BioQUEST home page ESTEEM Home Math Association of American home
Fractal Fern Generator

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.


Berend Meijer, STMicroelectronics

Published by: BioQUEST Curriculum Consortium


User Manuals and Curricular Materials
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).

Tutorial & Background materials

Bourke, P., 1993. Fractal Dimension Calculator User Manual, Online.

Fractal Coastline software used in "Properties of Fractals"

Science fractals FAQ

Biography about Benoit Mandelbrot

"What are Fractals?" is NASA Fractals

"Fractals in Nature" can be found at Fractal Images of CNAM Paris under Ifs Pictures

Meijer Berend () Fractal Fern Generator. A module of the Biological ESTEEM Collection, published by the BioQUEST Curriculum Consortium. URL: