Self-Assembly Without Instructions: How Robots Build Structures They Don't Understand
When simple robots follow local rules, complex structures emerge that no individual unit comprehends or controls.
Morphogenesis in Machines: How Swarms Generate Spatial Patterns
From Turing's chemical theory to robotic reality: programming spatial patterns through local interactions and emergent instabilities
Formation Control Through Potential Fields: Attractors, Repellers, and Emergent Geometry
How energy landscapes encode geometric arrangements and the mathematical machinery guaranteeing robots find their formations.
Why Random Motion Works: Ergodic Exploration in Bounded Environments
Mathematical foundations prove that random wandering guarantees complete coverage with predictable scaling
Phase Transitions in Swarm Behavior: Order Parameters and Critical Phenomena
Statistical mechanics reveals the sharp boundaries where robot swarms transform from chaos to collective order
Quorum Sensing in Silicon: How Robots Achieve Collective Decision-Making
Bacterial decision-making principles reveal the dynamical systems theory underlying distributed robotic consensus without central control.
Distributed Optimization: Gradient Descent Across a Swarm
How robot swarms solve global optimization problems through local gradients and neighbor communication—without any central coordinator.
Emergent Traffic Flow: Self-Organizing Paths in Robot Swarms
How simple navigation rules create ordered lanes, stable paths, and deadlock-free flow without central control
Stigmergy: How Robots Coordinate Through Environmental Memory
How encoding coordination state in shared environments enables robot swarms to achieve collective intelligence without communication networks
Why Ant Colonies Compute: P-Complete Problems and Emergent Optimization
How simple pheromone rules implement distributed algorithms that solve computationally hard optimization problems with mathematical guarantees
Gradient Climbing with Noisy Sensors: Collective Chemotaxis in Robot Swarms
How robot swarms extract reliable gradient information from unreliable sensors through biologically-inspired collective computation and distributed estimation
The Reynolds Rules at Fifty: Why Three Simple Rules Still Define Flocking
Three local rules created a field—understanding why separation, alignment, and cohesion remain mathematically necessary for collective motion.
Why Swarm Robots Don't Need Leaders: The Mathematics of Leaderless Coordination
How spectral graph theory proves that robot swarms can achieve guaranteed coordination through network structure alone, without any agent in charge.
Task Allocation Without Negotiation: Response Threshold Models in Swarm Robotics
Mathematical foundations reveal how individual response thresholds generate optimal collective task allocation without communication or central control.