The attractor of the iterated
function system given by the set of "fern functions"
(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).
See also Barnsley's Tree ,
Dynamical System ,
Fractal ,
Iterated
Function System
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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. Referenced
on Wolfram|Alpha Barnsley's Fern
Cite this as:
Weisstein, Eric W. "Barnsley's Fern."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/BarnsleysFern.html
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