[0,1] is not a Minimality Detector for [0,1]^2

This paper shows that there exists a non-minimal sequence $\bar{x} \in ([0,1]^2)^{\mathbb{N}}$ such that for any continuous function $f:[0,1]^2 \to [0,1]$, the sequence obtained by mapping terms of $\bar{x}$ by $f$ is minimal.