In  The Algorithmic Beauty of Shells, the author, Hans. Meinhardt, shows how he created mathematical models to explain patterns on seashells.

Shell Game: Creating shells out of nothing but mathematical equations, a computer scientist holds a mirror up to nature.
by Carl Zimmer

From the blue-and-black symmetries of a butterfly to the mazelike grooves of a brain coral, nature reveals itself as a great artist, switching off between painting and sculpture. Nature should also get credit, though, for being a first-class mathematician. The patterns and shapes of living things correspond to some of the most abstract ideas in math. The humble mollusk, for example, without a single course in algebra, can draw the equation r = ae . The philosopher and mathematician René Descartes discovered this formula for the curve of shells 354 years ago. To create the curve, technically known as a logarithmic spiral, Descartes’s equation guides your pen around a central point, degree by degree, and pushes it farther away from the center by a factor related to the angle it has reached.

Read More at Discover Magazine
God is a mathematician

Paul Dirac 1939
Nobel Prize Winner
The natural language of pattern and form is mathematics.  This may dismay some of you who never quite made friends with the universal tool of science….

Mathematics enables us to get to grips with the essence of pattern and form - to describe it at its most fundamental level, and thereby see what features need to be reproduced by an explanation or a model.   (Ball 1997)

The Algorithmic Beauty of Seashells
by Hans Meinhardt

Mathematical models and advanced computer-generated images are used to explain and illustrate structural growth patterns of seashells in nature. This fascinating and beautifully illustrated book conveys the intuitive appeal and the "touch of magic" that accompany the current research. A diskette, packaged with the book, contains the algorithms and simulations necessary to replicate the results. 150 illustrations.

Mathematics in Nature: Modeling Patterns in the Natural WorldBy John A. Adam
the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, "Mathematics in Nature" is an excellent and undaunting introduction to the ideas and methods of mathematical modeling.

Computer Simulations

Math is a tool that can be used for making models of the natural world.
Computer simulations use math to create models of pattern formation and growth

Coming Soon: Simulations as a tool to understand emergence, and complexity

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