Przemyslaw Prusinkiewicz

Department of Computer Science,University of Calgary
Canada

The seminal idea of using computers to model morphogenesis (the emergence of patterns and forms in living organisms) was introduced in 1952 by Turing. A few years later, Ulam proposed to model morphogenesis using cellular automata, a (then) non-standard computing device. In 1968, Lindenmayer extended cellular automata to take growth and division of cells into account. In spite of this history, only now the modeling of morphogenesis begins to attract a significant interest of biologist. This is largely driven by the growing amount of physiological, molecular, and genetic data, which open an unprecedented opportunity for understanding development in mechanistic terms. The modeling and simulations are viewed as a means that may contribute towards this understanding, by helping extract the algorithmic essence of the processes being studied. Reciprocally, the biological applications motivate a further development of modeling techniques. In the domain of plant modeling, these needs are often satisfied by extensions of Lindenmayer systems (L-systems).

In my presentation, I will first analyze the key concepts that underlie the usefulness of L-systems in the modeling of morphogenesis: (a) the assumption that computing takes place in some space, defined in topological and/or geometric terms, (b) the identification of the elements of this space in local terms, and (c) the support for dynamically changing numbers and configurations of the elements. I will then outline selected advancements that have been driven by the modeling and simulation needs, such as: (d) the support for simulating interactions between the modeled organisms and their environment, (e) support for specifying large, computationally efficient models, and (f) coupling of L-systems with other formalisms (e.g., numerical methods for solving PDEs). I will further show how the identification of key L-system features guided the development of new formalisms, which overcame the original limitation of L-systems to linear and branching structures. The presentations will be illustrated using examples of biological models and simulations, and biologically-inspired applications of L-systems and their derivatives to selected non-biological problems. Current research problems, including an extension of L-system-inspired techniques to non-Euclidean spaces, will also be presented.

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