File:Duffing oscillator strange attractor with color.gif

English: This shows the Duffing oscillator ${\displaystyle x''(t)=x-x^{3}-\alpha x'+\beta *\sin(t)}$ with ${\displaystyle \alpha =0.02}$, ${\displaystyle \beta =3.0}$, with ${\displaystyle x(t)}$ on the x axis and ${\displaystyle x'(t)}$ on the y axis. Points converge toward this strange attractor (here shown are 300k points). This animation starts at $t=0$ and evolves for $8\pi$ time, so four times it arrives at the same shape before the animation repeats. Points are initially colored based on the $x$ coordinate, so as they evolve with time the motion is apparent and one can see how they get folded into their fractal shape.