Interactive Particle Flow Explorer

Explore Particle Flow Dynamics

Particle flow systems demonstrate how mathematical vector fields create organic, flowing motion. Each particle follows complex flow equations while leaving beautiful trails that reveal the underlying mathematical structure.

Mathematical Concepts:
• Vector fields and flow equations
• Particle physics and dynamics
• Harmonic motion and turbulence

Applications:
• Fluid dynamics simulation
• Weather pattern modeling
• Electromagnetic field visualization

Live Particle Flow

Flow Dynamics

Flow Strength 0.3

Flow Complexity 0.02

Center Movement 50

Particle System

Max Particles 50

Particle Speed 2.0

Trail Length 20

Visual Effects

Flow Lines On

Flow Opacity 0.3

Presets

Instructions

• Adjust flow strength for particle attraction
• Higher complexity creates turbulence
• Clear particles to see immediate changes
• Try different presets for variety
• Watch mathematical flow patterns emerge

Flow Field Mathematics

Vector Fields: Mathematical functions assigning vectors to space points
Differential Equations: Describe how particles move through fields
Harmonic Motion: Sine/cosine waves create complex patterns
Turbulence: Chaotic behavior from nonlinear interactions
Phase Space: Mathematical representation of system states

Real-World Applications

Weather Systems: Air particle movement and storm formation
Ocean Currents: Water flow patterns and marine navigation
Electromagnetic Fields: Charged particle behavior in fields
Computer Graphics: Realistic fluid and smoke simulation
Biology: Cell movement and swarm behavior modeling