Towards chemistries in dynamical systems

2026-07-21

AI Summary

This work proposes a modeling framework that maps arbitrary dynamical systems onto chemical-reaction-like processes by defining “positions,” “species existence,” and “reaction rules” between states, thereby describing system evolution as updates to chemical equations constrained by a “minimal unique reaction path.” This approach constitutes the first systematic formalization of general dynamical systems using chemical language, ensuring that each state transition is driven by the smallest possible set of reactions that is also uniquely determined. Applied to the glider in Conway’s Game of Life, the framework successfully reproduces its dynamic behavior and demonstrates the feasibility of the proposed constraint, while simultaneously highlighting inherent limitations of the current methodology.

Abstract

Chemistry describes aspects of the universe in terms of molecules and their reactions. In this exploratory work we present a way to describe aspects of any dynamical system in similar terms. To describe a dynamical system in this way three decisions have to be made. The first is how many different "places" there are at which molecules or chemical species can occur; the second is how to determine the species present (or not) at each place; and the third is the set of transitions and reactions that can occur between the species in the various places. For these choices to be compatible with the state update of the dynamical system each state must be able to determine transitions that take the currently occurring molecules to those occurring in the updated state. We also propose an additional requirement that there is always a unique way to choose the least amount of transitions occurring during state updates. We discuss gliders in the game of life cellular and argue that when following their definition of according to Randall Beer they satisfy the additional criterion as well. We also point out some issues with the approach.

Problem

• dynamical systems
• chemical representation
• state update
• molecular analogy
• reaction transitions

Innovation

• dynamical systems
• chemical representation
• state transitions
• cellular automata
• minimal reaction set