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Data Science in R by Deborah Nolan, Duncan Temple Lang

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Chapter 8

A Self-Organizing Dynamic System with a Phase Transition

Deborah Nolan

University of California, Berkeley

Duncan Temple Lang

University of California, Davis

8.1 Introduction and Motivation

In this chapter, we will explore a very simple dynamic system. It exhibits two interesting characteristics – a phase transition and self-organization.

Most things in nature behave continuously. As inputs change a little, the outcomes change slightly. It is interesting when a slight change in an input causes a significantly different outcome. In some cases, as we vary an input over a range of values, we see continuous changes and then abruptly see qualitatively different outputs. This tipping point is called a phase transition. Basically, the system ...

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