The paper discusses the connection between emergence, pattern formation and nonlinear dynamics, focusing on the similarity between discrete patterns and fractal structures, and then describes different solutions to model reaction–diffusion systems as representative processes in morphogenesis. A specific example is the diffusion limited aggregation growth process, illustrated by the simulation of the evolution of a bacterial colony that shows the roles of instability and sensitivity in non–equilibrium pattern formation. Based on this particular case, it is shown how self–organization could be achieved from non–organized agglomeration of separate entities, in a region of space. We conclude with some brief remarks about universality, predictability and long–term prospects for this field of research.