Chaos by James Gleick

Chapter summaries

The table of contents in the book includes a multi-sentence summary for each chapter. Some of the them included bits that seemed unnecessarily cryptic - e.g. The computer misbehaves, A movie of chaos and a messianic appeal, Quakes in the schizosphere, etc. The book focuses on the personalities involved in the development of the field of chaos aka nonlinear dynamic systems, so my own dry, but clearcut summaries are basically lists of the scientists whose work is discussed in each chapter:

	chapter name	In this chapter...
1.	The Butterfly Effect	Edward Lorenz's work, culminating in the Lorenz attractor and the publication of his paper, Deterministic Nonperiodic Flow, in JotAS. The chapter title, "The Butterfly Effect", is a catchy term for the idea of "sensitive dependency on original conditions".
2.	Revolution	Several pages of filler, a brief introduction to Stephen Smale and the idea of phase space. Smale's horseshoe map. Philip Marcus models Jupiter's Great Red Spot.
3.	Life's Ups and Downs	Someone hands James Yorke a copy of Lorenz's paper and he passes it on to Smale. Yorke's paper, Period Three Implies Chaos (published in AMM) is mentioned. Cut to Robert May's modeling of animal populations using the equation xnext = rx(1 - x). First bifurcation diagrams appear. Frank Hoppensteadt's movie illustrating the appearance of bifurcations is mentioned.
4.	A Geometry of Nature	Opens with a hazy account of Benoit Mandelbrot's study of cotton prices. Flashback to Mandelbrot's youth during WW2 and his student days. The Cantor set and Cantor dust is introduced. Lewis F. Richardson's work (Does the Wind Possess a Velocity?, study of lengths of coastlines and national borders of various European countries) recycled by Mandelbrot (How Long is the Coast of Britain?). Fractals. Koch curve and Sierpiński carpet introduced. Fractals. The themes of this chapter are scaling and self-similarity.
5.	Strange Attractors	Turbulence. Swinney and Golub's investigations into the onset of turbulence in water flowing between two rotating cylinders (Couette-Taylor flow). Rouelle and Takens' 1971 paper "On the Nature of Turbulence" is mentioned. A side-by-side set of illustrations of a pendulum in motion and the evolution of the corresponding phase space diagrams is followed by an illustration of an attractor for that system. A different illustration of the Lorenz Attractor is shown. Poincaré maps are introduced. An account of Michel Hénon's studies of the orbits of stars around the Galactic core and the Hénon attractor appear at the end.
6.	Universality	Starts out with a biographical sketch of Mitchell Feigenbaum, first introduced to the reader for no apparent reason in the book's prologue and then set aside until now. The focus of the chapter never becomes clear, though the gist of it is that Feigenbaum had begun whatever it was he was working on by looking at Robert May's research on modeling animal populations. There's an aside (text plus graphs) titled "Zeroing in on Chaos", which is meaty and, in and of itself, makes sense. Unfortunately, the last paragraph of the aside begins Such images were a starting point for Feigenbaum when he tried to construct a theory and ends with a sort of "to be continued" .... As far as I can tell, Gleick never gets around to describing Feigenbaum's theory. After reading the Wikipedia entry on Feigenbaum, it seems as though Gleick was trying to describe the steps leading up to Feigenbaum's discovery of the first Feigenbaum constant.
7.	The Experimenter	Libchaber's study of the onset of turbulence in liquid Helium. Following the same pattern as in other chapters, Gleick devotes a lot of space here to, at best, tangentially-related topics, like the writings of a pseudoscientist obsessed with the flow of water (Theodor Schwenk) and the naturalist D'Arcy Wentworth Thompson, both of whom, Gleick suggests in a roundabout way, impacted Libchaber's thinking.
8.	Images of Chaos	Begins with the story of mathematician John Hubbard using Newton's Method (an iterative algorithm for finding the roots of a polynomial) to generate fractals (more explanation here and here). Julia sets and the Mandelbrot set are then discussed. Fractal basin boundaries get a couple of pages as well. Michael Barnsley's chaos game and Barnsley's Fern round out the chapter.
9.	The Dynamical Systems Collective	In the late 1970's, Robert Stetson Shaw was a physics grad student at UC Santa Cruz. A professor came back from a conference with the three equations used to generate the Lorenz attractor written on a piece of paper, gave the paper to Shaw, and asked him to try to run them on their old Systron-Donner, a model of analog computer that, evidently, was sitting gathering dust in the department basement. This chapter is Gleick's account of the rise and inevitable splintering apart of UCSC's "Dynamical Systems Collective", a group of physics graduate students that nucleated around Shaw and the Systron-Donner, which he had commandeered and dragged into his office after becoming fascinated with the Lorenz attractor. Lyapunov exponents get a brief prose explanation here. Information theory is introduced as well. Shaw's discovery of a strange attractor within the periodicity of the drips from a leaky faucet, eventually the subject of what seems to be his one and only book (1984's The Dripping Faucet as a Model Chaotic System), is also discussed.
10.	Inner Rhythms	Now the book tackles applications of chaos theory to biology - beginning with the eye and moving on to the heart and biological clocks. Daisy world is mentioned. Huberman, who made a brief appearance in the previous chapter as one of the factors that chipped away at the DSC (by getting one of the members to run his equations on what evidently was the sole remaining analog computer in the world and convincing him to agree to not share authorship on a groundbreaking paper later published in Physical Review Letters with the rest of the collective) reappears. This time, Huberman is presenting to a conference on chaos in biology and medicine about a physical model of the erratic movements of schizophrenics' eyes based, in part, on the motions of a pendulum. His model suggests that the erratic movements are due to noisiness in the signals from the nervous systems to the muscles controlling eye movements.
11.	Chaos and Beyond	This is the shortest chapter in the book (less than 15 pages). First, widely-held beliefs that the author believes were shown to be false with the advent of chaos theory are boiled down into three statements: Simple systems behave in simple ways, complex behavior implies complex causes, different systems behave differently. Later, some definitions of chaos are presented. If he had stopped here, he would have had a sensible ending for the book. Unfortunately, he goes down a bit of a rathole - getting into the second law of thermodynamics and snowflake formation and finishing up with the story of the chaos epiphany of ecologist William M. Schafer. Was this intended as a sort of cliffhanger for a follow-on book?

Chapter 6, Universality, is broken by a 8-page (4-page front and back) color insert depicting: the Lorenz attractor, the Koch snowflake, the Mandelbrot set and several zoomed-in sections of same, Newton's Method used to solve x4 - 1 = 0 , "fractal clusters", and the Great Red Spot on Jupiter and simulations of same.