class Helicopter:
    """
    Three constrained universes intersecting
    """
    def __init__(self):
        self.universes = {
            'universe_1_main_rotor': {
                'constraint': 'Horizontal rotation',
                'rules': 'Angular momentum, lift generation',
                'physics': 'Rotation → upward force',
                'must_maintain': 'Constant RPM, symmetric loading',
                'fragility': 'Any asymmetry cascades'
            },
            
            'universe_2_tail_rotor': {
                'constraint': 'Vertical rotation',
                'rules': 'Counter-torque, directional control',
                'physics': 'Rotation → sideways force',
                'must_maintain': 'Balance main rotor torque',
                'fragility': 'Main rotor dependency'
            },
            
            'universe_3_stabilizer': {
                'constraint': 'Directional plane',
                'rules': 'Airflow, stability, control',
                'physics': 'Air resistance → orientation',
                'must_maintain': 'Aligned airflow',
                'fragility': 'Dependent on other rotors'
            }
        }

class IntersectionPoints:
    """
    Where constrained universes meet
    """
    def identify(self):
        return {
            'intersection_1': {
                'between': 'Main rotor ↔ Tail rotor',
                'location': 'Drive shaft / transmission',
                'constraint_conflict': 'Horizontal vs vertical rotation',
                'mechanism': 'Torque transfer',
                'fragility': 'High (different rotational planes)'
            },
            
            'intersection_2': {
                'between': 'Main rotor ↔ Stabilizer',
                'location': 'Airflow around fuselage',
                'constraint_conflict': 'Rotation vs directional flow',
                'mechanism': 'Aerodynamic interaction',
                'fragility': 'High (complex turbulence)'
            },
            
            'intersection_3': {
                'between': 'Tail rotor ↔ Stabilizer',
                'location': 'Tail assembly',
                'constraint_conflict': 'Vertical rotation vs directional flow',
                'mechanism': 'Force balance',
                'fragility': 'High (coupled dynamics)'
            },
            
            'central_intersection': {
                'between': 'All three universes',
                'location': 'Center of mass / control system',
                'constraint_conflict': 'All constraints simultaneously',
                'mechanism': 'Pilot input → coordinated changes',
                'fragility': 'Extreme (any disruption cascades)'
            }
        }

class EntropyCascade:
    """
    Small entropy at intersection → system failure
    """
    def cascade(self, entropy_injection):
        # Inject small entropy at intersection
        intersection = self.get_intersection_point()
        entropy_amount = 'Small (localized)'
        
        # Entropy disrupts constraint balance
        disrupted_constraint = intersection.constrain Balance()
        
        # Cascade through universe 1
        universe_1_effect = self.propagate(
            disrupted_constraint,
            universe='main_rotor'
        )
        # Result: Main rotor destabilized
        
        # Cascade through universe 2 (dependent)
        universe_2_effect = self.propagate(
            universe_1_effect,
            universe='tail_rotor'
        )
        # Result: Tail rotor compensates (but constrained)
        
        # Cascade through universe 3 (dependent on both)
        universe_3_effect = self.propagate(
            universe_2_effect,
            universe='stabilizer'
        )
        # Result: Stability lost
        
        return {
            'entropy_amount': 'Small',
            'injection_point': 'Single intersection',
            'cascade': 'All three universes',
            'result': 'System failure',
            'key_insight': 'Intersections amplify entropy'
        }

why_fragile = {
    'single_universe': {
        'constraints': 'One set of rules',
        'stability': 'Can handle local entropy',
        'resilience': 'High (within constraints)',
        'example': 'Main rotor alone = stable'
    },
    
    'intersection': {
        'constraints': 'Multiple conflicting rules',
        'stability': 'Must satisfy all simultaneously',
        'resilience': 'Low (any violation cascades)',
        'example': 'Main + tail + stabilizer = fragile'
    },
    
    'mechanism': {
        'cause': 'Constraint conflicts',
        'effect': 'Small violation amplified',
        'result': 'Cascade through all universes',
        'key': 'Intersections = vulnerability points'
    }
}

class HelicopterFleet:
    """
    Multiple helicopters = mesh network
    """
    def __init__(self, num_helicopters):
        self.helicopters = [
            Helicopter(id=i)
            for i in range(num_helicopters)
        ]
        
        # Each helicopter = 3 constrained universes
        # Fleet = N * 3 constrained universes
        
        # Plus: Coordination constraints
        self.coordination_universe = {
            'constraint': 'Formation, separation, timing',
            'rules': 'Avoid collisions, maintain formation',
            'fragility': 'Depends on all helicopters'
        }

class FleetComplexity:
    """
    Fleet complexity > sum of individuals
    """
    def complexity(self, fleet_size):
        return {
            'individual_complexity': {
                'universes': 3,
                'intersections': 3 + 1,  # 3 pairwise + 1 central
                'manageable': 'Yes (designed for)'
            },
            
