Barnsley's Fern

The attractor of the iterated function system given by the set of "fern functions"

			(1)
			(2)
			(3)
			(4)

(Barnsley 1993, p. 86; Wagon 1991). These affine transformations are contractions. The tip of the fern (which resembles the black spleenwort variety of fern) is the fixed point of , and the tips of the lowest two branches are the images of the main tip under  and  (Wagon 1991).

REFERENCES:

Barnsley, M. Fractals Everywhere, 2nd ed. Boston, MA: Academic Press, pp. 86, 90, 102 and Plate 2, 1993.

Gleick, J. Chaos: Making a New Science. New York: Penguin Books, p. 238, 1988.

Trott, M. Graphica 1: The World of Mathematica Graphics. The Imaginary Made Real: The Images of Michael Trott. Champaign, IL: Wolfram Media, pp. 46, 55, and 87, 1999.

Wagon, S. "Biasing the Chaos Game: Barnsley's Fern." §5.3 in Mathematica in Action. New York: W. H. Freeman, pp. 156-163, 1991.