Quaternion (7/21/2009 10:56 pm)
Filed under: Computers
Most of the fractals I've posted so far are drawn by using complex numbers. With a complex number, it's rather intuitive how to turn one number, which is really composed of two real numbers, into points on a plain. This means you can take a simple formula like zn+1=zn2 + c, and calculate for all the points on a plain.
There does exist a mathematical concept known as a quaternion, which can be thought of as a number with four component real numbers. This lets you take the same fractal formulas and render then in three dimensions (Four, really. More on that later.). Here are the Mandelbrot and Julia fractals rendered in three dimensions.
Of course, what's fun for this for me are the silly lengths I went to do create these. Not only did I create the engine to calculate the fractals, but I even went so far as to write the ray-tracer to render them. Yeah, I know it doesn't sound like fun to you, but I'm enjoying it.