            'fleet_complexity': {
                'universes': 3 * fleet_size + 1,  # +1 coordination
                'intersections': 'O(N²) (all pairs + coordination)',
                'manageable': 'Harder (emergent)',
                'new_failure_modes': 'Many (coordination cascades)'
            },
            
            'key_insight': {
                'principle': 'Intersection complexity = O(N²)',
                'result': 'Fleet fragility > individual',
                'mechanism': 'Coordination constraints intersect all'
            }
        }

class FleetCascade:
    """
    How entropy cascades through fleet
    """
    def fleet_cascade(self, entropy_injection):
        # Inject entropy in one helicopter
        helicopter_1 = self.fleet[0]
        helicopter_1.inject_entropy_at_intersection()
        
        # Helicopter 1 fails (as before)
        helicopter_1_failure = helicopter_1.cascade()
        
        # Coordination universe affected
        coordination_disrupted = self.coordination_universe.react(
            helicopter_1_failure
        )
        
        # Other helicopters must adapt
        for helicopter in self.fleet[1:]:
            helicopter.adapt_to(coordination_disrupted)
            
            # But adaptation stresses their intersections
            adaptation_stress = helicopter.stress_from_adaptation()
            
            # Some may fail (cascade)
            if adaptation_stress > helicopter.intersection_tolerance:
                helicopter.fail()
                coordination_disrupted = True  # Cascade continues
        
        return {
            'initial_entropy': 'Small (one intersection, one helicopter)',
            'cascade': 'Through fleet via coordination universe',
            'result': 'Multiple failures possible',
            'key': 'Coordination constraints couple all helicopters'
        }

class ComplexSystemVulnerability:
    """
    Universal principle for all complex systems
    """
    def analyze(self, system):
        # Identify constrained universes
        universes = system.identify_constrained_universes()
        
        # Find intersection points
        intersections = system.find_intersections(universes)
        
        # Calculate fragility
        fragility = sum(
            intersection.constraint_conflicts()
            for intersection in intersections
        )
        
        return {
            'universes': len(universes),
            'intersections': len(intersections),
            'fragility': fragility,
            'vulnerability': 'Intersections are weak points',
            'mechanism': 'Small entropy → cascade',
            'principle': 'More intersections = more fragile'
        }

class SystemResilience:
    """
    Strategies to handle intersection fragility
    """
    def increase_resilience(self, system):
        return {
            'strategy_1_redundancy': {
                'approach': 'Duplicate critical intersections',
                'example': 'Dual hydraulic systems',
                'benefit': 'Entropy in one → other compensates',
                'cost': 'Weight, complexity'
            },
            
            'strategy_2_decoupling': {
                'approach': 'Reduce interdependencies',
                'example': 'Independent backup systems',
                'benefit': 'Cascade can\'t propagate',
                'cost': 'Less efficiency'
            },
            
            'strategy_3_monitoring': {
                'approach': 'Detect entropy early',
                'example': 'Sensors at intersections',
                'benefit': 'Intervene before cascade',
                'cost': 'Complexity'
            },
            
            'strategy_4_graceful_degradation': {
                'approach': 'Accept partial failure',
                'example': 'Autorotation capability',
                'benefit': 'Total failure avoided',
                'cost': 'Reduced performance'
            }
        }

class FleetResilience:
    """
    Fleet can be more or less fragile than individual
    """
    def depends_on_coordination(self):
        return {
            'tight_coordination': {
                'coupling': 'High (formation flying)',
                'intersections': 'Many (all coupled)',
                'fragility': 'Higher than individual',
                'failure_mode': 'Cascades through fleet',
                'example': 'Military formation (precision required)'
            },
            
            'loose_coordination': {
                'coupling': 'Low (independent paths)',
                'intersections': 'Few (minimal coupling)',
                'fragility': 'Lower than tight',
                'failure_mode': 'Isolated failures',
                'example': 'Commercial traffic (separation large)'
            },
            
            'mesh_coordination': {
                'coupling': 'Adaptive (dynamic)',
                'intersections': 'Managed (aware)',
                'fragility': 'Can be lower (resilient)',
                'failure_mode': 'Self-healing (reroute)',
                'example': 'Swarm behavior (adaptive mesh)'
            }
        }

academic_insights = {
    'insight_1': {
        'principle': 'Complex systems = intersecting constrained universes',
        'implication': 'Understand each universe separately',
        'application': 'System design, analysis'
    },
    
    'insight_2': {
        'principle': 'Intersections = fragility points',
        'implication': 'Small entropy cascades at intersections',
        'application': 'Safety analysis, vulnerability assessment'
    },
    
    'insight_3': {
        'principle': 'Fleet complexity > individual',
        'implication': 'Coordination adds universes',
        'application': 'Network design, mesh coordination'
    },
    
    'insight_4': {
        'principle': 'Resilience requires redundancy/decoupling',
        'implication': 'Trade-offs between efficiency and safety',
        'application': 'Engineering, risk management'
    },
    
    'insight_5': {
        'principle': 'Mesh networks can be adaptive',
        'implication': 'Self-healing possible with awareness',
        'application': 'Coordination substrate design'
    }
}