>Most systems "minimizing their potential" exhibit a crystalline, ordered arrangement.
crystalline structures have lower entropy compensated by increase in the entropy of the environment due to heat being transferred out of crystalline structure during its formation.
It is kind of intuitively obvious that hyperuniform(random) forest have higher entropy than crystalline style ordered forest would have. I don't see connection to environment (like heat transfer in crystal case) that would allow to compensate for decrease of entropy in an ordered forest.
That is a good point. But without getting too technical (although I'd love too if wanted), there are 2 caveats with your thought:
1. Order does not need heat transfer. Flying birds form a V-shaped pattern (to minimize drag, whatever), fish "order" into a packed school instead of being random, a honeycomb is hexagonal. Those are (near) optional solutions for constraints. There is an analogy with crystal formation but the math is not totally clear.
2. Crystals can have higher entropy than disordered states. Actually, a (crystalline) dense packing of Brownian spheres have higher entropy than a random close packing of spheres.
Trees are a kind of literal poisson disk. Because trees capture light and nutrients, there's a minimum viable spacing between them which enforces some separation. But seed distribution either clusters around each tree, or looks for gaps, depending on the seeding strategy.
So I'm not surprised you get a hyperuniform distribution. It's not truly random, because there's a pull towards maximum packing density in one direction, balanced by a push towards a spatial expansion distribution around each tree in the other.
Intuitively, I'd suspect this pull/push balance explains most hyperuniform distributions.
crystalline structures have lower entropy compensated by increase in the entropy of the environment due to heat being transferred out of crystalline structure during its formation.
It is kind of intuitively obvious that hyperuniform(random) forest have higher entropy than crystalline style ordered forest would have. I don't see connection to environment (like heat transfer in crystal case) that would allow to compensate for decrease of entropy in an ordered forest.