Brendan Lane

The use of positional information in the modeling of plants

We integrate into plant models three elements of plant representation identified as important by artists: posture (manifested in curved stems and elongated leaves), gradual variation of features, and the progression of the drawing process from overall silhouette to local details. The resulting algorithms increase the visual realism of plant models by offering an intuitive control over plant form and supporting an interactive modeling process. The algorithms are united by the concept of expressing local attributes of plant architecture as functions of their location along the stems.

Evolution and Development of Inflorescence Architectures

To understand the constraints on biological diversity, we analyzed how selection and development interact to control the evolution of inflorescences, the branching structures that bear flowers. We show that a single developmental model accounts for the restricted range of inflorescence types observed in nature and that this model is supported by molecular genetic studies. The model predicts associations between inflorescence architecture, climate, and life history, which we validated empirically. Paths, or evolutionary wormholes, link different architectures in a multidimensional fitness space, but the rate of evolution along these paths is constrained by genetic and environmental factors, which explains why some evolutionary transitions are rare between closely related plant taxa.

Modeling and visualization of leaf venation patterns

We introduce a class of biologically-motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodes and auxin sources. In addition, a vein connection graph is maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree-like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research.

Self-organizing tree models for image synthesis

We present a method for generating realistic models of temperate-climate trees and shrubs. This method is based on the biological hypothesis that the form of a developing tree emerges from a self-organizing process dominated by the competition of buds and branches for light or space, and regulated by internal signaling mechanisms. Simulations of this process robustly generate a wide range of realistic trees and bushes. The generated forms can be controlled with a variety of interactive techniques, including procedural brushes, sketching, and editing operations such as pruning and bending of branches. We illustrate the usefulness and versatility of the proposed method with diverse tree models, forest scenes, animations of tree development, and examples of combined interactive-procedural tree modeling.

Modeling trees with a space colonization algorithm

We extend the open leaf venation model by Runions et al. [RFL*05] to three dimensions and show that it generates surprisingly realistic tree structures. Model parameters correspond to visually relevant tree characteristics identified in landscaping, offering convenient control of tree shape and structure.

Quantitative Modeling of Arabidopsis Development

We present an empirical model of Arabidopsis (Arabidopsis thaliana), intended as a framework for quantitative understanding of plant development. The model simulates and realistically visualizes development of aerial parts of the plant from seedling to maturity. It integrates thousands of measurements, taken from several plants at frequent time intervals. These data are used to infer growth curves, allometric relations, and progression of shapes over time, which are incorporated into the final three-dimensional model. Through the process of model construction, we identify the key attributes required to characterize the development of Arabidopsis plant form over time. The model provides a basis for integrating experimental data and constructing mechanistic models.

The L+C Plant-Modelling Language

L+C is a modelling language that combines features of L-systems and C++. It extends the Lsystem formalism with the notion of fast transfer of information, and supports a number of standard programming constructs absent from its predecessor, the cpfg language. These include modules with structured parameters, productions with multiple successors, and user-definable functions. Visualizations of L-system models can be enhanced using multiple views and the selective display of frames. These features extend the overall range of simulation models that can be conveniently expressed using Lsystems, and are particularly advantageous when creating and visualizing complex plant models. A biomechanical model of a growing pendulous branch is given as the key example.

Modeling Morphogenesis in Multicellular Structures with Cell Complexes and L-systems

We consider computational modeling of biological systems that consist of discrete components arranged into linear structures. As time advances, these components may process information, communicate and divide. We show that: (1) the topological notion of cell complexes provides a useful framework for simulating information processing and flow between components; (2) an index-free notation exploiting topological adjacencies in the structure is needed to conveniently model structures in which the number of components changes (for example, due to cell division); and (3) Lindenmayer systems operating on cell complexes combine the above elements in the case of linear structures. These observations provide guidance for constructing L-systems and explain their modeling power. L-systems operating on cell complexes are illustrated by revisiting models of heterocyst formation in Anabaena and by presenting a simple model of leaf development focused on the morphogenetic role of the leaf margin.

Metric-Driven Grammars and Morphogenesis (Extended Abstract)

Expansion of space, rather than the progress of time, drives many developmental processes in plants. Metric-driven grammars provide a formal method for specifying and simulating such processes. We illustrate their operation using cell division patterns, phyllotactic patterns, and several aspects of leaf development.