Sticky Pixels: Evolutionary Growth by Random Drop Ballistic Aggregation

Over the years many techniques have been developed for simulating and modelling trees, ferns, crystals and natural structures. Indeed, many complex and realistic images have been formed. Often, these rely on rule based systems to create the structure, they start with a simple form and progressively refine it into a more complex form by applying rules. We use the notion of Sticky Pixels to form textures. The pixels (or objects) move around the space, when they touch another object they stick together to form a larger cluster. The objects aggregate and stop at the place and position where they first touched. Such an aggregation generates neighbourhoods of pixels that form natural looking shapes. The pixels may randomly walk around (such as using Brownian motion), or be guided along pre-defined routes (often described as ballistic), to obtain different structures. We use a ballistic aggregation technique, where the particles are randomly dropped onto a canvas, migrate and stick onto the closest position of the nearest cluster. We present Sticky Pixels, explain different parameters and describe our algorithm

A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models

In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one dimensional models to two dimensions and then propagate a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical conceit (rather than a physical representation of fire spread) that coincidentally simulates the spread of fire. Other papers in the series review models of an physical or quasi-physical nature and empirical or quasi-empirical nature. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.Comment: 20 pages + 9 pages references + 1 page figures. Submitted to the International Journal of Wildland Fir

Conformal mapping methods for interfacial dynamics

The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the article begins with an overview of continuous conformal-map dynamics. This includes problems of interfacial motion driven by harmonic fields (such as viscous fingering and void electromigration), bi-harmonic fields (such as viscous sintering and elastic pore evolution), and non-harmonic, conformally invariant fields (such as growth by advection-diffusion and electro-deposition). The second part of the article is devoted to iterated conformal maps for analogous problems in stochastic interfacial dynamics (such as diffusion-limited aggregation, dielectric breakdown, brittle fracture, and advection-diffusion-limited aggregation). The third part notes that all of these models can be extended to curved surfaces by an auxilliary conformal mapping from the complex plane, such as stereographic projection to a sphere. The article concludes with an outlook for further research.Comment: 37 pages, 12 (mostly color) figure

Modeling gap dynamics, succession, and disturbance regimes of mangrove forests: MANDY (MANgrove DYnamics)

Despite their important ecosystem benefits for terrestrial and marine flora and fauna and the human livelihood mangrove forests suffer a high loss rate mainly due to human activity. Aside from these impacts, natural forest disturbances exist more commonly in mangroves compared to other forests as a direct consequence of their exposed coastal location. Within this thesis I investigate the influence of natural disturbance regimes on the mangrove forest dynamics focusing in particular on the ecological role of disturbances, disturbance patterns, forest structure, succession behavior and long-term vulnerability evaluation. The study areas were set in the Indian River Lagoon in Florida (USA) and in Can Gio an UNESCO Biosphere Reserve (Vietnam). In addition, theoretical simulation studies were carried out to complement the field studies. Thereby, in our study at the Indian River Lagoon site I investigated the ecosystem response to hurricane events of an artificially impounded mangrove forest. In Can Gio, the suitability of lightning strike – caused gaps for setting a homogenous plantation into more natural-like state according to species composition and forest structure was analyzed. Finally, a theoretical simulation study was carried out to compare lightning strike and hurricane events regarding their homogenization and heterogenization effects on the spatio-temporal forest structure. The findings of the field study in the Indian River Lagoon indicate that hurricane events had a severe impact on forest areas in higher successional stages by creating open patches, whereas areas in lower successional stages remained largely undisturbed. Furthermore, the impoundment determines the species selection of the post-hurricane succession by favoring flooding-tolerant species. However, regeneration was found to be impaired by the artificially high inundation regime at some disturbed patches. The lightning-strike disturbances enhance the species composition in the monospecific plantation in Can Gio by providing a sufficient light regime for entering seeds to establish. In addition, lightning-strike gaps increased the plantation structure complexity. Regenerating lightning-strike gaps remained as “green islands” within windthrow sites in the plantation due to their low stature and provided seeds for surrounding disturbed areas thereby accelerating their recolonization. The results of the simulation analysis of a theoretical landscape showed that in the simulated highly complex natural mature forests all disturbance regimes entail homogenization on the spatial structure compared to an undisturbed scenario. The hurricane scenario showed an increased temporal variation of the forest dynamics whereas lightning-strike gaps were not able to contribute to additional heterogeneity in the simulated area, despite of having the same tree mortality probability during disturbances. The interaction of the large-scale impoundment in the Indian River Lagoon and medium-sized hurricane events is characterized by partially impeded post-hurricane regeneration. In contrast, small-scaled lightning strikes influenced the regeneration of medium-sized windthrow sites positively within the homogenous plantation. We therefore suggest management activities aimed at creating small clearances within the plantation in Can Gio to simulate additional small-scale disturbances in order to facilitate heterogenization of the plantation structure. Natural disturbances are found to be able to enhance the species diversity and the interactions of ecological processes. In particular, where sustainable management strategies focused on maintaining ecosystem services especially in restored sites or plantations act as a supportive part. Natural disturbances are an integral component of mangrove forests and fulfill specific ecological functions. However, our findings indicate that these disturbances, on top of altered environmental conditions associated with climate change and direct human impacts, might jeopardize the natural development in unnatural forest structures as on plantations or restored sites. This thesis gives an extensive overview about the effect of various disturbances in different mangrove forest systems, including semi-natural forests and strongly modified plantations, on species composition and forest structure. Field studies and simulation analyses contribute in equal parts to the results of the thesis