Iterating the first step. Constructing the Sierpinski Triangle. The Sierpinski Triangle. This time we get a value between 1 and 2. The trajectory of a strange attractor cannot intersect with itself.
Nearby trajectories diverge exponentially.
But the attractor is bounded to the phase space. The trajectory does not fill the phase space. A strange attractor is a fractal, and its fractal dimension is less than the dimensions of its phase space. The Mandelbrot set is the set of points that are not in the Escape Set. The Mandelbrot set.