Ecology and evolution Unlike theoretical
fractal curves which can be easily measured and the underlying
mathematical properties calculated;
natural systems are sources of heterogeneity and generate complex space-time structures that may only demonstrate partial
self-similarity. Using fractal analysis, it is possible to analyze and recognize when features of complex
ecological systems are altered since fractals are able to characterize the natural complexity in such systems. Thus, fractal analysis can help to quantify patterns in nature and to identify deviations from these natural sequences. It helps to improve our overall understanding of
ecosystems and to reveal some of the underlying structural mechanisms of nature. For example, it was found that the structure of an individual tree's
xylem follows the same architecture as the spatial distribution of the trees in the forest, and that the distribution of the trees in the forest shared the same underlying fractal structure as the branches, scaling identically to the point of being able to use the pattern of the trees' branches mathematically to determine the structure of the forest stand. The use of fractal analysis for understanding structures, and spatial and temporal complexity in biological systems has already been well studied and its use continues to increase in ecological research. Despite its extensive use, it still receives some
criticism.
Architecture, urban design and landscape design In his publication
The Fractal Geometry of Nature,
Benoit Mandelbrot suggested fractal theory could be applied to architecture. In this context, Mandelbrot was talking about the self-similar feature of fractal objects, rather than fractal analysis. In 1996, Carl Bovill applied the
box counting method of fractal analysis to Architecture. Bovill's work, using a manual version of box counting, has since been refined by others and computational approaches have been developed. Fractal analysis is one of the few quantitative analysis methods available to architects and designers to understand the visual complexity of buildings, urban areas and landscapes. Typical uses of fractal analysis of the built environment have been to understand the visual complexity of cities and skylines, the fractal dimensions of works of different architects and the landscape. Combining the fractal analysis of ecology (see above) with fractal analysis of architecture, fractal dimensions have been used to explore the possible relationship between nature and architecture. Promising results suggest further research is needed in this area.
Animal behaviour Patterns in animal
behaviour exhibit fractal properties on spatial and temporal scales. This has generated ecological interpretations such as the
Lévy Flight Foraging hypothesis, which has proven to be a more accurate description of animal movement for some species. Spatial patterns and animal behaviour sequences in fractal time have an optimal complexity range, which can be thought of as the homeostatic state on the spectrum where the complexity sequence should regularly fall. An increase or a loss in complexity, either becoming more stereotypical or conversely more random in their behaviour patterns, indicates that there has been an alteration in the functionality of the individual. Using fractal analysis, it is possible to examine the movement sequential complexity of animal behaviour and to determine whether individuals are experiencing deviations from their optimal range, suggesting a change in condition. For example, it has been used to assess welfare of domestic hens, and parasitic infection in Japanese macaques When it comes to animal welfare and
conservation, fractal analysis makes it possible to identify potential sources of stress on animal behaviour, stressors that may not always be discernible through classical behaviour research. This approach is more objective than classical behaviour measurements, such as
frequency-based observations that are limited by the counts of behaviours, but is able to delve into the underlying reason for the behaviour. Another important advantage of fractal analysis is the ability to monitor the health of
wild and free-ranging animal populations in their natural habitats without invasive measurements. == Applications include ==