We construct a nontrivial three-dimensional subshift of finite type whose projective $\Z$-subdynamics, or $\Z$-trace, is 2-sparse, meaning that there are at most two nonzero symbols in any vertical column. The subshift is deterministic in the direction of the subdynamics, so it is topologically conjugate to the set of spacetime diagrams of a partial cellular automaton. We also present a variant of the subshift that is defined by Wang cubes, and one whose alphabet is binary.

翻译：我们构造了一个非平凡的三维有限型子转移，其投影$\Z$-子动力学（或$\Z$-迹）具有2-稀疏性，即任一垂直列中至多包含两个非零符号。该子转移在子动力学方向上具有确定性，因此拓扑共轭于某部分元胞自动机的时空图集合。我们还给出了该子转移的两个变体：一个由Wang立方体定义，另一个的字母表为二进制。