A Mathematical Model, Implementation and Study of a Swarm System
This work addresses pattern transformation in swarm systems, but it appears incremental as it builds on existing macroscopic primitives without demonstrating broad applications or significant breakthroughs.
The authors tackled the problem of modeling swarm systems by developing a mathematical model for pattern formation and transformation, proposing two general transformation methods and confirming their feasibility through simulations.
The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation and mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to confirm the feasibility of the proposed models and transformation methods are presented. Comparison between the two transformation methods is also reported.