I made the Mandelbrot fractal in Blender

using nothing but the node system.
^{1)}

If you like, download and play with it.
^{2)}

Click on any picture to see a full-sized version.

The fractal exists in the complex plane.
^{3)}

A 2D image, with Red and Green values

for Real and Imaginary numbers, suffices.

This equation is applied to each point:

Z_{n+1} = Z_{n}^{2} + C

where C is the point, and Z_{0} = C.

With real X and Y values,

the equivalent equations are:

X_{n+1} = X_{n}^{2} - Y_{n}^{2} + X_{0}

Y_{n+1} = 2 * X_{n} * Y_{n} + Y_{0}

If a C's Z_{n} is farther than 2 from 0+0*i*,

then its later Zs are all far from 0+0*i*,

and that C is not a part of the fractal.

Cs that remain have blue added.

Here are all of the nodes

to calculate on iteration:

Nodes are grouped together

for organization and density.

In the end, each shade of blue

is turned into a different color,
^{4)}

and the center is turned to black.

The image is sharpened

by calculating repeatedly.

This gives a pretty result.

With more iterations,

the color bands get

harder to tell apart.

Multiplying the normalized steps

and moduloing them back to 0-to-1

makes the colors easier to distinguish.

After figuring this much out,

I found out regerogarc did, too.

I am working on better versions

and neat tricks for this project.

I will post updates when they're done.