If the 4th dimension is time, then there is literally nothing to this.
Export as a pivot painter material. Import it to the engine and play the animation over whatever time you want it to play at.
Also, lets not go around making idiotic terms so that people know what we mean when we say things? (More of a comment for whatever idiot came up with “4D fractals”. But really its a societal problem. If we shovel dirt in these type of people’s face we all live a better life. If we adopt their iodicy we all end up as idiots).
And on that note. There is probably nothing fractal about anything to do with this (based on google results).
Its literally the leaves of a tree moving with wind.
Content examples have (or had) a melting candle.
The exact same idea here.
If you want to introduce a real Fractal part to it. Then you need a system that generates geometry - as such you can code something up using the procedural mesh generator and re-using the same texture, which is the real “essence” of a fractal.
Its easier to fake this in 2d than it is in 3d ofc.
In 3d due to hardware limits you have a maximum vert count to respect…
Infinite geometry isn’t really a thing - but manipulating a vertex position over time is (and its relatively cheap).
So you can come up with actual fractal formulas that allow you to zoom in on a piece of geometry that re-arranges it self to re-present the same element over and over…
Start with exporting whatever you have as an alembic cache - the engine will play that over time without the need for pivot painter.