There must be endless possibilities this was just the first test. im guessing 4D means that the math is done in 4D and the result we see is its projection down into 3D similar to a hypercube.

It just means there are four input parameters. The examples I can think of are:

- Simply connect the 4th to object info/random. Instances of the material will vary.
- For a 3D texture, connect the 4th to time to animate it.
- For a 2D texture, connect the 3rd and 4th to animate it, loopable.
- For a 2D texture, you can construct the 3rd and 4th to make the texture seamless. I believe two generators are required (one with cylindrical lookup for seamless in one dimension), but there should be no spatial density variations, something I’ve not been able to avoid for blended repeats in 2 dimensions (toroid lookup also has spatial density variation).

A hypercube is just the 3D shadow of a 4 dimensional cube (in 4D, all those lines are perpendicular to eachother, similar to how two connected squares in 2D we can imagine is an actual 3D box). Not relevant for anything we do afaik.