Predicting Emergent Behavior in Cellular Automata and 3D-Printed Bioinspired Hierarchical Architected Metamaterials with Generative Pre-Trained Transformer Models

Biological materials, such as bone, nacre, tendon, and wood, owe their exceptional mechanical properties to their complex hierarchical structures. Current structural metamaterial design often mimics these end structures without incorporating the dynamic processes of their formation, such as multicellular behavior. Real biological materials are not static; they continuously evolve through processes that span multiple orders of magnitude in scale, often involving the emergent effects of cellular cooperation. Some have argued that biological systems intrinsically favor information-based solutions to save energy, using collective cellular dynamics to process data from their environments. In this work, we demonstrate the potential of bioinspired and biomimetic strategies that manipulate information using cellular automata (CA) for hierarchical material design. We find that these strategies can create fractal-like structures, optimized for multiple purposes, such as strength, toughness, and lightweighting. Multicellular organisms can be thought to algorithmically utilize ‘biological CA’ to create complex (somewhat ordered and disordered) hierarchical biological materials. The emergence of these biostructures is remarkable, as their geometries and functionalities are not readily discernible through a formal analysis of the rules governing their cell-mediated self-assembly. Likewise, CA, as computational models, generate emergent, complex behavior from a set of simple, local rules applied recursively through time on a multidimensional lattice of virtual cells. CA have been useful across disparate fields of study for phenomenologically modeling systems ranging from urban traffic flow to neuronal dynamics and chemical systems, making them widely applicable to the study of biological self-assembly and morphogenesis. We demonstrate the application of 2D CA and inverse tomography for architecting structural metamaterials, leveraging their ability to produce complex, branch-like forms through local recursive rules in a discrete, 3D configuration-space. We also 3D-print and mechanically test these architected structures to show that they overcome the strength/toughness tradeoff, like other hierarchically organized biological materials. Furthermore, we relate these mechanical properties to the informational entropy of the 2D initial conditions (seeds) from which each structure is generated, which suggests property tunability is feasible in these systems. Moreover, we show that generative pre-trained transformer models (GPTs) can learn the rules of CA systems via training off large synthetic datasets. We believe that this shows promise for the future of CA-architected hierarchical materials, as future GPTs may be able to learn the bidirectional relationships between rulesets, initial conditions, and mechanical properties. Finally, we outline the potential for GPTs to take in data from real-world, dynamic biological materials, to create CA models approximating the time-evolution of these systems, which may be applicable to tissue engineering, and for the inverse design of bioinspired materials.