Embryonic development of multi-cellular organisms is governed by gene regulatory networks (GRNs), which are a collection of genes that interact with one another and with other chemicals in the cell. Inspired by the morphogenesis of biological organisms, in this paper, we propose a morphogenetic approach using a gene regulatory network (GRN) for swarm robotic systems to form complex shapes in a distributed manner. The target pattern, represented by non-uniform rational BB-spline (NURBS), is embedded into the gene regulatory model, analogous to the morphogen gradients in multi-cellular development. Since the total number of robots is unknown to each robot, a dynamic neighborhood adaptation mechanism is proposed to evenly deploy the robots on the boundary of the target pattern. A theoretical proof of the system convergence is provided. Various simulation studies demonstrate that the proposed algorithm offers an effective and robust distributed control mechanism for swarm robotic systems to construct complex shapes. Furthermore, proof-of-concept experiments were successfully undertaken using e-puck mobile robots, which demonstrate that the proposed model works well with physical constraints of real robots.