Essentially, this is a kind of symmetry breaking. Any two processes that act as an activator and an inhibitor will produce periodic patterns and can be modeled using the Turing diffusion function. The challenge is to move from the admittedly simplistic Turing model to defining the precise mechanisms that serve as activator and inhibitor.
This is especially difficult to do in biology. According to the authors of this latest paper, the classical Turing mechanism approach balances reaction and diffusion using a single scale, but biological patterns often involve multiscale structures, grain-like textures, or certain inherent imperfections. And the resulting patterns are often much more diffuse than those found in nature.
Can we say “diffusionpherosis”?
Simulated hexagonal and striped patterns obtained by diffusion-phoretic assembly of two cell types on top of chemical patterns.
Photo: Siamak Mirfendereski and Ankur Gupta/CU Boulder.
In 2023, UCB biochemical engineers Ankur Gupta and Benjamin Alessio developed new model this added diffusiopherosis to the mix. This is the process by which colloids are transported by differences in solute concentration gradients—the same process by which soap diffuses from laundry into water, pulling dirt particles out of the fabric. Gupta and Alessio successfully used their new model to imitate the distinctive hexagonal pattern (alternating purple and black) on an ornate box native to Australia, achieving a much sharper outline than the model originally proposed by Turing.
The problem was that the simulation created too-ideal models: hexagons of the same size and shape and at the same distance from each other. Animal patterns in nature, on the other hand, are never completely homogeneous. So Gupta and his UCB co-author on this latest paper, Siamak Mirfendereski, figured out how to tweak the model to get the pattern results they wanted. All they had to do was determine the specific dimensions of the individual cells. For example, larger cells create thicker outlines, and when they cluster, they form wider patterns. And sometimes the cells get stuck and tear the strip. Their revised simulations created patterns and textures very similar to those found in nature.
“Imperfections are everywhere in nature” Gupta said. “We came up with a simple idea that could explain how cells come together to create these variations. We take inspiration from imperfect beauty [a] natural system and hope to use these shortcomings to create new types of functionality in the future.” Possible future applications include smart camouflage fabrics that can change color to better blend in with their surroundings, or more effective targeted drug delivery systems.
Matter, 2025. DOI: 10.1016/j.matt.2025.102513 (About DOI).
