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.

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

© 1996-9

1999-05-26