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Particle Simulator

Visualize complex particle trajectories through dynamic mathematical formulas

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What is Particle Simulator?

Particle Simulator is a real-time physics simulation and visualization engine that lets you define particle motion through custom mathematical formulas. Built with React and Three.js, it provides an interactive 3D environment for exploring complex force equations and particle dynamics. Whether you’re studying physics, prototyping simulations, or just exploring beautiful mathematical patterns, Particle Simulator makes it easy to visualize particles in motion.

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Key Features

Mathematical Formula Engine

Define forces using dynamic mathematical expressions with trigonometry, hyperbolic functions, and custom operators

Dual Simulation Modes

Choose between kinematic mode for pure trajectories or dynamic mode for mass-based physics

3D Visualization

Real-time 3D rendering with particle trails, force vectors, axes, and interactive camera controls

Event System

Create conditional triggers that pause simulation or change particle properties when conditions are met

Physics Accuracy

Velocity Verlet integration ensures accurate particle motion even with complex force fields

Configuration Management

Save and load complete simulation setups including all particles, forces, and environment settings

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Quick Example

Define a particle affected by a Lissajous resonance pattern: 
// Position
x₀ = 10, y₀ = 0, z₀ = 0

// Forces
Fx = -x
Fy = -2.25 * y
Fz = sin(t * 0.5) * 5
Watch as the particle creates beautiful 3D patterns in real-time.

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Getting Started

Quickstart

Get up and running in minutes with your first particle simulation

Formula Syntax

Learn the mathematical functions and operators available for defining forces

Physics Guide

Understand the physics principles behind the simulation engine

Examples

Explore pre-built examples of complex particle trajectories

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Use Cases

  • Physics Education: Visualize force fields, trajectories, and particle interactions in real-time
  • Simulation Prototyping: Test and validate physics equations before implementing in production
  • Mathematical Art: Create beautiful patterns through parametric equations and force dynamics
  • Research: Explore complex multi-particle systems with customizable physics parameters

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