Self-organization is a process that increases the order of a system as a result of local interactions among low-level, simple components, without the guidance of an outside source. Spatial self-organization is a process in which shapes and structures emerge at a global level from collective movements of low level shape primitives. Spatial self-organization is a stochastic process, and the outcome of the aggregation cannot necessarily be guaranteed. Despite the inherent ambiguity, self-organizing complex systems arise everywhere in nature. Motivated by the ability of living cells to form specific shapes and structures, we develop two self-organizing systems towards the ultimate goal of directing the spatial self-organizing process. We first develop a self-sorting system composed of a mixture of cells. The system consistently produces a sorted structure. We then extend the sorting system to a general shape formation system. To do so, we introduce morphogenetic primitives (MP), defined as software agents, which enable self-organizing shape formation of user-defined structures through a chemotaxis paradigm.
One challenge that arises from the shape formation process is that the process may form two or more stable final configurations. In order to direct the self-organizing process, we find a way to characterize the macroscopic configuration of the MP swarm. We demonstrate that statistical moments of the primitives’ locations can successfully capture the macroscopic structure of the aggregated shape. We do so by predicting the final configurations produced by our spatial self-organization system at an early stage in the process using features based on the statistical moments. At the next stage, we focus on developing a technique to control the outcome of bifurcating aggregations. We identify thresholds of the moments and generate biased initial conditions whose statistical moments meet the thresholds. By starting simulations with biased, random initial configurations, we successfully control the aggregation for a number of swarms produced by the agent-based shape formation system. This thesis demonstrates that chemotaxis can be used as a paradigm to create an agent-based spatial self-organization system. Furthermore, statistical moments of the swarm can be used to robustly predict and control the outcomes of the aggregation process.