Fractal Patterns in Nonlinear Dynamics and Applications

<p>Most books on fractals focus on deterministic fractals as the impact of incorporating randomness and time is almost absent. Further most review fractals without explaining what scaling and self-similarity means. This book introduces the idea of scaling self-similarity scale-invariance and their role in the dimensional analysis. For the first time fractals emphasizing mostly on stochastic fractal and multifractals which evolves with time instead of scale-free self-similarity are discussed. Moreover it looks at power laws and dynamic scaling laws in some detail and provides an overview of modern statistical tools for calculating fractal dimension and multifractal spectrum.</p>