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dendrite puzzle inspiration

Our puzzle cut style was inspired by a number branching, interlocking patterns in nature. We began by examining the suture patterns of ammonites, experimented with a fluidic experiment called a Hele-Shaw Cell before finally studying dendritic solidifcation, a crystal growth process that occurs in the super-cooled fluids.

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Floraform inspiration

How does an organism go from a single cell to a complex differentiated structure? If a single cell were to divide and grow uniformly, it would result in a wrinkled blob. However, through carefully coordinated subdivision and differentiation, biological systems produce structures with specific, reproducible forms and functions. Growth isn’t uniform but instead differential. To put it simply, some areas grow more than others, and this leads to the formation of macroscopic shape. These shapes result from the interplay between the underlying cellular growth processes and the mechanics of the materials themselves. Plant tropisms are an example of this process that you can observe directly. Tropisms are directional responses to directional stimuli. A plant can bend towards light by elongating cells on its stem that are in shadow (phototropism). Or vines can strangle another plant by responding to touch and wrapping around them (thigmotropism). We started developing Floraform after coming across two papers by L. Mahadevan: “The shape of the long leaf” (2010) and “Growth, geometry and mechanics of the blooming lily” (2011). Looking at the shapes of rippled leaves and blooming flowers, Mahadevan proposed that their ruffled forms could be described by a surface growing differentially from its edge. We found this interesting because complex ruffles develop from a very simple procedure: grow more at the edge. This is in contrast to other differential growth models where curvature is specified locally, by growing on one side more than another, like the bending stem example we gave above. At the same time, we became enamored with a flower called Cockscomb, a mutant cultivar of Celosia that produces dense, convoluted blooms instead of its normal branching, tree-like blossoms. It exhibits this amazing ruffled shape that is unlike any flower we’d ever seen (people often refer to it as brain flower). We hypothesized that you could simulate the growth of Cockscomb with this type of preferential growth toward the edge. The Celosia flower suggested that there was a space of form between the normal and the mutant, between branching and ruffling. We wanted to explore that space. With our minds now contemplating this growth model, we began to see rippled forms in diverse ecosystems and kingdoms of life: Sparassis fungi, lettuce sea slugs, lace bryozoans, kale and lettuce leaves, plumose anemone, iris flowers, jellyfish arms. So we started to build a digital environment where we could investigate these ideas.

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Xylem + Hyphae inspiration

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.