In my last post , we played The Chaos Game and ended up with a Sierpinski Triangle. It’s quite nice as far as it goes, but there is not a lot of variation and visual interest beyond the initial surpise of finding it buried in the chaos at all. This time around, lets look at the de Jong attractor. First, some terminology! An Attractor is a dynamic system with a set of numeric values to which the system tends to evolve over time, no matter what state it starts in. An attractor is called a Strange Attractor if it contains a fractal element. The Sierpinski Triangle we came up with last week is an example of a strange attractor. It doesn’t matter what your starting point is (it could be miles away from the triangle), you will eventually get pretty much the same result for any given triangle. The de Jong attractor is another example of a strange attractor.
Today, we’ll play The Chaos Game! It’s easy to play, and it goes like this: First, put three points on your paper. These will be the vertices of a triangle (so don’t put them in a straight line!) Any triangle will work, but be sure to leave lots of area inside where the triangle will be to make it easier to see what it going on. Next, you need a way to randomly choose one of those vertices over and over. You can roll a die, and if you get a 1 or a 2, that could reference the first vertex, a 3 or a 4 could reference the second vertex, and a 5 or a 6 could reference that last vertex. If you are a Dungeons and Dragons player and happen to have a 3-sided die, feel free to use that!