L-System Tree Grow
While researching how to generate realistic trees, I came across The Grove, a plant generating plugin for the popular 3D modeling software Blender. Unfortunately the plugin is about $130, so I wasn’t able to play around with it. But they do have a nice little educational section of their website that has some information on how they achieved such life-like growth in their own trees. In this section, I found a post on “the golden angle” of trees. In order to prevent branches from overlapping and to maximize exposure to sunlight, many tree species distribute their branches by rotating them around their central trunk at an angle roughly equal to 137.5 degrees. I was curious about how something as complex as the canopy of a tree could be based on a single angle, so I used Houdini to start playing around with the Roll parameter in its L system function.
The Roll function allows the L system to branch into three dimensions by “rolling” the branch direction around the y axis by some amount of degrees. Simply by inserting the roll function with 137.5 degrees as the angle, “/(137.5)” in rule A, I was able to achieve a remarkably realistic tree. Even more surprising was that the growth animation looked relatively realistic as well.
Gravity Test
The above trees were generated using the same algorithm except that the right tree has a “gravity” force applied to it. The T(10) on the right tree’s C rule is adding a tilt in the negative y direction to each new generation. As the numerous Cs in rule A are replaced, the multiple sequential T(10)s start compounding and bend the branches further and further towards the “ground.”
A natural result does not always come from a natural growth pattern. The addition of an extra rule dictating the thickness of branches and increasing the variation between generations creates a much more realistic tree. However, the increased change generation to generation makes the growth curve very haphazard, appearing jerky when animated over time.
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