Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)

Pages 119–126

An order-*n* half-domino space-filling curve converges to a
tile of area *n*^{2}, two copies of which form the
congruent halves of an *n*×2*n* domino. The
order-2 Hilbert Curve and its square-filling order-*n*
generalizations are special cases where the length of the cut
dividing the halves is *n*. But in a more general case, the
division between the two congruent halves is infinitely long,
self-similar, yet almost-everywhere linear. The most extremely
convoluted half-domino tiles are generated by motifs that are
double-stranded, self-avoiding tendrils. These patterns form an
interesting medium for mathematical, biological, ornamental, tiling,
fabric pattern, and æesthetic exploration.

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