# Fractal Fern Generator

Author(s):
Berend Meijer

From the Biological ESTEEM collection

ESTEEM Category

Biometrics

Description

The Fractal Fern Generator creates graphical images of a certain type of fractals that can be constructed by linear transformations: rotations, mirror operations, multiplications and translations. Simply, fractals generate points to plot on a graph that are the result of iterated calculations. The answer from one calculation is used as the input value to the next calculation. One sort of fractal is known as the Iterated Function System, or IFS. You start with shapes plotted on a graph, and iterate the shapes through a calculation process that transforms them into other shapes on the graph. Starting with four shapes, one of which is squashed into a line segment (this becomes the fern s rachis or stalk), you apply the shapes to the calculation to generate more shapes, feed them back into the calculation process, etc. Eventually a pattern emerges that bears a startling resemblance to a fern, if you choose the right starting shapes and positions. The longer you continue the iteration process, the more intricate the tiny detail in the pattern becomes.

Go the the Fractal Fern Generator module  in a new window

# Fractal Fern Generator

Author(s):
Berend Meijer

From the Biological ESTEEM collection

ESTEEM Category

Biometrics

Description

The Fractal Fern Generator creates graphical images of a certain type of fractals that can be constructed by linear transformations: rotations, mirror operations, multiplications and translations. Simply, fractals generate points to plot on a graph that are the result of iterated calculations. The answer from one calculation is used as the input value to the next calculation. One sort of fractal is known as the Iterated Function System, or IFS. You start with shapes plotted on a graph, and iterate the shapes through a calculation process that transforms them into other shapes on the graph. Starting with four shapes, one of which is squashed into a line segment (this becomes the fern s rachis or stalk), you apply the shapes to the calculation to generate more shapes, feed them back into the calculation process, etc. Eventually a pattern emerges that bears a startling resemblance to a fern, if you choose the right starting shapes and positions. The longer you continue the iteration process, the more intricate the tiny detail in the pattern becomes.

Go the the Fractal Fern Generator module  in a new window

# Fractal Fern Generator - References

Author(s):
Berend Meijer

Popular Text Citations

Peitgen, H.O. and Richter, P. (1986). The Beauty of Fractals, Springer-Verlag: Heidelberg, 1986.

Barnsley, M. (1989). Fractals Everywhere. Boston: Academic Press.

Ball, P. (1999). The Self-made Tapestry: Pattern Formation in Nature. Oxford University Press: Oxford, U.K.

Devaney, R. (1989). Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics. Menlo Park: Addison-Wesley.

Bassingthwaighte, J., L. Liebovitch, & B. West. (1994). Fractal Physiology. Oxford University Press: New York.

Gleick, J. (1987). Chaos: Making a New Science, Viking, New York.

Liebovitch, Larry S. (1998). Fractals and Chaos Simplified for the Life Sciences. Oxford University Press: New York.

McGuire, Michael. An Eye For Fractals, Addison-Wesley Publishing Company: Redwood City, CA, 1991

Mandelbrot, B. (1983). The Fractal Geometry of Nature. San Francisco: Freeman, 1983.

Peitgen, H.-O., et. al. (1991-92). Fractals for the Classroom Vols. 1 and 2. Springer-Verlag: New York.

Research Articles

Ben-Jacob, E., Cohen, I. & Levine, H. The cooperative self-organization of microorganisms. Adv. Phys. 49: 395-55 ().

Ben-Jacob, E. & Levine, H. The artistry of microorganisms. Sci. Am. 279(4), 82-87 (1998).

Ben-Jacob, E. & Garik, P. The formation of patterns in non-equilibrium growth. Nature 343, 523-530 (1990).

Kessler, D. A., Koplik, J. & Levine, H. Pattern selection in fingered-growth phenomena. Adv. Phys. 37, 255 (1988).