What polynomials occur in "nature"? I am interested in polynomials of degree three and higher. I am aware of Stefan Boltzmann Law and Chemical Equilibrium Examples.
Edit:
There are some formulas under beam deflection category.
I am particularly interested in full polynomials, as opposed to pure power laws. For example $y=at^2+v_0 t + y_0$ for a projectile uses a complete polynomial, while Boltzman law is just a power law.
Power Laws are probably what you are looking for and are very, very prevalent in physics, economics, linguistics and well, nature. They occur for phenomena that exhibit scale invariance. All forms of exponents occur. The M-sigma law has a power of 4 for example.