Chaos Theory Poster

More information than you probably wanted to know about this poster: I made the program that generated this poster using C++. The background is a Julia fractal. (If you have fractal software and want to recreate this fractal, its coordinates in imaginary space are .383333 + .4125i ...) The full image of the fractal has dimensions of 4000x2000 pixels. But each pixel is rendered with "subpixel resolution" (for lack of a better term) anti-aliasing. Essentially, for every pixel, instead of computing the colour value for just that pixel, the software computes the values for smaller, finer values of the fractal in a 4x4 matrix and then colours the pixel based on the average colour of the precomputed 4x4 matrix corresponding to that point. In other words, it's the same as if I rendered the original image with a size of 16000x8000 and resized it to 25% of its original size taking an average value for each pixel. The triangle things are 3D variations of a fractal called the sierpinski triangle. (A quick search on the internet can bring up hundreds of pictures of the sierpinski set.) The 3D variation is in the shape of a tetrahedron, but (in the case of this poster at least) the three-dimensional shape is rendered using the same algorithm as its two-dimensional counterpart. The algorithm is called the "Chaos Game" algorithm, which can also be found with a quick Google search. The fuzziness of the sierpinski fractals is due to the fact that the Chaos Game algorithm is an explicit formula, which means rather than being able to compute exactly the colour value for each pixel (as I was able to do with the Julia fractal) the triangles must be drawn as a series of random dots. (A better (i.e. implicit) algorithm for drawing this fractal might exist, but I didn't want to do a whole lot of research, I just wanted a cool poster.) As far as I know, the poster doesn't have anything directly to do with chaos theory, but I like the name.