It is hard to make predictions about something that requires 30 dimensions to simulate but we can at least offer a possible mechanism for some of the weak force particles.
Our candidate formula at 30 dimensions takes 5 sets of 6-dimensions at each point and averages them. If these are identical then we get the same stable patterns as in the 6-dimensional approximation.
If we conjecture that we could change 2 of the 5 sets somehow that the differences cancel each other out while maintaining the stability of the pattern, we have 3 possible combinations. One where all 5 6-dimensional subsets are identical, one where 3 are identical and 2 cancel each other out and one where 4 cancel each other out.
Here we show this possibility graphically.
This would explain the generations II and III of the fermions in the standard model.
Up-quarks, down-quarks and electrons are patterns in 6-dimensional space. When we apply the pattern above to them we expect to get a particle with similar properties in 30-dimensional space.
Neutrinos at first appear to pose a problem. They are clearly particles only affected by the weak force. As such they cannot exist in only 6-dimensional space. This means that the left-most state of the diagram cannot exist because it implies a 6-dimensional neutrino. Neutrinos must be able to oscillate between these 3 states (called “flavours” in Physics).
Order 6 does not create any extra dimensions, we remain at 30. Therefore no new particle patterns are possible.