×

Brownian Motion Simulation

What is Brownian Motion?

Brownian motion is the random movement of particles suspended in a fluid (liquid or gas) resulting from their collision with fast-moving molecules in the fluid. This simulation demonstrates the physics of particle interactions, including:

• Particle collisions: Particles repel each other when they get too close
• Brownian forces: Random forces that cause particles to move erratically
• Boundary interactions: Particles bounce off the walls of the container
• Gravity: Optional gravitational force can be applied

Controls:

• ⏯️ Playback: Reverse time direction, Pause/Resume, increase/decrease simulation speed (×2, ÷2)
• ⚙️ dt (Time Step): Adjust precision - Reset, ×2, ×10, ÷2, ÷10. Smaller dt = more accurate but slower
• 👁️ Display: Toggle particle visibility
• 🔷 Object: Create predefined shapes:
  • None: No object
  • HV Shape (small): Small H-V pattern
  • Geometric Shapes: Hexagon, Spiral, Flower, Diamond, Plus, Pentagon, Octagon
  • Rings: Double Ring, Big Ring
  • Spiral Star: Star-shaped spiral pattern
  • Fractal Tree: Starfish-like fractal pattern
  Set object radius (R) before creating
• ⚛️ Particles:
  • Count: Number of particles (0-10000)
  • Layout: Grid (ordered) or Random placement
  • Radius: Particle size
  • Zero velocity: Start particles with zero initial velocity
• 🌍 Gravity: Enable and set X/Y components (default Y=60 for downward gravity)
• ⚙️ Integration Method:
  • Euler (Semi-Implicit): Fast, good for most cases, stable
  • Runge-Kutta 4 (RK4): More accurate, better for complex dynamics, slower
  • Verlet: Best energy conservation, ideal for long simulations, symplectic
• 💥 Collision Model:
  • Elastic (Spring): Particles repel with spring-like forces, energy conserved (default)
  • Inelastic (Damped): Damped spring forces, energy dissipates over time
  • Hard Body: Instantaneous impulse-based collisions, perfect momentum transfer, no overlap
• 🔄 Actions: Restart simulation, Show Help
• 👋 HotHand: Click on canvas to create a particle manipulator. Click and drag to move particles, click again to release

Status Bar:

• Left side: Legend showing particle types (Normal, Under Force, HotHand)
• Right side: Real-time statistics:
  • Particles: Current particle count
  • Time Step: Current dt value
  • Kinetic Energy: Total kinetic energy (0.5 × m × v²)
  • Potential Energy: Total potential energy from particle compressions
  • Total Energy: Sum of kinetic + potential energy

Tips:

• Start with default settings (36 particles, Euler, Elastic) to see basic Brownian motion
• Create different shapes and watch how they interact with particles - shapes are made of particles too!
• Enable gravity (Y=60) to see particles fall and settle at the bottom
• Use HotHand to push particles around and observe their reactions
• Try different integration methods: Euler for speed, RK4 for accuracy, Verlet for energy conservation
• Hard Body collisions work best with RK4 or Verlet integration - particles won't stick to boundaries
• Watch the energy statistics - in Elastic mode with Verlet, total energy should remain relatively constant
• Adjust dt for faster (larger dt, less accurate) or slower (smaller dt, more accurate) simulations
• Try creating a Fractal Tree object with many particles for interesting dynamics
• Use "Zero velocity" checkbox to start particles at rest, then watch them accelerate due to collisions

(c) kusaku 2001 - Brownian Motion Simulation
No rights reserved - Modernized for modern browsers