Linkage Font

Erik Demaine and Martin Demaine


Angle code font:

Each letter or number in this alphabet is type of linkage called a “fixed-angle unit 6-chain”, meaning that it is a chain of six unit-length segments, and the measured angle between every two consecutive segments is determined. Because only the measured (convex/3D) angle is constrained, each vertex can be configured in two ways, as either a left or a right turn. Equivalently, for each segment, half of the chain can “spin” 180° around that segment, and all measured angles will remain the same. The two ends of the chain (occasionally at the same place) are marked red; this is sometimes necessary to figure out the sequence of angles from the diagram.

Each linkage is designed to have a unique configuration that looks like a letter or number. In the solved font, each linkage is in the intended configuration, so the text can be read directly. In a randomized font, each linkage is in a random configuration (occasionally the intended one), and it is a puzzle to reconstruct the text. In the angle code font, we just give the sequence of measured angles for each chain, making for an even more challenging puzzle to reconstruct the text. Fixed-angle linkages arise in geometric folding algorithms as mechanical models of protein folding; see, e.g., Chapters 8-9 of Geometric Folding Algorithms.

See our paper about this font.

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