# Strange Attractors Gallery - 奇异吸引子集锦

Interactive 3D visualization of chaotic attractors beyond Lorenz — Rössler, Halvorsen, Clifford, Aizawa, Thomas, Dadras, Sprott systems

> Canonical page: https://elysiatools.com/en/visualizations/strange-attractors

- **Category:** Math

## Overview

Interactive 3D visualization of chaotic attractors beyond Lorenz — featuring 7 systems: Rössler (1976, simplest chaotic autonomous system with period-doubling route to chaos, dx/dt = -y-z, dy/dt = x+ay, dz/dt = b+z(x-c)), Halvorsen (3D chaotic system with 3-fold symmetry, a=1.89), Clifford (discrete 2D iterated map producing fractal patterns with density-based rendering, x'=sin(ay)+c·cos(ax)), Aizawa (bowl-shaped attractor with spiral structure), Thomas' cyclically symmetric attractor (only sin() nonlinearities, b=0.208186), Dadras-Momeni (two-scroll and four-scroll chaotic attractors with multiple equilibria), and Sprott Case A (one of the simplest known chaotic systems from Sprott's exhaustive 1994 search, dx/dt=y, dy/dt=-x+yz, dz/dt=a-y²). Features RK4 numerical integration for continuous systems, discrete iteration for Clifford map, interactive 3D rotation with mouse/touch drag, adjustable parameters a/b/c/d per system with real-time trail reset, variable integration steps per frame (10-200), trail length (2000-30000 points), time step dt (0.001-0.05), auto-rotation speed control, toggle axes and depth coloring, system equations display, coordinate readout, Clifford density map rendering with hot colormap, distinct color palettes per attractor, bright trajectory head with glow effect, perspective projection, blowup detection with automatic reset, and comprehensive educational content covering strange attractor theory (fractal geometry, Hausdorff dimension, sensitive dependence), Lyapunov exponents (λ₁>0 expansion, λ₂=0 flow, λ₃<0 contraction, Lyapunov dimension), bifurcation routes to chaos (period-doubling, intermittency, crisis, quasi-periodicity breakdown), detailed system descriptions with equations and default parameters, and applications in chaos-based cryptography, engineering control (OGY method), biological systems (cardiac dynamics, neural networks, epidemiology, Takens' theorem), and physics/chemistry (lasers, BZ reactions, turbulence, 3-body problem, plasma). Perfect for nonlinear dynamics education, chaos theory exploration, and discovering the diverse topology of strange attractors beyond the Lorenz system.

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