We were inspired to create our algorithm by the reticulated patterns of veins in leaves and similiar patterns which are seen in coral and fungal rhizomes.
Leaves are plant organs specialized for photosynthesis--they absorb sunlight and convert it to sugars that feed the plant. To perform this function, leaves must receive water and nutrients from roots and distribute the sugars they produce to the rest of the plant. These distribution tasks are performed by veins, which serve as a material transportation system. Vein networks exhibit a hierarchy similiar to a tree structure with small veins branch out from larger veins, but unlike a tree, they ramify to form closed loops. These closed loops create redundancy that allows a leaf to continue functioning even when some veins are damaged.
Though venation patterns share an overall organization and hierarchy, no two leaves have the same structure. Rather each leaf has its own peculiarities emerging from its unique circumstances. Across species the patterns differ drastically; they can be radial like a lilypad, parallel like a blade of grass or reticulate like a tomatillo husk. How can one mechanism explain such variety?
How do they form?
Auxin flux canalization is the leading hypothesis of how veins form in leaves. This theory links the development of veins with the presence of the growth hormone auxin. Auxin is produced at the growing edge of a leaf and flows away from the leaf’s edge toward the stem. Proteins in leaf cells pull auxin into the cells, and cells with a higher concentration of auxin have a higher likelihood of pulling in more auxin. This feedback mechanism causes auxin to be more likely to flow where it has flowed before. Cells with a higher concentration of auxin eventually differentiate into veins.