An order-n half-domino space-filling curve converges to a tile of area n², two copies of which form the congruent halves of an n×2n 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.