How do those "perfectly imperfect" spots and stripes on animals come to be?

The latest research from the University of Colorado Boulder (UC Boulder) reveals the cause of the "imperfect beauty" of spots and stripes on animals, providing an important theoretical basis for scientists to decipher the complex skin patterns in nature, and is expected to promote the development of adaptive, color-changing materials.

Spots and stripes have long served a variety of functions in nature, but exactly how these exquisite patterns are formed has always puzzled scientists. This time, the research team combined mathematical simulations with real biological processes for the first time to reveal how these natural patterns, which appear to be regular but always have subtle changes, are generated.

"Nature is full of imperfections," said project leader Ankur Gupta of the Department of Chemical and Biological Engineering. "We propose a simple theory that explains how cells assemble and create diverse patterns."

As early as 2023, the team proposed a new theory based on the Turing reaction-diffusion model and introduced the physical process of 'diffusiophoresis' to explain how cells or particles migrate along concentration gradients. This breakthrough provides a mathematical basis for explaining the formation of clear patterns in tropical fish, snakes and other species. However, early models are more like physical simulations and have not yet completely simulated the behavior of real biological tissues and pigment cells, nor can they explain that patterns in nature are not "perfect replicas."

The latest model is further improved by representing cells as individuals of specific sizes and simulating their movement and distribution among tissues. The patterns generated by the new algorithm are closer to real animals, showing patterns with natural "imperfections" and rich layers. For example, pigment cells do not remain stationary but move, divide, and respond to chemical gradients. In addition, the animal's true body shape is not a regular plane, and every bend and fold affects the distribution of chemicals and the direction of its markings. The combination of these biological and physical mechanisms results in what scientists call "beautiful imperfection."

Gupta said, "You only need to give cells dimensions to capture these flaws and textures in nature." The new model provides new answers to explain the phenomenon of orderly yet full of personality in natural patterns, and may inspire new ideas for future biomaterials and smart surface design. In the future, the research team hopes to simulate more complex interactions between cells and chemicals to further improve the simulation effect.

Gupta added, "We are drawing inspiration from imperfect natural systems and hope to use these qualities to develop new functional materials in the future." The research has been published in the journal Matter.