Shape Dynamics and Complexity
Differential Geometry, Topology, and Algorithms for Understanding Growth in Complex Systems
Created by DanielWhat if the shapes of living organisms follow mathematical laws as precise as those governing planetary motion? This book reveals how differential geometry, topology, and advanced algorithms decode the hidden mathematics of biological growth. You'll discover why fractal patterns appear across scales in nature, how entropy quantifies complexity in living systems, and why symmetry groups constrain evolutionary possibilities. Moving beyond abstract theory, you'll learn to apply manifold learning algorithms to biological networks, use topological invariants to predict system behavior, and implement computational methods that transform raw biological data into actionable insights. Whether analyzing tumor growth dynamics, understanding neural network organization, or predicting protein folding patterns, these mathematical frameworks provide the precision tools needed for 21st-century biological research. This book integrates recent 2025 discoveries with established theory, offering both the conceptual depth mathematicians demand and the practical applications biologists require.
Est. Length
222 pages (10 chapters)
Language
English
Publication date
Dec 2, 2025
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