
The attractor of the iterated function system given by the set of "fern functions"
(1)
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(2)
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(3)
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(4)
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(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).