Click the image to see how the initially random points are transformed again again, according to the discrete Lotka-Volterra equations: $$\left\{ \begin{aligned}x_{n+1} &= x_n(S - \alpha x_n - \beta y_n)\\ y_{n+1} &= y_n(S - \gamma y_n) \end{aligned}\right.$$ with the parameter values: \(S=\frac{512}{137}, \alpha=\frac{1.17}{137}, \beta=\frac{0.15}{137}, \gamma= \frac{1.09}{137}\).

The first ten transformations show the stretching, folding and squeezing explicitly. This is just interpolation added for viewing pleasure, and such transition does not really occur in the system itself: the discrete "time" has only integer values. The animation then speeds up, showing only actual states at each step. Finally, you get to see the attractor reconstructed from (just!) 1000 iterations. All computed by your browser (JS), as you read.

What else...