Fractals and chaos simplified for the life sciences
Fractals and chaos are currently generating excitement across various scientific and medical disciplines. Biomedical investigators, graduate students, and undergraduates are becoming increasingly interested in applying fractals and chaos (nonlinear dynamics) to a variety of problems in biology and medicine. This accessible text lucidly explains these concepts and illustrates their uses with examples from biomedical research. The author presents the material in a very unique, straightforward manner which avoids technical jargon and does not assume a strong background in mathematics. The text uses a step-by-step approach by explaining one concept at a time in a set of facing pages, with text on the left page and graphics on the right page; the graphics pages can be copied directly onto transparencies for teaching. Ideal for courses in biostatistics, fractals, mathematical modeling of biological systems, and related courses in medicine, biology, and applied mathematics, Fractals and Chaos Simplified for the Life Sciences will also serve as a useful resource for scientists in biomedicine, physics, chemistry, and engineering.
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2-dimensional action potentials analyze attractor average beat behavior bifurcation Biological Implications biological systems blood vessels box counting Capacity Dimension cell membrane chaotic system coastline computed Control of Chaos Determining the Fractal deterministic mechanism distributions electrical embedding dimension equations Examples of Self-Similarity Fano factor finer resolution fractal dimension fractal object frequency Glycolysis Hausdorff-Besicovitch dimension Heart Cells increases independent variables initial conditions integer ion channel Ion Channel Kinetics ion channel protein Koch curve length Liebovitch line segments Log N(r logarithm Lorenz system lung mathematical mean measured at resolution motion mutations nerve cells Non-Fractal nonlinear number of independent open and closed output perimeter phase space set plot power law scaling produced Properties of Fractals property Q(r Q(ar random mechanism rescaled range retina scaling relationship self-similarity dimension sensitivity to initial sequence of values Sets Constructed statistical properties statistical self-similarity surface Theorem topological dimension trajectory values measured variance voltage X(t+At