Vector Field vs PerturbLab

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.

See how a tiny change at the start grows into a completely different world. PerturbLab is a chaos and physics simulator with 176 experiments – Double Pendulum, Three-Body orbits, the Lorenz butterfly, Game of Life and more – that run live on your device. Free, offline, no ads, no account. WHAT YOU SEE • Side-by-side comparison: the same system runs twice, one copy nudged by a tiny amount. Watch them move together, then split apart. Overlay both runs and follow the distance between them on a live log-scale chart. • Simple rules, surprising order: Langton's Ant, cellular automata, chip-firing and walkers grow complex patterns from a single rule. • Tipping points: percolation, the Ising magnet, epidemics, traffic jams and synchronization sweep across a critical value so you can see the sudden change happen. WHO IT IS FOR • Students: see sensitive dependence, strange attractors and phase transitions instead of just reading about them. • Teachers: a ready-made classroom demo on iPhone or iPad, with side-by-side runs in landscape on iPad. • Curious minds: endless generative patterns to watch, tweak and share. 176 EXPERIMENTS IN 9 CATEGORIES • Classics and pendulums: Double Pendulum, Triple Pendulum, Spring Pendulum, Driven Damped Pendulum • Celestial and particles: Three-Body, Restricted Three-Body, N-Body, Billiards, Magnetic Pendulum • Oscillators and circuits: Duffing, Van der Pol, Chua's Circuit, Coupled Oscillators • Maps: Logistic Map, Hénon Map, Standard Map, Arnold's Cat Map, Clifford and De Jong attractors • Flows: Lorenz, Rössler, Thomas, Aizawa, Halvorsen and the Sprott family of chaotic flows • Fields and grids: Gray-Scott reaction–diffusion, Kuramoto oscillators, sandpiles, aggregation • Visual systems: fractal ferns, dragon curves, flow fields, iterated function systems • Rule emergence: Langton's Ant, Wireworld, turmites, rule 184 traffic, Pascal's triangle modulo n • Phase transitions: percolation, Ising magnetization, epidemic threshold, forest fires, Kuramoto locking NEW IN THIS VERSION • A short note for every experiment: what it is, what to watch, what to try • Favorites, recent experiments and search • Share the current picture as an image, with the settings that made it • Opens where you left off • Divergence chart and full dark mode • Now in English, Simplified Chinese, Traditional Chinese, Japanese, German and French CONTROLS Presets (Calm, Chaotic, Dramatic), perturbation and trail sliders, 0.25x to 4x speed, random seeds, pause and reset. Every run is reproducible from its seed. PRIVACY Everything runs on your device. PerturbLab has no ads, no tracking, no account and collects no data. Privacy policy: https://anymk.app/privacy/perturblab