Polynomials in nature 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.
 A: 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. 
A: The heart of science is inference of how physical, observed, latent and derived quantities that constitute the natural universe are interrelated, to better predict how they will behave in the future and better understand the structure underlying them. This is an aim, regardless of whether the relationship is a universal law or a transient one, such as in stock market fluctuations. Polynomials are vital for describing these relationships, due to their simplicity and practicality and are a staple of approximation theory. Higher degree polynomials often make better approximations *. Functions can represent how these quantities are interrelated but, unless otherwise stated, there is no reason these functions should be inherently well-behaved; they are not necessarily computable, differentiable, and so on. However, when we approximate a set of observed data-points by a polynomial, we are endowed with useful properties of the polynomial that make it tractable to find properties of the function such as roots and slope. In this sense, polynomials occur almost everywhere in nature, as a lens we can use to feasibly view the relationships between natural quantities.
This approach is justified by the Stone-Weierstrass Theorem, which states that continuous functions can be uniformly approximated by a polynomial. The natural quantities we observe can typically be assumed to be continuous, at least to some degree, so this approach applies. If the true function can be represented by a convergent power series, then higher degree polynomials will make better approximations **. For instance, consider the set of discrete observations of a time series, $\big((1,\sin1),\ (2,\sin2),\ (3,\sin3),\ldots,\ (n,\sin n)\big)$. Then, a good approximation of the time series would be $\sin t$, which could be used to interpolate and extrapolate for all real values. Since $\sin t$ can be given by a power series, in this case higher degree polynomials are indeed better approximations to the data set. However, in practice, it is typically better to approximate a function with just a sufficiently high degree polynomial. Using arbitrarily high degree polynomials takes longer to compute and does not always make a better approximation; Runge's phenomenon shows that raising the degree of interpolating polynomials can sometimes increase approximation error.
The advantage of using polynomials over other computable functions (e.g. exponential or trigonometric functions), is that polynomials can be easily evaluated with addition and multiplication alone, which can be easily encoded in bitwise operations; they are continuous, smooth, entire, closed under multiplication and composition, and have asymptotes given simply by their highest power. They also have useful geometric and statistic properties of polynomial roots and have derivatives and integrals, easily obtained by the power rule, which not only describe their slope and quadrature but can sometimes aid root-finding algorithms such as the Newton-Raphson method. These properties all fortify the ability of polynomials to describe the true function they represent.

* This is not always the case. See: Runge's phenomenon.
** See also: Approximating functions by Taylor Polynomials.. 
