https://christopherolah.wordpress.com/2011/08/08/the-real-3d-mandelbrot-set/ Perhaps more than any other area of serious mathematics, fractals and more specifically the Mandelbrot set, have attracted a great deal of public interest. Continuing this pattern, the <http://www.skytopia.com/project/fractal/mandelbulb.html>Mandelbulb set caused a great deal of excitement. As the Mandelbulb website it says, however, theres good reason to believe that it isnt the real McCoy. And so the question is left hanging, what is the real 3D Mandelbrot Set? In this essay, I will present the fractal that I believe deserves this position and why this is the case. <http://christopherolah.files.wordpress.com/2011/08/zrxc800001_doover_fixed_rotated.png> [] What is the Mandelbrot Set? Before we can try and generalize the Mandelbrot set, we need to understand what it is. Answering this requires a substantial amount of mathematical context and I will move somewhat quickly through the basics. If you have trouble following, look up complex numbers or ask me in the comments. Some Basic Complex Analysis The real numbers (the numbers on the number line, 0, 2, -½, ) are extremely useful things that we use in our day to day lives, but in a certain sense, they are missing something. In particular, not all polynomials have real roots, for example, x² = -1 has no real solution for x. If we introduce a number i such that i²=-1, however, it turns out that all polynomials have roots of the form a+bi where a and b are real numbers. While it took mathematicians a surprising amount of time to realize it, the complex numbers have a simple geometric interpretation. Ask yourself, where is i relative to the real number line? It isnt a positive number, since positive numbers times positive numbers are positive numbers and isnt a negative number since negative numbers times negative numbers are postive numbers and it certainly isnt 0! So it isnt on the number line. Then it must be beside the number line! Once one thinks about it this way, the complex plan interpretation is obvious: ... --- co-chair http://ocjug.org/