pattern formation : intro page

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Pattern Formation (Intro Page)
	•	Introduction

Slide Show
	•	Introduction

Reflections and Rotations
	•	Symmetry Operations, Abstract and in Nature
	•	Symmetry Identification Exercise

Links, Chains, & Spirals
	•	On the Spiral Growth of Shells
	•	Spiral Growth and Plants
	•	Chains, Double Chains, & Spirals

Packing and Tesselations
	•	Bubbles in a bowl activity
	•	Crystal Structures in Two Dimensions
	•	Symmetry in Tesselations
	•	Group Reports

Platonic Solids
	•	Platonic Solids activity
	•	Ionic and Other 3-D Crystal Structures

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Breaking Symmetry
	•	Breaking Symmetry in Inorganic and Living Systems
	•	Breaking Symmetry Activity

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In this chapter we assess the properties of some common patterns that emerge repeatedly in the natural world. We analyze these patterns in the context of their symmetries.

• First, we establish some basic rules of symmetry.
  
  
• Then, we use a series of case studies to illustrate important 1-dimensional, 2-dimensional and 3-dimensional patterns that appear in many different systems.
  
  
• Finally, we introduce the concept of breaking symmetry. This lies at the heart of evolution, for the emergence of novelty or complexity in a system invariably requires the breaking of some prior symmetry.