On the distribution of leaves. Katie Lewis, April 2004 Finding the Light On the distribution of leaves. Katie Lewis, April 2004

Introduction Why do Plants look the way they do? How might one model this structure? How might one generate plant like structures computationaly and how would these compare to the real thing? What causes may lead a plant to look the way it does?

The Question(s) Qualitative: What effect does the cost of a plants structure and the source of light have on desirable leaf distributions? Quantitative: If one sets numbers how do the different cases compare?

General Simplifying Assumptions I.e. We restrict ourselves to considering those plants for which the following is true: Plants consist of straight line support structures with discrete points at which these strutures ‘branch’ A single plant leaves the ground in only one place

Further Assumptions... A plants likelyhood of survival may be calculated in terms of the cost of maintaining the structure of the plant and the benefit brought in by photosynthesis. I.e. The likelyhood of a plants survival may be calculated as a function of the structure of the plant and function of the amount of sunlight on leaf surfaces.

The Simplest Model In the simplest case one may take: *Sun directly down *Leaves as flat rectangles coming off a branching point at some angle *Assume no light gets through leaves *Assume the ‘leaf benefit’ to corelate to the leaf area projected on the horizontal plane *Count structure simply in terms of the length of branches and number of leaves

Further Thoughts: Sun & Leaves For Sun: Directly down At an Angle Filtered through randomly generated canopy “ambient” (Joint modeling) (moving) For leaves: flat rectangles spherical “fingers” (actual leaf shape) Consider: Parameter of how much light gets thorugh a leaf

Further Thoughts: Consider light intensity or simply existence? Charge more for structure farther from root? Higher up? Consider reasonable restrictions: Ex: no “underground” leaves Consider how much variance the plant is allowed to have. Could there be an advantage for a plant to have a cap on branchings, for example? Should these restrictions also mutate?

The Method In order to see what sort of plant patterns are favored for given parameters, I coded a plant class in C++, consisting of location nodes conected by pointers, and an evolutionary program, which cycles through a number of iterations generating, mutating, crossing, and culling plants.

The Results?

Where do we go from here.... ....Reality.