Interestingly enough, the shape to which all orbits converge looks something like the proverbial butterfly of the paper Lorenz presented in Texas. Although it also looks something like a mask as the image below illustrates. While the attractor appears as two warped disks, their actual structure is far more complex. The Lorenz attractor is less like two CDs melted together and more like two puff pastries baked together. A geometric figure of this sort with an infinite level of detail is called a fractal .
Fractals are the second essential characteristic of chaos.
Sensitive dependence, you will recall, is the first. Chaos always results in the formation of a fractal, but not all fractals are associated with chaos. Probably, the right way to say it is that chaos makes fractals. A puff pastry, by the way, is made by starting with a ball of dough, rolling it out flat, folding it over like a newspaper, rolling that out flat again, folding the result, and so on. Imagine a spot of food coloring added to a sheet of pastry dough.