Patterns in Motion
How Cellular Automata Reveal the Hidden Calculus of Change
What if the mathematics of continuous change could emerge from simple discrete rules? Most people encounter derivatives and differentiation in the smooth, continuous world of calculus, while cellular automata seem to belong to an entirely different realm of discrete computation. Yet these two mathematical frameworks share profound connections that illuminate how complexity arises from simplicity and how local interactions generate global patterns. This book reveals the surprising bridges between cellular automata and calculus, showing you how discrete systems can approximate continuous processes and how differentiation concepts apply to grid-based worlds. You'll discover how simple rules governing individual cells create intricate patterns whose evolution can be analyzed using derivative-like tools. Through clear explanations and visual intuition, you'll explore how spatial and temporal changes in cellular automata mirror the rates of change studied in calculus, and how these discrete systems can even solve differential equations numerically. Whether you're fascinated by emergent complexity, interested in computational approaches to mathematical problems, or curious about the deep unity underlying different branches of mathematics, this book will reshape how you think about change, patterns, and the relationship between discrete and continuous worlds.
Est. Length
222 pages (11 chapters)
Language
English
Publication date
Oct 27, 2025
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