Vector Field vs Physarum

Vector Field lets you create and visualize mathematical vector fields with thousands of animated particles. Enter your own equations, adjust the simulation instantly, and watch how particles move through 2D, 3D, or spherical spaces. Whether you are studying differential equations, experimenting with dynamical systems, teaching vector calculus, or simply exploring mathematical patterns, Vector Field turns equations into interactive motion. Features: • Visualize vector fields in 2D, 3D, and on a sphere • Define custom dx, dy, and dz equations using x, y, z, and time t • Use built-in function presets or save your own • Adjust particle speed, density, lifetime, colors, and ranges • Animate time-dependent fields • Normalize vectors to focus on direction • Rotate 3D views interactively • Powered by Metal for smooth real-time rendering • Create, tweak, and discover vector fields directly from your device.

Explore artificial life through a living, flowing simulation inspired by Physarum polycephalum, the slime mold famous for forming networks, solving paths, and showing intelligence without a brain. Physarum turns simple local rules into complex motion. Thousands of agents sense trails, turn, move, and deposit new traces. As the field evolves, branching networks, waves, and organic textures emerge in real time. Use Physarum to: - Tune sensor distance, turn angle, movement, and trail strength - Paint into the field and guide the simulation by touch - Explore chaotic, branching, and self-organizing patterns - Save and restore interesting agents, fields, and rules - Create vivid generative visuals with color controls It is part science toy, part generative art studio, and part meditative visual instrument. Whether you study emergent systems, teach artificial life, or simply enjoy hypnotic motion, Physarum gives you a hands-on way to watch complexity grow from simple behavior.