Floraform – an exploration of differential growth

Introducing Floraform, the latest generative design system from Nervous System. Floraform is inspired by the biomechanics of growing leaves and blooming flowers and explores the development of surfaces through differential growth. We used this system to computationally craft a new 3D-printed jewelry collection, now available on our website.

Floraform is a simulation of a differentially growing elastic surface that we created to explore how biological systems create form by varying growth rates through space and time. It began with an unusual flower, Celosia cristata, and led us through a journey of cellular differentiation, discrete differential geometry, kleptoplastic sea slugs, nastic movements, and 19th century zoetropes. The result is a series of 3D-printed sculptures and jewelry generated through a computational process of differential growth.

Table of Contents // what is differential growth | inspiration | mapping out the simulation space | digital gardening | florescence jewelry collection | what’s next | technical details | bibliography

What is Differential Growth?

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 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.

Mapping out the simulation space

The first step in our investigation was to map out how different spatial distributions of growing signal result in different structural typologies.

1. Point-based / tip splitting

The active growth area is a single point. This is similar to the growing tip of the stem in plants, called the apical meristem. We can allow this point to split into multiple points over time. When the growing zone bifurcates, the new points naturally grow apart, forming branches.

2. Line-based / fasciated

The active growth area starts as a point, but instead of splitting into two separate points, those points stay connected forming an expanding line. This is inspired by fasciated plants, and the results bears remarkable similarity to fasciated cacti and succulents..

3. Edge-based

The active growth area is the edge. This is our original inspiration from leaves and flowers, and it forms sinuous, hyperbolic geometries.

Of these growth phenotypes, we were most intrigued by the edge-based scenario and decided to explore it in greater detail.

Digital Gardening

We developed a set of mechanisms that allowed us to control, manipulate, and sculpt the growing process. These act as a set of material and environmental conditions that we can vary through space and time to produce finely differentiated structures. In the video below you can see examples of some of the variations we introduced into the system.

Our first results were a series of sculptures that we produced for our “Growing Objects” exhibition at Stonybrook University. This included pieces 3D-printed in full color, where the coloration of the surface reflects the growth rates that produced it, as well as a zoetrope that acts as a physical animation of the growth process.