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We consider the hexagonal circle packing with radius $1/2$ and perturb it by letting the circles move as independent Brownian motions for time $t$. It is shown that, for large enough $t$, if ${𝛱}_t$ is the point process given by the center of the circles at time $t$, then, as $t\to \infty$, the critical radius for circles centered at ${𝛱}_t$ to contain an infinite component converges to that of continuum percolation (which was shown – based on a Monte Carlo estimate – by Balister, Bollobás and Walters to be strictly bigger than...