A Fractal curve, also called the C-Curve (Beeler et al. 1972, Item 135). The base curve and motif are illustrated below.
See also Lévy Tapestry
References
Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT
Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972.
Dixon, R. Mathographics. New York: Dover, pp. 182-183, 1991.
Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press,
pp. 45-48, 1991.
Weisstein, E. W. ``Fractals.'' Mathematica notebook Fractal.m.