Emergent Canopy Architecture from Discrete Leaf Dynamics: A Latent Environmental Encoding

Why are trees shaped the way they are? We present a minimal discrete-leaf growth model in which canopy architecture emerges from two local rules: (1) new leaves are placed by a species-specific strategy, and (2) leaves that receive insufficient light die off. No global shape is prescribed — the form is an emergent consequence of the growth–death equilibrium. We simulate six biologically motivated strategies (spherical, conical, columnar, umbrella, multi-stem, climber) and compare them to a greedy-optimal strategy that places each leaf where light is maximal. The key finding is that the optimal canopy shape is not universal but is a smooth function of a low-dimensional environmental latent vector \(\boldsymbol{z} = (\theta, E, T)\) encoding sun elevation angle, energy availability, and tree age. Under overhead illumination, the optimal form converges to a flat disk — matching the Acacia archetype. As the sun angle decreases, the optimal form continuously deforms through Oak-like hemispheres to Spruce-like cones. Energy scarcity removes the selection pressure entirely: below a critical leaf density, self-shading is negligible and the canopy shape is arbitrary. This provides a concrete biological instance of the Latent Representation Principle: the environment's generative structure selects the organism's optimal form.