Computation at levels beyond storage and transmission of information appears in physical systems at phase transitions. We investigate this phenomenon using minimal computational models of dynamical systems that undergo a transition to chaos as a function of a nonlinearity parameter. For period-doubling and band-merging cascades, we derive expressions for the entropy, the interdependence of-machine complexity and entropy, and the latent complexity of the transition to chaos. At the transition deterministic finite automaton models diverge in size. Although there is no regular or context-free Chomsky grammar in this case, we give finite descriptions at the higher computational level of context-free Lindenmayer systems. We construct a restricted indexed context-free grammar and its associated one-way nondeterministic nested stack automaton for the cascade limit language. This analysis of a family of dynamical systems suggests a complexity theoretic description of phase transitions based on the informational diversity and computational complexity of observed data that is independent of particular system control parameters. The approach gives a much more refined picture of the architecture of critical states than is available via

Defining structure and detecting the emergence of complexity in nature are inherently subjective, though essential, scientific activities. Despite the difficulties, these problems can be analyzed in terms of how model-building observers infer from measurements the computational capabilities embedded in nonlinear processes. An observer’s notion of what is ordered, what is random, and what is complex in its environment depends directly on its computational resources: the amount of raw measurement data, of memory, and of time available for estimation and inference. The discovery of structure in an environment depends more critically and subtlely, though, on how those resources are organized. The descriptive power of the observer’s chosen (or implicit) computational model class, for example, can be an overwhelming determinant in finding regularity in data. This paper presents an overview of an inductive framework — hierarchical-machine reconstruction — in which the emergence of complexity is associated with the innovation of new computational model classes. Complexity metrics for detecting structure and quantifying emergence, along with an analysis of the constraints on the dynamics of innovation, are outlined. Illustrative examples are drawn from the onset of unpredictability in nonlinear systems, finitary nondeterministic processes, and

In this paper we present a method for modeling herbaceous plants, suit-able for generating realistic plant images and animating developmental processes. The idea is to achieve realism by simulating mechanisms which control plant growth in nature. The developmental approach to the modeling of plant architecture is extended to the modeling of leaves and flowers. The method is expressed using the formalism of L-systems.

This paper presents a simulation framework and computational testbed for studying multicellular pattern formation. The approach combines several developmental mechanisms (chemical, mechanical, genetic and electrical) known to be important for biological pattern formation. The mechanisms are present in an environment containing discrete cells which are capable of independent movement (cell migration). Experience with the testbed indicates that the interactions between the developmental mechanisms are important in determining multicellular and developmental patterns. Each simulated cell has an artificial genome whose expression is dependent only upon its internal state and its local environment. The changes of each cell's state and of the environment are determined by piecewise continuous differential equations. The current two-dimensional simulation exhibits a variety of multicellular behaviors, including cell migration, cell differentiation, gradient following, clustering, lateral inhibition, and neurite outgrowth (see color plates). We plan to perform simulated evolution on developmental models as part of a long range goal to create artificial neural networks which solve problems in perception and control [Fleischer]. The testbed is a step on the path towards this goal. 1 Introduction

Development is an important, powerful and integral element of biological evolution. In this paper we present two models of development that can be used to evolve functional autonomous agents, complete with bodies and neural control systems. The first and most complex model is more biologically defensible in its details. It has been used to hand-design a genome for the development of complete agents capable of executing a simple avoidance task. These agents were then incrementally improved through evolution. The second model is simpler and uses a random Boolean network model for the genome and cell state that is somewhat more removed from the biological realm, making it easier to analyze and more amenable to artificial evolution. Using this model, we have successfully evolved complete agents from scratch that are capable of following curved lines.

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This paper explores the application of interactive genetic algorithms to the creation of line drawings. We have built a system that starts with a collection of drawings that are either randomly generated or input by the user. The user selects one such drawing to mutate or two to mate, and a new generation of drawings is produced by randomly modifying or combining the selected drawing(s). This process of selection and procreation is repeated many times to evolve a drawing. A wide variety of complex sketches with highlighting and shading can be evolved from very simple drawings. This technique has enormous potential for augmenting and enhancing the power of traditional computer-aided drawing tools, and for expanding the repertoire of the computer-assisted artist.

Recent advances in computer graphics have made it possible to visualize mathematical models of biological structures and processes with unprecedented realism. The resulting images, animations, and interactive systems are useful as research and educational tools in developmental biology and ecology. Prospective applications also include computer-assisted landscape architecture, design of new varieties of plants, and crop yield prediction. In this paper we revisit foundations of the applications of L-systems to the modeling of plants, and we illustrate them using recently developed sample models.

In these notes we survey applications of L-systems to the modeling of plants, with an emphasis on the results obtained since the comprehensive presentation of this area in The Algorithmic Beauty of Plants [61]. The new developments include: ffl a better understanding of theoretical issues pertinent to graphical applications of L-systems, ffl extensions to programming techniques based on L-systems, and ffl an extension of the range of phenomena expressible using L-systems. Keywords: L-system, fractal, plant, modeling, simulation, realistic image synthesis, emergence, artificial life. 1 Introduction In 1968, Aristid Lindenmayer introduced a formalism for simulating the development of multicellular organisms, subsequently named L-systems [36]. This formalism was closely related to abstract automata and formal languages, and attracted the immediate interest of theoretical computer scientists [67]. The vigorous development of the mathematical theory of L-systems [70, 27, 66] was follow...

Abstract — We explain how a small set of molecular building blocks will allow the implementation of “universally programmable intelligent matter, ” that is, matter whose structure, properties, and behavior can be programmed, quite literally, at the molecular level. I. DEFINITIONS Intelligent matter is any material in which individual molecules or supra-molecular clusters function as agents to accomplish some purpose. Intelligent matter may be solid, liquid, or gaseous, although liquids and membranes are perhaps most typical. Universally programmable intelligent matter (UPIM) is made from a small set of molecular building blocks that are universal in the sense that they can be rearranged to accomplish any purpose that can be described by a computer program. In effect, a computer program controls the behavior of the material at the molecular level. In some applications the molecules self-assemble a desired nanostructure by “computing ” the structure and then becoming inactive. In other applications the material remains active so that it can respond, at the molecular level, to its environment or to other external conditions. An extreme case is when programmable supra-molecular clusters act as autonomous agents to achieve some end. Although materials may be engineered for specific purposes, we will get much greater technological leverage by designing a “universal material ” which, like a generalpurpose computer, can be “programmed ” for a wide range of applications. To accomplish this, we must identify a set of molecular primitives that can be combined for widely varying purposes. The existence of such universal molecular operations might seem highly unlikely, but there is suggestive evidence that it may be possible to discover or synthesize them. II. APPROACH Accomplishing the goals of UPIM will require the identification of a small set of molecular building blocks that is