Sunday, August 12, 2007

The morphology of plants is structured in such a way that repetitive patterns occur. This is termed modular organization and is a method of defining certain repetitive structures of a plant. If we consider a single instance of a leaf or a branch as a module then we can reduce a (very) simplified tree to being just a collection of these two components. If we are in need of representing a tree programmically then realizing the above makes things much easier. Even more interesting Ferra et al. (2005) states that “in some cases, the modules are arranged into compound, recursively nested, fractal-like structures, with similar patterns appearing at different scales.”


Ferra et al. mentioned that many plants have fractal-like structures. So what are they? Fractals are statistically self-similar structures, which, according to Mandelbrot (1982), is “when each piece of a shape is geometrically similar to the whole, both the shape and the cascade that generate it are called self-similar.” To see this graphically it'll help to refer to the picture of the fern. Each pinnule (the smallest 'leaf') of the fern is geometrically similar to each pinna which is geometrically similar to the entire fern. Nature repeats and beauty is a result.

Below is a flash application that I created by modifying code written by Matt Pearson (2007). The tree is composed of a 'trunk' and a 'leaf' both of which are laid down by a recursive function. Click it to randomly generate a new tree.


[1] B. B. Mandelbrot. The fractal geometry of nature. W. H. Freeman, San Francisco, 1982.
[2] Ferrao P., Godin C., Prusinkiewicz P. Toward a quantification of self-similarity in plants. Fractals, 2005.
[3] Pearson, M. Fractals in ActionScript 3 - A Flash Tutorial. 2007.


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