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
Cesàro, E. "Remarques sur la courbe de von Koch." Atti della R. Accad. della Scienze fisiche e matem. Napoli12, 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.
is given by
