Lévy Fractal

A fractal curve, also called the C-curve (Gosper 1972). The base curve and motif are illustrated below.

Duvall and Keesling (1999) proved that the Hausdorff dimension of the boundary of the Lévy fractal is rigorously greater than one, obtaining an estimate of 1.934007183.

REFERENCES:

Dixon, R. Mathographics. New York: Dover, pp. 182-183, 1991.

Duvall, P. and Keesling, J. "The Hausdorff Dimension of the Boundary of the Lévy Dragon." 22 Jul 1999. http://arxiv.org/abs/math.DS/9907145.

Gosper, R. W. Item 135 in Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, pp. 65-66, Feb. 1972. http://www.inwap.com/pdp10/hbaker/hakmem/flows.html#item135.

Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, pp. 45-48, 1991.

Lévy, P. "Les courbes planes ou gauches et les surfaces composées de parties semblales au tout." J. l'École Polytech., 227-247 and 249-291, 1938.

Lévy, P. "Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole." In Classics on Fractals (Ed. G. A. Edgar). Reading, MA: Addison-Wesley, pp. 181-239, 1993.ش