Density of possible pentagon centers outside a disk

Let $P_0$ be the original pentagon in the Eden model, and let $u_1,u_2,u_3,u_4,u_5$ be the five possible translation vectors between centers of neighboring pentagons. The set of possible centers is generated subject to the non-overlapping constraint of the model. Density conjecture. The set of possible centers of pentagons in the model is dense outside a disk around the origin. The claim concerns how the irrational relations among the translation vectors interact with the geometric non-overlap constraint; the source gives no further result establishing or disproving this density.