It is difficult to model emergence in biological systems using reductionist paradigms. A requirement for computational modeling is that individual entities can be recorded parametrically and related logically, but their transformation into whole systems cannot be captured this way. The problem stems from an inability to formally represent the implicit influences that inform emergent organization, such as context, shifts in causal agency or scale, and self-reference. This lack hampers biological systems modeling and its computational counterpart, indicating a need for new fundamental abstraction frameworks that support system-level characteristics. We develop an approach that formally captures these characteristics, focusing on the way they come together to enable transformation at the ‘peak’ of the emergent process. An example from virology is presented, in which two seemingly antagonistic systems – the herpes cold sore virus and its host – are capable of altering their basic biological objectives to achieve a new equilibrium. The usual barriers to modeling this process are overcome by incorporating mechanisms from practices centered on its emergent peak: design and katachi. In the Japanese science of form, katachi refers to the emergence of intrinsic structure from real situations, where an optimal balance between implicit influences is achieved. Design indicates how such optimization is guided by principles of flow. These practices leverage qualities of situated abstraction, which we understand through the intuitive method of physicist Kôdi Husimi. Early results indicate that this approach can capture the functional transformations of biological emergence, whilst being reasonably computable. Due to its geometric foundations and narrative-based extension to logic, the method will also generate speculative predictions. This research forms the foundations of a new biomedical modeling platform, which is discussed.