A Program for Simulating Brownian Motion of a Single Particle

I have developed a compact program for simulating Brownian motion that has been thoroughly verified for accuracy. The program generates random particle trajectories through numerical implementation of stochastic differential equations, typically using Wiener processes or random walk algorithms. Users can observe the emergent random motion patterns through real-time visualization of particle paths. The simulation supports adjustable parameters including diffusion coefficients, time steps, and boundary conditions, enabling the study of Brownian motion under various physical scenarios. This implementation helps demonstrate the fundamental nature of random particle motion and facilitates investigation into the regularity and practical applications of this phenomenon through customizable experimental setups. The core algorithm employs Monte Carlo methods with Gaussian-distributed step sizes, ensuring physically realistic motion simulation.