3d stuff

I’ve been messing around in the 3D space a bit lately with Clover Point and thought I’d throw this cool thing out. 3D Fractals.

Ran across the concept a couple of days ago and they’re awesome…so unbelievably organic.

You know what fractals are right?

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same “type” of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension. The prototypical example for a fractal is the length of a coastline measured with different length rulers. The shorter the ruler, the longer the length measured, a paradox known as the coastline paradox....more (http://mathworld.wolfram.com/Fractal.html)

The following is a 2D Mandelbrot fractal.

In mathematics the Mandelbrot set, named after Benoît Mandelbrot, is a set of points in the complex plane, the boundary of which forms a fractal. Mathematically the Mandelbrot set can be defined as the set of

complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial z_n+1 = z_n² + c remains bounded. That is, a complex number, c, is in the Mandelbrot set if, when starting with z₀=0 and applying the iteration repeatedly, the absolute value of z_n never exceeds a certain number (that number depends on c) however large n gets.

For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,…, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set.

On the other hand, c = i (where i is the square root of -1) gives the sequence 0, i, (?1 + i), ?i, (?1 + i), ?i…, which is bounded and so i belongs to the Mandelbrot set. (from Wikipedia)

OK so that’s all cool, but check out the 3D fractal in this video:

and more here.

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