Earlier, I made the Mandelbrot Fractal
using only Blender's built-in graphics tools. 
Now, it is easier to modify and animate.
Here it is to download and play with. 
Click on any picture to see a full-sized version.
The first stage, generating the coordinate texture,
has been simplified by using geometry nodes
which are intended for manipulating normals. 
The new setup has fewer nodes, supports rotation,
and has explicit inputs for center, angle, and size.
The first version required planning and math
to make renders of different parts of the set.
The explicit inputs in the new version
make it easy to predict and control
the new image that will be rendered.
Self-similar images, like the Mandelbrot set,
look very good in looping zoom animations.
The new coordinate inputs make these easy.
Keyframe a starting location, size, and rotation,
keyframe another for the end, and render.
Blender supports Python scripting,
but no scripts are used in this project.
To learn how this project works,
read the original blog post.
Like the original, this project
was made with Blender 2.79b.
It should also work in the latest version.
I am happy with this screenshot.
It shows every unique node in the project.
This works because normals
are represented as RGB values.
Similarly, this project uses RGB values
to represent real, imaginary, and iterations.
Since they just manipulate RGB values,
the normal transformation nodes work perfectly
for transforming complex numbers.