Essentially, this is a type of symmetry breaking. Two processes acting as activator and inhibitor will produce periodic patterns and can be modeled using the Turing diffusion function. The challenge is to move from Turing’s admittedly simplified model to identifying the precise mechanisms playing the roles of activator and inhibitor.
This is particularly difficult in biology. According to the authors of the latter paper, the classic Turing mechanism approach balances reaction and diffusion using a single length scale, but biological models often incorporate multi-scale structures, grainy textures, or some inherent imperfections. And the resulting patterns are often much fuzzier than those found in nature.
Can you say “diffusiopherosis”?
Simulated hexagonal and striped patterns obtained by diffusiophoretic assembly of two cell types on top of chemical patterns.
Credit: Siamak Mirfendereski and Ankur Gupta/CU Boulder
In 2023, UCB biochemical engineers Ankur Gupta and Benjamin Alessio developed a new model integrating diffusiopherosis. This is a process by which colloids are transported via differences in solute concentration gradients – the same process by which soap diffuses out of laundry into water, carrying dirt particles out of the fabric. Gupta and Alessio successfully used their new model to simulate the distinctive hexagonal pattern (alternating purple and black) of the ornate boxfish, native to Australia, achieving much sharper contours than the model initially proposed by Turing.
The problem was that the simulations produced patterns that were too perfect: hexagons that were all the same size and shape and the same distance from each other. On the other hand, animal patterns in nature are never perfectly uniform. So Gupta and his UCB co-author on this latest paper, Siamak Mirfendereski, figured out how to modify the model to get the model results they wanted. All they had to do was set specific sizes for each cell. For example, larger cells create thicker outlines, and when they group together, they produce larger patterns. And sometimes the cells get stuck and break a band. Their revised simulations produced 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 can explain how cells come together to create these variations. We are inspired by the imperfect beauty of [a] natural system and I hope to exploit these imperfections for new types of functionality in the future. Possible future applications include “smart” camouflage fabrics that can change color to better blend into the environment, or more effective targeted drug delivery systems.
Matter, 2025. DOI: 10.1016/j.matt.2025.102513 (About DOIs).
