  We describe a curious dynamical system that results in sequences of real
numbers in $[0,1]$ with seemingly remarkable properties. Let the function
$f:\mathbb{T} \rightarrow \mathbb{R}$ satisfy $\hat{f}(k) \geq c|k|^{-2}$ and
define a sequence via $$ x_n = \arg\min_x \sum_{k=1}^{n-1}{f(x-x_k)}.$$ Such
sequences $(x_n)_{n=1}^{\infty}$ seem to be astonishingly regularly distributed
in various ways (satisfying favorable exponential sum estimates; every interval
$J \subset [0,1]$ contains $\sim |J|n$ elements). We prove $$ W_2\left(
\frac{1}{n} \sum_{k=1}^{n}{\delta_{x_k}}, dx\right) \leq \frac{c}{\sqrt{n}},$$
where $W_2$ is the 2-Wasserstein distance. Much stronger results seem to be
true and it seems like an interesting problem to understand this dynamical
system better. We obtain optimal results in dimension $d \geq 3$: using
$G(x,y)$ to denote the Green's function of the Laplacian on a compact manifold,
we show that $$ x_n = \arg\min_{x \in M} \sum_{k=1}^{n-1}{G(x,x_k)} \quad
\mbox{satisfies} \quad W_2\left( \frac{1}{n} \sum_{k=1}^{n}{\delta_{x_k}},
dx\right) \lesssim \frac{1}{n^{1/d}}.$$
