Tuesday, October 16, 2007

Koch Snowflakes

The snow crystal has gone on to inspire a range of design motifs. Its radial symmetry is seen through a range of symbols ranging from the Star of David to Japanese Heraldry to Arabian desgins. Snowflakes are also reminescent of fractals, in fact, one of the earliest Fractal curves is know as the Koch Snowflake. The Koch Snowflake first appeared in a paper written by Swedish mathematician Helge von Koch. The Koch Snowflake is also known as Lindenmayer fractal since it can be produced with the computer langauge, know as L-systems. Devised by biologist Aristid Lindenmayer in 1968, the L-systems code is a formal computer langauge which uses a series of rules to create recursive structures. L-systems are also known as a genetic algorithm since the langauge is fundimental in visualizing botanical growth patterns. There is a range of software products that implement systems, such as Houdini. It is my belief, but I haven't varified this, that L-systems drive the growth patterns of Paint Effects in Maya.

An excellent resource for L-systems is http://algorithmicbotany.org/papers/.

You can also download the book The Algorithmic Beauty of Plants at the site as well (http://algorithmicbotany.org/papers/#abop)

-joe

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