The exact dynamics of emergence remains one of the most prominent outstanding questions for the field of complexity science. I first discuss various perspectives on emergence, then offer a perspective on understanding emergence in a graph-theoretic representation. To test this, I analyze the dynamics of all possible spatial state spaces near the critical temperature in a 2-D Ising model. The size of different state spaces constrains a system's ability to explore various states within a finite time frame. In addition, the distribution of topological “determinism” for these state spaces remains constant for any particular temperature. At the critical temperature, this distribution is nearly linear, which is distinct from other temperatures. This approach may provide a path forward in building a mathematical framework that captures the dynamics of emergent phenomena. This is key to understanding emergence in biological systems, which are layered with various state spaces and observational perspectives.

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