Swarthmore's Scott Arboretum traditionally gives incoming students a plant to care for in their dorms. Shockingly, the Hawaiian Schefflera I received in 2007 is still going 17 years later! Over the years as I've moved from place to place and kept the plant in different environments, I've been impressed by its ability to track the sunlight, frequently growing lopsided as it reaches toward the nearest window until I think to turn it. This has resulted in some twisting, gnarled branches:
If you've been reading this blog, you can probably guess where this is going – I was curious if I could make a simulation of my plant's heliotropic tendencies. I decided to model the plant as a collection of connected branch segments, each a fixed length and pointing at an angle relative to the vertical. At each step, we iterate over all the segments and pick an action:
- If the segment has no children, i.e. it's at the tip of a branch, we add a new segment on the end with a probability p_grow/size, where size is the number of existing segments.
- If the segment does have children, we add a new one with probability p_sprout/size.
- If neither of those occur, we adjust the angle of the branch to point closer to the sun's current position. The adjustment is proportional to how far off the angle is, how many branches are on the end of this one, and a constant stiffness for the plant.
I tried a bunch of values for the different parameters until I landed on a range that gave plants looking reasonably similar to the real thing (click to enlarge):
The numbers along the top give the stiffnesses, and the ones on the left give the sprout probability. The sun moves back and forth sinusoidally, which you can see in the snaking of the plants. I wasn't able to get my digital plants to spread as much as the analog one, possibly because I'm not accounting for the plant casting shadow on itself, but I'm still pleased with the results – The top center one seems particularly good. If you'd like to try for yourself, the code is here.
