Odd brain exercise I find entertaining: Using only knowledge about this universe, try to determine what kind of universe would be most likely to simulate our kind of universe.

For example, to my eye, general relativity, plus the propensity of pi to pop up in odd places, implies something like a hierarchy-relative polar coordinate system is the standard mathematical model in our host universe, as opposed to the Cartesian coordinate system we tend to default to. So, what would a universe look like such that this is the most intuitive way of considering data? Seems most likely that such a view is most likely to arise in a nonoriented universe; gravity would be unlikely, as gravity provides a natural plane of orientation, so something like universal attractive and repulsive forces probably wouldn't exist.