Fractal analysis

It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset, or a pattern or signal extracted from phenomena including topography,[1] natural geometric objects, ecology and aquatic sciences,[2] sound, market fluctuations,[3][4][5] heart rates,[6] frequency domain in electroencephalography signals,[7][8] digital images,[9] molecular motion, and data science.

[11] Fractal analysis is valuable in expanding our knowledge of the structure and function of various systems, and as a potential tool to mathematically assess novel areas of study.

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.

[23][24] 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.

[14][36] 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.

[37][38] For example, it has been used to assess welfare of domestic hens,[20] stress in bottlenose dolphins in response to human disturbance,[39] and parasitic infection in Japanese macaques[38] and sheep.

[36] 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.