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Conformal geometry --- Discrete groups --- Manifolds (Mathematics) --- 514.763.4 --- Geometry, Differential --- Topology --- Groups, Discrete --- Discrete mathematics --- Infinite groups --- Circular geometry --- Geometry of inverse radii --- Inverse radii, Geometry of --- Inversion geometry --- Möbius geometry --- Geometry --- 514.763.4 Manifolds with complex or almost-complex structure. Hermitian manifolds. Kähler manifolds --- Manifolds with complex or almost-complex structure. Hermitian manifolds. Kähler manifolds --- Differential geometry. Global analysis

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This book provides a short, hands-on introduction to the science of complexity using simple computational models of natural complex systems-with models and exercises drawn from physics, chemistry, geology, and biology. By working through the models and engaging in additional computational explorations suggested at the end of each chapter, readers very quickly develop an understanding of how complex structures and behaviors can emerge in natural phenomena as diverse as avalanches, forest fires, earthquakes, chemical reactions, animal flocks, and epidemic diseases.Natural Complexity provides the necessary topical background, complete source codes in Python, and detailed explanations for all computational models. Ideal for undergraduates, beginning graduate students, and researchers in the physical and natural sciences, this unique handbook requires no advanced mathematical knowledge or programming skills and is suitable for self-learners with a working knowledge of precalculus and high-school physics.Self-contained and accessible, Natural Complexity enables readers to identify and quantify common underlying structural and dynamical patterns shared by the various systems and phenomena it examines, so that they can form their own answers to the questions of what natural complexity is and how it arises.

Complexity (Philosophy) --- Physics --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Philosophy --- Emergence (Philosophy) --- Methodology. --- Burridge-Knopoff stick-slip model. --- Gutenberg-Richter law. --- Johannes Kepler. --- Olami-Feder-Christensen model. --- Python code. --- accretion. --- active flockers. --- agents. --- automobile traffic. --- avalanches. --- cells. --- cellular automata. --- chaos. --- clusters. --- complex behavior. --- complex structure. --- complex system. --- complexity. --- computational model. --- computer program. --- contagious diseases. --- criticality. --- diffusion-limited aggregation. --- earthquake forecasting. --- earthquakes. --- emergence. --- emergent behavior. --- emergent structure. --- epidemic spread. --- epidemic surges. --- excitable system. --- flocking. --- forest fires. --- fractal clusters. --- fractal geometry. --- growth. --- hodgepodge machine. --- infection rate. --- iterated growth. --- lattice. --- lichens. --- natural complex system. --- natural complexity. --- natural order. --- natural phenomena. --- nature. --- open dissipative system. --- panic. --- passive flockers. --- pattern formation. --- percolation threshold. --- percolation. --- phase transition. --- planetary motion. --- power-law. --- random walk. --- randomness. --- repulsion. --- rule-based growth. --- sandpile. --- scale invariance. --- segregation. --- self-organization. --- self-organized criticality. --- self-propulsion. --- self-similarity. --- simple rules. --- small-world network. --- solar flares. --- spaghetti. --- spatiotemporal pattern. --- spiral. --- tagging algorithm. --- traffic jams. --- waves. --- wildfire management.