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Inspired by the major principles of gene regulation and cellular interactions in multi-cellular organism's development, we propose a distributed self-organizing algorithm for swarm robot pattern formation. In this approach, swarm robots are able to self-organize themselves into complex shapes driven by the dynamics of a gene regulatory network based model. This is a distributed approach, since only local interaction is needed for each robot to make decisions during shape formation without any global controller. The target shape is represented by the non-uniform rational B-spline (NURBS) and embedded into the gene regulation model, analogous to the morphogen gradients in morphogenesis. Since the self-organization algorithm does not need a global coordinate system, the target shape can be formed anywhere within the environment based on the current distribution of the robots. Simulation and experimental results demonstrate that the proposed algorithm is effective for complex shape construction and robust to environmental changes and system failures.