Stacking Disorder in Periodic Minimal Surfaces

We construct 1-parameter families of non-periodic embedded minimal surfaces infinite genus in $T \times \mathbb{R}$, where $T$ denotes a flat 2-tori. Each our converges to foliation \mathbb{R}$ by $T$. These then lift $\mathbb{R}^3$ that are periodic horizontal directions but not the vertical direction. In language crystallography, construction can be interpreted as disordered stacking layers periodically arranged catenoid necks. Our work is motivated experimental observations twinning defects surfaces, which we reproduce special cases disorder.