Combinatorial Mechanical Metamaterials

The structure of most mechanical metamaterials is periodic so that their design space is that of the unit cell. Here we introduce a combinatorial strategy to create a vast number of distinct mechanical metamaterials, each with a unique spatial texture and response. These are aperiodic stackings of anisotropic building blocks, and their functionality rests on both the block design and their stacking configuration which is governed by a tiling problem. We realize such metamaterials by 3D printing, and show that they act as soft machines, capable of pattern recognition and pattern analysis.