approaches: hierarchical, top-down control or spontaneously self-organizing dynamics such as reaction-diffusion Turing patterns. Here, we provide a demonstration of purely self-organizing behaviors to create emergent morphologies in large swarms of real robots. The robots achieve this collective organization without any self-localization and instead rely entirely on local interactions with neighbors. Results show swarms of 300 robots that self-construct organic and adaptable shapes that are robust to damage. This is a step toward the emergence of functional shape formation in robot swarms following principles of self-organized morphogenetic engineering.@en