Puckering and wrinkling in a growing composite ring

Pattern formation driven by differential strain in constrained elastic systems is a common motif in many technological and biological systems. Here we introduce a biologically motivated case of elastic patterning that allows us to explore the conditions for the existence of local puckering and global wrinkling patterns: a soft growing composite ring adhered elastically to a constraining rigid ring. We explore how differential growth of the soft ring and the elastic resistance to shear and stretching deformations induced by soft adherence lead to a range of phenomena that include uniform aperture-like modes, localized puckers that are Nambu–Goldstone-like modes and global wrinkles in the system. Our analysis combines computer simulations of a discrete rod model with a nonlinear stability analysis of the differential equations in the continuum limit. We provide phase diagrams and scaling relations that reveal the nature and extent of the deformation patterns. Overall, our study reveals how geometry and mechanics conspire to yield a rich phenomenology that could serve as a guide to the design of programmable localized elastic deformations while being relevant for the mechanical basis of biological morphogenesis.

Machines for living in: Connections and contrasts between designed architecture and the development of living forms

There is a growing interest in applying principles of biological morphogenesis to architectural practice. Biological morphogenesis differs from conventional architectonics in several important ways; architecture is teleological, biology has no purpose; architecture is blueprinted and top-down, morphogenesis is bottom-up and emergent; construction uses external agents and skills (builders) whereas embryos build themselves from largely internal information; control of construction sites is hierarchical while morphogenesis uses rich feedback and distributed control; biological systems show adaptation and self-repair. Many materials are, however, common to the two, and both use techniques of scaffolding. There are several ways in which the fields can be brought together, either using biological systems directly (for example in synthetic biological approaches), or by engineering inorganic systems to realize the potentially useful processes characteristic of living things, such as automatic adaptation to the environment, and self-repair.

Interactive Evolution of Camouflage

This article presents an abstract computation model of the evolution of camouflage in nature. The 2D model uses evolved textures for prey, a background texture representing the environment, and a visual predator. A human observer, acting as the predator, is shown a cohort of 10 evolved textures overlaid on the background texture. The observer clicks on the five most conspicuous prey to remove (“eat”) them. These lower-fitness textures are removed from the population and replaced with newly bred textures. Biological morphogenesis is represented in this model by procedural texture synthesis. Nested expressions of generators and operators form a texture description language. Natural evolution is represented by genetic programming (GP), a variant of the genetic algorithm. GP searches the space of texture description programs for those that appear least conspicuous to the predator.

A PRAGMATIC APPROACH TO MODELING MORPHOGENESIS

The mathematical modeling of biological morphogenesis processes is considered. Emphasis is placed throughout on the lessons of experience in modeling three-dimensional forms that evolve in time. The qualitative requirements of a model, the general components of a dynamic system, and the products of a morphogenesis modeling program are discussed. Examples are drawn frequently from phyllotaxis.