Mathematically modeling a Leaf is a multi-physics problem. Static and dynamic structure in relation to vascular transport, insolation, aerodynamics, aeroelasticity, allometry, and so on, all figure in morphological expression.

Biological leaves perform Transpiration and Guttation via their Vascular Transport Networks. Typically >97% of moisture transported to the leaf passes out of its Stomatal Pores. Modeling a leaf realistically as vascular transport network therefore needs to account for stomatal valve function.

Leaf transport networks are therefore substantially a one-way transport of bulk flow, with a small return flow of sugar syrup and other solutes. This reduces "turning cost" of two-way transport accordingly. Return flow is more viscous, as a further transport "cost" factor to introduce in modeling.

A heat stressed leaf needs to transpire to cool off, with sufficient surface area. A thick cactus can buffer midday heat by its thermal inertial bulk. These are morphological factors.

Further regarding Allometric scaling, tropical rain forest and wetland plants in non-windy locations can sustain the largest leaves, and hot-desert and alpine-polar zone plants the smallest leaves.

Mass Scaling Exponents relate to the form of leaves. We recall that stems and leaves evolved from common ancestral segments. Thin stems and pine-needles would scale somewhat linearly, were it not for non-dimensional transport distance; broad-leaves scale nearly quadratically; and thick bodies, more-or-less cubically. Scaling exponents constrain how big a plant and its parts may grow. Kelp's buoyancy gives it enhanced vertical aspect ratio. Some vines exceed 1km long (ie. Entada phaseoloides), freed from a self-support requirement.