Self-organization in computation and chemistry: Return to AlChemy

Area of Science:

• Complex adaptive systems
• Theoretical computer science
• Origin of life studies

Background:

• The emergence of complex systems from simple components is a fundamental question in science.
• Walter Fontana and Leo Buss's 1990s AlChemy model, based on lambda calculus, explored this using computational rules.
• The AlChemy model has been understudied for three decades.

Purpose of the Study:

• Revisit and reproduce the original AlChemy model results.
• Analyze the robustness and emergent properties of the system with modern computational resources.
• Investigate the impact of random generators on system outcomes and explore potential extensions.

Main Methods:

• Utilized lambda calculus as the formal computational model.
• Employed extensive computation to reproduce and test the AlChemy model.
• Analyzed the dynamics of emergent organizations and their stability.
• Characterized random expression generators and their influence on system behavior.
• Developed a constructive proof for extending the model using typed lambda calculus.

Main Results:

• Complex, dynamically stable organizations emerge more frequently than anticipated.
• Emergent organizations exhibit robustness against collapse but fragility in combining into higher-order structures.
• Random generators significantly influence the initial conditions and outcomes.
• The typed lambda calculus extension can simulate transitions in chemical reaction networks.

Conclusions:

• The AlChemy model demonstrates a surprising mix of dynamical robustness and fragility in emergent systems.
• The findings provide a quantitative link between computational models and biochemical reaction networks.
• Potential applications include self-organization in programming languages and quantitative origin-of-life research.