![]() This results in a phenomenon where if we attempt to measure the length of e.g. The scaling of the buckled feature on a fractal coastline, and more generally the scaling of a feature on any fractal structure, would appear at intervals that follow a characteristic order ( Fig. For instance, the buckled shape of a coastline may be observed on the range of 100 km, again at 50 km, and even at 10 km and so on. This reflects a form of organization in complex structures, that may be quantified with the fractal dimension ( D f) parameter. They contain features that are preserved across multiple levels of observation, according to a precise scaling law. Fractals may be described as structures that have infinitely iterated self-similar patterns. Often, chaotic systems are well approximated by geometries that are fractal. the weather, or single cells that assemble into a coordinated tissue 3. These are typically systems with collective behaviour, e.g. It tends to be the governing order in systems that are sensitive to small factors and perturbations, and single systems may transition between the appearance of ordered and chaotic dynamics. These sensitive nonlinear dynamical systems have now been explained using chaos theory and fractal geometry 11, 2.Ĭhaos is a behavior of dynamics that appears random, even though it has well-defined underlying order. When large iterations of complex computations were first enabled by computers, strange phenomena were revealed 1, 2, such as contradicting results from weather models despite increased computational precision. Overall, we promote the effectiveness of fractals in characterizing natural systems, and suggest moving towards using fractal frameworks as a basis for the research and development of better tools for the future of biomedical engineering. Finally, we explain important mathematical concepts of fractals and chaos, such as fractal dimension, criticality, bifurcation, and iteration, and how they are related to biology. We also discuss rising examples of the implementation of fractal theory in designing novel materials, biomedical devices, diagnostics, and clinical therapies. We compare how reports of either too little or too much chaos and fractal complexity can be damaging to normal biological function, and suggest that aiming for the healthy dose of chaos may be an effective strategy for various biomedical applications. ![]() Here, we review how measures of fractality that quantify the dose of chaos may reflect the state of health across various biological systems, including: brain, skeletal muscle, eyes and vision, lungs, kidneys, tumours, cell regulation, wound repair, bone, vasculature, and the heart. Growing bodies of work are demonstrating both the importance of chaotic dynamics for proper function of natural systems, as well as the suitability of fractal mathematics for characterizing these systems. ![]() Chaos is a type of nonlinear dynamics that tends to exhibit seemingly random structures, whereas fractality is a measure of the extent of organization underlying such structures. Optimal levels of chaos and fractality are distinctly associated with physiological health and function in natural systems. ![]()
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