steps: given the following parametric equations: $x_{n+1} = a_0 + a_1x + a_2x^2 + a_3y + a_4y^2 + a_5xy$ $y_{n+1} = a_6 + a_7x + a_8x^2 + a_9y + a_{10}y^2 + a_{11}xy$ 1. Assign random values (from -1 to 1) to all values of $a_i$ it will look something like this: $x_{n+1} = -0.3 - 0.5x - 0.9x^2 + 0.9y + 0.8y^2 - 0.6xy$ $y_{n+1} = -0.1 + 0.9x - 0.6x^2 - 0.3y - 0.7y^2 + 0.9xy$ We now have our attractor! ...But what do we actually do with it? 2. Pick an initial point, lets call it $P$ For simplicity we can start at $(0, 0)$, giving us $P = (0, 0)$ Using our $x_{n+1}$ and $y_{n+1}$ equations we can plug $P$ into them as many times as we wish, generating a new point $P_{n+1}$ using the equation $P_{n+1} = (x_{n+1}(P_x, P_y), y_{n+1}(P_x, P_y))$ 3. Calculate $P_{n+1}$ and plot! 1 Use the slider to generate points 2 through 10 This is what we get after repeating step 3 nine times!

The result of our work is a little cool--at least to me--but it's really nothing "strange". Why then are they called "strange attractors" and what is an "attractor" anyways? Put simply, an attractor is a system that attracts points to certain positions in 2D space. In the example above, our point $P$ is being attracted to the point (-infinity, -infinity), which is called diverging. Since we randomly generated our example, there's an infinite number of other attractors! Some of which converge to a single point or certain paths. Okay... But what makes them strange? Well, 99% of the time an attractor will simply diverge to infinity, but the rest you will find act pretty strangely. That's really the only reason they're named that! generate new attractor I don't know about you, but I really find these beautiful. at least some of them. You can use the "generate new attractor" button if you're displeased. add dimension