Abstract Surface‐based pattern simulations have proven valuable for texture design and scientific visualization, but existing methods face several limitations. Most simulations either target a narrow range of pattern types (e.g. spots, branching) or support a broad range of patterns at the cost of time‐consuming parameter tuning. In either case, local and global control over the character of patterns is desirable, but often not supported. Additionally, transferring 2D simulations to 3D surfaces can introduce distortions, and is sensitive to mesh topology and quality. Finally, colourization further complicates the use of simulations for texturing, often relying on ad hoc mapping of simulation values to colours. To address these challenges, we introduce a unified framework for generating expressive, controllable patterns that are naturally embedded on curved surfaces. We reformulate Physarum polycephalum slime mold simulations in terms of continuous rates and PDEs, allowing greater consistency across varying space and time discretizations. We introduce agent‐based stochastic chemical kinetics to regulate agent turnover, which permits direct control over the uniformity of final patterns. Together, these modifications enable fine‐grained control of pattern synthesis using spatially varying parameter maps, directional biases, stimuli, and agent sinks/sources. We demonstrate that our approach allows for the generation of new pattern classes in Physarum slime mold simulations, including stripes, branching, and hierarchical structures. To eliminate distortion and artifacts, we re‐purpose intrinsic triangulations proposed for geometry processing to dynamic simulations. Finally, we introduce a simple colourization method to transfer colours from an exemplar image to simulation results. Notably, while demonstrated through slime mold simulations, our framework generalizes to other patterning models (e.g. reaction‐diffusion), thus providing a versatile tool for complex, controllable surface‐based pattern synthesis.

We present a sketch-based system for the creation and editing 3D content such as Digital Elevation Models, vegetation and bodies of water for Digital Earth representations. The proposed system employs a set of sketch-based tools to integrate commonly available data sources, such as orthophotos and Digital Elevation Models (DEM), to facilitate the rapid creation and integration of detailed geospatial content. Consequently, our system can be used to enhance the quality of Digital Earth data by enabling the straightforward creation of new 3D landscape elements.

The hormone auxin plays a crucial role in plant morphogenesis. In the shoot apical meristem, the PIN-FORMED1 (PIN1) efflux carrier concentrates auxin into local maxima in the epidermis, which position incipient leaf or floral primordia. From these maxima, PIN1 transports auxin into internal tissues along emergent paths that pattern leaf and stem vasculature. In Arabidopsis thaliana, these functions are attributed to a single PIN1 protein. Using phylogenetic and gene synteny analysis we identified an angiosperm PIN clade sister to PIN1, here termed Sister-of-PIN1 (SoPIN1), which is present in all sampled angiosperms except for Brassicaceae, including Arabidopsis. Additionally, we identified a conserved duplication of PIN1 in the grasses: PIN1a and PIN1b. In Brachypodium distachyon, SoPIN1 is highly expressed in the epidermis and is consistently polarized toward regions of high expression of the DR5 auxin-signaling reporter, which suggests that SoPIN1 functions in the localization of new primordia. In contrast, PIN1a and PIN1b are highly expressed in internal tissues, suggesting a role in vascular patterning. PIN1b is expressed in broad regions spanning the space between new primordia and previously formed vasculature, suggesting a role in connecting new organs to auxin sinks in the older tissues. Within these regions, PIN1a forms narrow canals that likely pattern future veins. Using a computer model, we reproduced the observed spatio-temporal expression and localization patterns of these proteins by assuming that SoPIN1 is polarized up the auxin gradient, and PIN1a and PIN1b are polarized to different degrees with the auxin flux. Our results suggest that examination and modeling of PIN dynamics in plants outside of Brassicaceae will offer insights into auxin-driven patterning obscured by the loss of the SoPIN1 clade in Brassicaceae.

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.

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.