AVHn

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_n² + C

where C is the point, and Z₀ = C.

With real X and Y values,
the equivalent equations are:

X_n+1 = X_n² - Y_n² + X₀
Y_n+1 = 2 * X_n * Y_n + Y₀

If a C's Z_n is farther than 2 from 0+0i,
then its later Zs are all far from 0+0i,
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.