Research Paper#Cellular Automata, Category Theory, Functional Programming, ALife🔬 ResearchAnalyzed: Jan 3, 2026 20:14
Comonads for Cellular Automata
Published:Dec 26, 2025 15:43
•1 min read
•ArXiv
Analysis
This paper introduces a category-theoretical model of Cellular Automata (CA) computation using comonads in Haskell. It addresses the limitations of existing CA implementations by incorporating state and random generators, enabling stochastic behavior. The paper emphasizes the benefits of functional programming for complex systems, facilitating a link between simulations, rules, and categorical descriptions. It provides practical implementations of well-known CA models and suggests future directions for extending the model to higher dimensions and network topologies. The paper's significance lies in bridging the gap between theoretical formalizations and practical implementations of CA, offering a more accessible and powerful approach for the ALife community.
Key Takeaways
- •Introduces a category-theoretical model of CA using comonads.
- •Implements CA with state and random generators for stochastic behavior.
- •Emphasizes the benefits of functional programming for CA modeling.
- •Provides practical implementations of well-known CA models.
- •Suggests future directions for extending the model to higher dimensions and network topologies.
Reference
“The paper instantiates arrays as comonads with state and random generators, allowing stochastic behaviour not currently supported in other known implementations.”