Loopa: Nonlinear Dynamics

Dive into the fascinating world of non-linear dynamics and chaos theory. This simulator provides an interactive environment to explore mathematical models and observe how small changes in parameters lead to vastly different outcomes.

• 90+ continuous systems: Lorenz, Rössler, Chen, Aizawa, Lü, the full Sprott family, hyperchaotic 4D attractors, Duffing, Van der Pol, FitzHugh-Nagumo, Hindmarsh-Rose, Lotka-Volterra, Chua circuit, double pendulum, and more

• 35+ discrete maps: Logistic, Hénon, Tent, Standard, Gauss, Sine, Circle, Lozi, Ikeda, Tinkerbell, Baker, Bogdanov, Kaplan-Yorke, Zaslavskii, Arnold cat map, and more with cobweb diagram visualization

• Phase space visualization in 2D and 3D with nullclines, flow field, and speed coloring

• Analysis suite: bifurcation diagram, Lyapunov exponent, recurrence plot, basin of attraction, power
spectrum, sensitivity to initial conditions, manifolds, orbit diagram

• Multiple simulation slots for parallel exploration and side-by-side comparison

• Custom system editor for user-defined equations

• Script editor for user-defined scripts that can be applied to the simulation

• Export to SVG, PDF, PNG, and CSV

Loopa is free to try with the Lorenz attractor in 2D and 3D phase space. Unlock all of Loopa with a one-time purchase. No subscription, no ads.