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 lowesttwo branches are the images of the main tip under 
and 
(Wagon 1991).See also Dynamical System, Fractal, Iterated Function System
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.
- Inclusion Map
- Incommensurate
- Incomplete Gamma Function
- Incompleteness
- Increasing Function
- Increasing Sequence
- Indefinite Integral
- Indefinite Quadratic Form
- Indegree
- Independence Axiom
- Independence Complement Theorem
- Independence Number
- Independent Equations
- Independent Sequence
- Independent Statistics
- Independent Vertices
- Indeterminate Problems
- Index
- Index Set
- Index Theory
- Indicatrix
- Indicial Equation
- Indifference Principle
- Induced Map
- Induced Norm