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Self-assembly formation is a key research topic for realizing practical applications in swarm robotics. Due to its inherent complexity, designing high-performance self-assembly formation strategies and proposing corresponding macroscopic models remain formidable challenges and present an open research frontier. Taking inspiration from crystallization, this paper introduces a distributed self-assembly formation strategy by defining <i>free</i>, <i>moving</i>, <i>growing</i>, and <i>solid</i> states for robots. Robots in these states can spontaneously organize into user-specified two-dimensional shape formations with lattice structures through local interactions and communications. To address the challenges posed by complex spatial structures in modeling a macroscopic model, this work introduces the structural features estimation method. Subsequently, a corresponding non-spatial macroscopic model is developed to predict and analyze the self-assembly behavior, employing the proposed estimation method and a stock and flow diagram. Real-robot experiments and simulations validate the flexibility, scalability, and high efficiency of the proposed self-assembly formation strategy. Moreover, extensive experimental and simulation results demonstrate the model’s accuracy in predicting the self-assembly process under different conditions. Model-based analysis indicates that the proposed self-assembly formation strategy can fully utilize the performance of individual robots and exhibits strong self-stability.