Fractal patterns can be displayed on NxNxN virtual cubes, for large enough sizes.
Patterns can roughly be divided into 2 groups, depending on wether corners and edges are included or not.
For complex patterns, it may be more straightforward to permute centers only, at the expense of a slight increase in cube size (+2), though.
Algorithms to display patterns have been found by solving the cube layer by layer. Although quite lengthy, this approach works well for all kinds of patterns.
Knowing that fractals are self-similar by nature, I wonder if shorter scalable/self-similar algorithms could be found too, at least for a few patterns. I haven't gone any further yet, so this is an open subject.
A few patterns are shown below. See document Fractal Cube Patterns
for more details and better resolution pictures.