Computational Military Science is introduced as a sub-discipline of Computational Social Science and examines military conflict and simulations in the form of wargames by focusing on three related, conceptual level aspects: Complex Adaptive Systems, Symmetry and Symmetry Breaking, and Large Language Models. Wargames are a form of conflict representation that has evolved over the years to influence military planning, training, decision making, and commercial entertainment. This examination uses the well documented United States Civil War (1861-1865) as an illustrative environment. Complex Adaptive Systems in the context of military conflict are thoroughly examined to better understand the nature of hierarchical structures, interactions, adaptation, and emergence. A means to describe and mathematically measure complexity in military hierarchies and interactions is provided. These descriptions and measurements are applied using the physics concepts of symmetry and symmetry breaking to comprehend the dynamic complexities and adaptabilities of military hierarchies under stress as their interactions increase or change. Large Language Models, having recently gained wide attention, are shown to have applicability in wargame design, impacting the future trajectory of military operations, planning, and leadership training. Current use cases are considered and the transformative potential of future applications are forecast. This interdisciplinary approach weaves a thread of complexity and emergence throughout the three topics and provides a perspective otherwise unavailable in a single disciplinary method.