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Fractal Fern Generator

Berend Meijer

From the Biological ESTEEM collection

ESTEEM Category



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.

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Berend Meijer, "Fractal Fern Generator," Convergence (December 2006)