Summary: We describe a curious dynamical system that results in sequences of real numbers in \([0,1]\) with seemingly remarkable properties. Let the even function \(f:\mathbb{T}\to\mathbb{R}\) satisfy \(\hat{f}(k)\geq c|k|^{-2}\) and define a sequence via \[ x_n =\arg\min\limits_x\sum\limits_{k=1}^{n-1}f(x-x_k). \] 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 \[ W_2(\mu,\nu)\leq\frac{c}{\sqrt{n}},\text{ where }\mu=\frac{1}{n}\sum_{k=1}^n\delta_{x_k} \] is the empirical distribution, \(\nu=dx\) is the Lebesgue measure and \(W_2(\mu,\nu)\) is the 2-Wasserstein distance between these two. Much stronger results seem to be true and it is 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 \[ x_n=\arg\min\limits_{x\in M}\sum_{k=1}^{n-1}G(x,x_k )\text{ satisfies }W_2\left(\frac{1}{n}\sum\limits_{k=1}^n\delta_{x_k},dx\right)\lesssim\frac{1}{n^{1/d}}. \]