The 2D Random Walk Model

The simulation begins with a dense cluster of particles all positioned at the exact center of a grid. At every time step, each particle independently chooses a random cardinal direction (up, down, left, or right) and takes a single step on the lattice. As particles move, they leave behind temporary trails that slowly fade in opacity and disappear after a short duration to visualize the path history. The color of a particle is determined by local density. Areas with many particles crowded together appear darker, while isolated particles remain lighter.