Cesàro Fractal

The Cesàro fractal is a fractal also known as the torn square fractal. The base curves and motifs for the two fractals illustrated above are shown below.

Starting with a unit square, the area of the interior for bend angle  is given by

(K. Sinha, pers. comm., Jul. 20, 2005).

REFERENCES:

Cesàro, E. "Remarques sur la courbe de von Koch." Atti della R. Accad. della Scienze fisiche e matem. Napoli 12, No. 15, 1905. Reprinted as §228 in Opere scelte, a cura dell'Unione matematica italiana e col contributo del Consiglio nazionale delle ricerche, Vol. 2: Geometria, analisi, fisica matematica. Rome: Edizioni Cremonese, pp. 464-479, 1964.

Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, p. 43, 1991.

Mandelbrot, B. B. The Fractal Geometry of Nature. New York: W. H. Freeman, pp. 64-65, 1983.

Pappas, T. The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 79, 1989.