| title |
type |
status |
created |
tags |
semantic_relations |
| Systems Index |
index |
stable |
2024-02-07 |
| systems |
| complexity |
| emergence |
|
|
Systems Index
Core Systems Theory
Fundamental Concepts
System Properties
System Dynamics
Complex Systems
Emergence Patterns
# Basic emergence simulation
class EmergentSystem:
def __init__(self, config):
self.agents = initialize_agents(config)
self.environment = create_environment(config)
def update(self, dt):
"""Update system state."""
# Local interactions
for agent in self.agents:
neighbors = self.get_neighbors(agent)
agent.interact(neighbors)
# Global patterns emerge
patterns = analyze_patterns(self.agents)
return patterns
Collective Behavior
# Collective behavior framework
class CollectiveBehavior:
def __init__(self, config):
self.population = create_population(config)
self.interaction_rules = define_rules(config)
def simulate(self, steps):
"""Simulate collective behavior."""
for step in range(steps):
# Update individual behaviors
for individual in self.population:
local_info = get_local_information(individual)
individual.update(local_info)
# Analyze collective patterns
collective_state = analyze_collective(self.population)
record_state(collective_state)
Self-Organization
# Self-organizing system
class SelfOrganizingSystem:
def __init__(self, config):
self.components = initialize_components(config)
self.energy = config.initial_energy
def evolve(self, time):
"""Evolve system organization."""
while self.energy > 0:
# Local interactions and reorganization
self.components = update_organization(
self.components,
self.energy
)
# Energy dissipation
self.energy = dissipate_energy(self.energy)
# Measure organization
organization = measure_organization(self.components)
record_organization(organization)
Implementation Examples
Ant Colony System
class AntColony:
def __init__(self, config):
self.agents = create_agents(config)
self.environment = create_environment(config)
self.pheromone_grid = np.zeros(config.grid_size)
def update(self, dt):
"""Update colony state."""
# Agent updates
for agent in self.agents:
# Sense environment
local_state = self.environment.get_local_state(
agent.position
)
# Update agent
agent.update(dt, local_state)
# Modify environment
self.environment.update(agent.position)
# Environment updates
self.pheromone_grid *= self.config.pheromone_decay
Neural Networks
class EmergentNetwork:
def __init__(self, config):
self.neurons = create_neurons(config)
self.connections = initialize_connections(config)
def update(self, dt):
"""Update network state."""
# Compute activations
for neuron in self.neurons:
inputs = gather_inputs(neuron, self.connections)
neuron.activate(inputs)
# Update connections
for connection in self.connections:
connection.update(dt)
Swarm Systems
class SwarmSystem:
def __init__(self, config):
self.agents = create_swarm_agents(config)
self.space = create_space(config)
def update(self, dt):
"""Update swarm state."""
# Update agent positions
for agent in self.agents:
neighbors = self.space.get_neighbors(agent)
agent.update_position(neighbors, dt)
# Analyze swarm behavior
coherence = compute_coherence(self.agents)
alignment = compute_alignment(self.agents)
Mathematical Foundations
Dynamical Systems
Network Theory
Statistical Physics
Applications
Biological Systems
Social Systems
Artificial Systems
Research Directions
Current Research
Open Questions
Related Resources
Documentation
Knowledge Base
Learning Resources
