To create the Mandelbrot set, you just repeat these geometrical actions for every point in the plane. Multiplying numbers on the complex plane is the same as rotating it, and addition is like shifting the plane in a particular direction. This approach works thanks to the properties of the “complex plane”, a mathematical landscape where ordinary numbers run from “east” to “west”, while “imaginary” numbers, based on the square root of -1, run from “south” to “north”. “You can use complex maths but you can also look at things geometrically.” “I was trying to see how the original 2D Mandelbrot worked and translate that to the third dimension,” he explains. Two years ago, he decided to find a “true” 3D version of the Mandelbrot. Yet none of these techniques offer the detail and self-similar shapes that White believes represent a true 3D fractal image. Spinning the 2D Mandelbrot fractal like wood on a lathe, raising and lowering certain points, or invoking higher-dimensional mathematics can all produce apparently three-dimensional Mandelbrots.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |