A | B | C | D | E
F | G | H | I | J
K | L | M | N | O
P | Q | R | S | T
U | V | W | X | Y
Bold–faced page numbers indicate illustrations
Abraham, Ralph, 52–53, 247, 267, 279
accelerators, 7, 115, 125, 263, 271
Agnew, Harold, 2
Air Force (United States), 249
air resistance, 41–42
American Mathematical Monthly, 69
aperiodicity, 12, 15, 139, 246
and life, 299–300
and unpredictability, 22
Aristotle, 40–42
Arizona, University of, 317
Army (United States), 13
Arnold, V. L, 182
art, 94, 116–17, 186–87, 222, 229
AT&T Bell Laboratories, 127, 208, 255
Atlantic Ocean, 55
chaos in, 17
fixed–point (steady state), 64, 134, 227, 233, 237, 253, 255
limit cycles (oscillating), 73, 134, 227, 253, 255
stability of, 150
see also strange attractors
automobiles, 246
Barnsley, Michael, 215–16, 220–21, 226, 236–39
baseball, 67
Bateson, Gregory, 243
bees, 316–17
Belgium, 132
bell–shaped curve, see normal distribution
Beluzov–Zhabotinsky reaction, 287
Bergé, Pierre, 127
bifurcation, 71, 73, 74–75, 76, 78, 128, 173, 204–5, 211, 215, 223, 265, 305
see also period–doubling; intermittency; quasiperiodicity
biological clock, see circadian rhythms
biology, 198–200, 230, 239, 299, 314
mathematics in, 76, 198–201, 278, 282
models in, 60
see also physiology
Birkhoff’s bagel, 254
Blake, William, 115
Bohr, Niels, 7
boundaries, 114, 165, 198, 218–19, 220, 227, 232–33
in snowflake formation, 309
Bourbaki, 88–90
brain, 3, 7, 163–64, 239, 298–99, 307
Bremen (West Germany), University of, 229
Brookhaven National Laboratory, 306
Brown, Norman O., 243
Burke, William, 244–45, 262, 267
Butterfly Effect, 8, 20–23, 246–47, 261, 328, 329
calculus, see equations, differential California Institute of Technology, 243
California, University of
at Berkeley, 4, 45, 52, 247, 272
at Santa Cruz, 37, 52, 229, 243–245, 248–49, 264, 267, 269, 271–272
Cambridge University, 6
Cartwright, Mary Lucy, 332
Casati, Giulio, 184
causality, 201
Cayley, Arthur, 218
Central Intelligence Agency, 4, 249
in astronomy, 4–5, 14, 53–56, 144, 244, 245, 314
as creative process, 43
in dripping faucet, 262–66, 269
in earth’s magnetic field, 29
in economics, 307
in experiments, 68
formal definitions, 306
in galactic orbits, 147
government financing of, 4
as health, 298
in human heart, 288–90
and Ice Ages, 170
interdisciplinary character of, 5
on Jupiter, 53
language of, 4
named, 69
and perception, 164
resistance to ideas of, 31, 37–38, 106, 131, 139, 180, 303–6
sensitive dependence on initial conditions in, 8, 23, 44, 52, 67–68, 152, 230, 246–47, 253, 311
in shapes, 195–202
teaching of, 244
see also strange attractors; disorder; aperiodicity
chaotic attractors, see strange attractors
Chicago, University of, 307
China, 306
chromosomes, 5
circadian rhythms, 285–86, 288
City College of New York, 128, 131, 150, 159
White Earth equilibrium, 170
clouds, 2–3, 7, 11–12, 18, 26, 107, 157, 185–86
clustering, 91
coastlines, 94–96, 95, 105, 161, 237
cocaine, 283
Cohen, I. Bernard, 111
Cohen, Richard J., 290
color, 164–65
Comet Halley, 14–15
Communications in Mathematical Physics, 216
complex numbers, 215–20, 222–23, 226–32, 240
computers, 1, 7, 18, 209–10, 217, 227
and “artifacts,” 222
at Los Alamos, 178
attitudes toward, 13
and economics, 85
experimentation on, 230–31
graphics, 4, 15, 30, 38, 55, 71, 77, 114, 150, 178, 222–23, 226–40, 255, 269, 283
and heart rhythms, 289
and iterative fractals, 102
interactive use of, 38, 178–79
in laboratory experiments, 131, 289
personal, 7, 110–11, 114, 144, 146, 150, 231
simulating nonlinear systems, 44, 185, 209–10
supercomputers, 1, 7, 19, 123, 137
Systron–Donner, 244–7, 264, 267
Von Neumann and, 18
weather modeling on, 11–12, 14–15, 19, 21, 168–70
Control Data Corporation, 19
convection, 24–26, 25, 47, 128, 135, 139–41, 192–95, 202–6, 208–211, 314
Cornell University, 54, 158–59, 229, 285, 306
Corsica, 215
Couette–Taylor flow, 128–31, 129, 194, 203
Courant Institute of Mathematical Sciences (New York University), 77, 283
Cousteau, Jacques Y., 197
Creti, Donati, 53
crisis, 23
Crutchfield, James P., 248–51, 259, 264, 267, 270, 272, 306
cryptology, 256
Cvitanović, Predrag, 183
in ecology, 59, 73, 75, 78, 171
in economics, 68
cyclones, 12
Dartmouth College, 13
determinism, 5, 12, 14, 237, 250–51
differential equations, see equations
in phase space, 135
see also fractal
in phase transitions, 127
in price changes, 93
disease, 292
disorder, 3, 7, 15, 30, 56, 68, 266, 308
measuring, 257
dissipation, 42–43, 144, 182, 209, 314
attractors and, 138
in turbulence, 122–23, 138, 201
DNA (deoxyribonucleic acid), 110, 181, 201, 299
Douady, Adrien, 221–22, 227–28, 240
drugs, in psychiatry, 298–99
Duffing equation, 304–5
Duke University Medical Center, 289
Dynamical Systems Collective, 248–272
dynamical systems, 4, 24, 42, 52, 66, 118, 132, 134, 144, 169, 227, 252
Poincaré on, 46
Smale on, 45
dripping faucet as, 262–66, 269
in ecology, 59
dynamo, 29
Dyson, Freeman, 37, 73, 130, 161
earth, magnetic field of, 29
École Normale Supérieure, 87–88, 90, 191
École Polytechnique, 87–88, 191 ecology, 4, 59, 61–63, 69, 77–79, 166, 315–17
cycles in, 73
equilibrium in, 64, 70, 73, 79
models in, 69
economics, 4, 20, 83, 92–93, 271
cotton prices, 83–84
cycles in, 68
Eiffel Tower, 100
Eilenberger, Gert, 117
Einstein, Albert, 7, 14, 52, 111, 181, 245, 314, 324
Energy, Department of (United States), 4, 249
Enola Gay, 2
entropy, 7, 257–58, 261–62, 268, 271, 306, 308
differential, 12, 17, 44, 46, 61, 67, 187, 195, 208, 264
Duffing, 304–5
and global behavior, 174–75
logistic, 166–68, 170–72, 174–75
Lorenz system, 23–25, 47, 60, 116, 135, 139–41, 245–17, 329–30
as metaphors, 77
Navier–Stokes, 24
Newton’s method for solving, 217–220, 220
polynomial, 216–20
in climate, 169–70
in pattern formation, 309–14
in physiology, 298
see also attractors
errors, 8, 15–17, 21, 193, 256, 261
in communications, 91–92
in weather forecasting, 21
European Centre for Medium Range Weather Forecasts, 19–20
evolution, 5, 109, 116, 201, 251, 261, 314, 346
experimentation, 41, 125, 192–95, 202–6, 208–11, 263
Couette–Taylor flow, 128–31, 129
erratic behavior in, 68
numerical, 70, 112, 167, 178–79, 209–10
vs. theory, 125–26
Exxon Corporation, 114
Farmer, J., Doyne, 248–52, 258–59, 266, 268, 270–72, 303
Faust (Goethe), 163
feedback, 61, 167–68, 193, 223, 226, 279, 292, 314
Feigenbaum, Mitchell J., 1–4, 157–87, 194, 197, 206–10, 215, 268–69, 303, 305, 307, 314, 321
and art, 186
and childhood, 159
and color theory, 164–66
discovery of universality, 172–74, 206
and Libchaber, 208–9
and mathematical proof, 183
–ology, 182
and perception, 163
rejection letters, 180
theory for onset of chaos, 175–79
Feigenbaum numbers, 175, 183, 209, 211, 215–16, 223, 290
Feynman diagrams, 162
Feynman, Richard P., 137, 161, 324
fibrillation, see heart, arrhythmia in Fields Medal, 45–46
fireflies, 293
Fisher, Michael, 160
flames, 196
fluid dynamics, 38, 121–22, 131, 245
experiments in, 122, 124–28, 130–131, 152, 192–95, 202–6, 208–11
Ford, Joseph, 6, 38, 184, 252, 304–6, 314, 321
optimism about, 18
tides and eclipses, 18
Foucault, Jean Bernard Léon, 40
Fowles, John, 117
Fox, Ronald, 305
fractal basin boundaries, 43, 233–36, 235, 299
fractals, 4, 98, 110, 161–62, 215, 310, 316, 322
in cinematic effects, 114
computer programs for, 110–11, 114
as “dusts,” 228
earthquakes as, 103–4
dimension of, 102, 106–7, 162, 247, 271
goose down as, 110
Koch curve, 98–100, 99, 102–3, 237, insert following page 114
Menger sponge, 101
as “monstrosities,” 102
in pattern formation, 310, 311, insert following page 114
as shapes, 118, 219, 221, 227, 236, 237
Sierpinski carpet and gasket, 100, 101, 237
in wildness, 117
see also Mandelbrot set; strange attractors
France, 88, 90, 127, 144, 191, 197, 217, 258
Franceschini, Valter, 209
Franklin, Benjamin, 36
frequency spectrum, 205–6, 206, 207
friction, 24–25, 41–42, 50, 63, 122, 134, 144, 204, 209
functions, iteration of, 61–64, 69–71, 73, 167–68, 170–72, 174–75, 176–77, 222
modeling, on computers, 146
General Electric Corporation, 114
geodynamo, see earth, magnetic field
geometry
classical vs. fractal, 94, 226, 238
dimension in, 97
of surfaces, 104–6
Georgia Institute of Technology, 38, 216, 252, 304
Giglio, Marzio, 127
Global Atmosphere Research Program, 18
God, 8, 12, 121, 168, 185, 201, 314
Goethe, Johann Wolfgang von color theory of, 163–65
on plants, 197
Goldberger, Ary L., 281–82, 293
Gollub, Jerry P., 127–28, 150, 152, 194, 209
Gould, Stephen Jay, 200
gout, 277
Guckenheimer, John, 182
Guevara, Michael, 290–91
Halley, Edmond, 14–15
Hao Bai–Lin, 306
Harvard University, 69, 83, 164, 222–223, 243–44, 290
Haverford College, 128
Hawking, Stephen, 6–7
“Is the End in Sight for Theoretical Physics?” 6
arrhythmia in, 281, 283–84, 288–289, 291
defibrillating devices for, 284, 289, 292
Heiles, Carl, 147
Hénon, Michel, 44, 144–49, 303
on galactic orbits, 146–47, 148
Hénon attractor, see strange attractors
Hiroshima, 2
Holmes, Philip, 306
Hooke, Robert, 53
Hoppensteadt, Frank, 77
horseshoe, see Smale
Houthakker, Hendrik, 83–84
Hubbard, John, 217–19, 226–29, 240, 306
Huberman, Bernardo, 269–70, 275–278, 307, 324
Hudson’s Bay Company, 79
Ice Ages, 170
Ideker, Raymond E., 288–89
imaginary numbers, see complex numbers
immune system, 263, 272, 280, 314
information theory, 255–62, 268
information, 222, 239, 255–57, 261, 293, 321, 324
instability, 18, 169, 198, 299
in pattern formation, 309
Institut des Hautes Études Scienti–fiques, 132, 134
Institute for Advanced Study, 14, 37, 69, 132, 272
Institute for Physical Science and Technology (University of Maryland), 65
International Business Machines Corporation, 83–84, 86–87, 90, 222–223, 249
International Congress of Mathematicians, 45–46, 139
iteration, see feedback; functions
Jacot, Louis, 258
Jensen, Roderick V., 306
jet lag, 286
Johns Hopkins University, 126, 285
Journal of Atmospheric Sciences, 31
Journal of the Institute of Water Engineers, 197
Julia, Gaston, 216, 221, 226–27
Julia sets, 216, 221–22, 222, 228–29, 236–37
Jupiter, 53–56, insert following page 114
Kac, Mark, 183–84
Koch curve, 98–100, 99, 102–3, 237, insert following page 114
Kolmogorov, A. N., 76, 123, 182, 261
Kuhn, Thomas S., 35–39, 262, 315
concept of paradigms, 37, 39, 42, 52, 107, 269
problem–solving vs. scientific revolutions, 36–37
Lamont–Doherty Geophysical Observatory (Columbia University), 103
Landau, Lev D., 123–24, 130–32, 137, 152, 194
language, 256
Laplace, Pierre Simon, 14, 144
Lehrer, Tom, 243
Leibniz, Gottfried Wilhelm, 115–16
Leontief, Wassily, 84
Libchaber, Albert, 191–97, 202–11, 314
conception of “flow,” 195–202
“Helium in a Small Box,” 192–95, 193, 202–6, 208–11
measures period–doubling, 205–6
light, 164–65
lightning, 4
linguistics, 90
Littlewood, J. E., 332
logistic difference equation, 63–64, 69–70, 79, 166–68, 170–72, 174–175
Lorenz, Edward, 11–31, 44, 48, 52–53, 55–56, 65, 69, 71, 76, 116, 135, 139–40, 144, 149, 168–69, 182, 194, 244, 246, 253, 259, 264, 303, 314, 316–17, 321
and aperiodicity, 22
Butterfly Effect, 8, 20–23, 246–7, 261
childhood, 13
and climate, 168–69
and coffee cup, 25
“Deterministic Nonperiodic Flow,” 30, 66–67, 139–41
discovered by physicists, 67
discovers sensitive dependence on initial conditions, 16, 17
and mathematics, 13
and weather modeling, 15
Lorenz attractor, 28, 30, 140, 149, 218, 245–47, 269, insert following page 114
as music, 244—45
infinite complex of surfaces, 139–141
Los Alamos National laboratory, 14, 157, 160, 178
Center for Nonlinear Studies, 4
Theoretical Division, 1, 158, 179, 248, 272
Lovelock, James E., 279, 307, 308
Lyapunov exponent, 247, 253, 255, 262, 268, 316
lynx, 79
MacArthur, Robert, 315
Magellan, Ferdinand, 226
Mahler, Gustav, 163
Malkus, Willem, 31
Malthusian growth, 62–63
Mandelbrot, Benoit, 4, 83–118, 161–162, 182, 191, 216, 219–21, 223, 226–28, 237–38, 240, 303, 321
childhood, 87
and biology, 108–10
and cotton prices, 84–86
and dimension, 96–98
and economics, 83
and fractal constructions, 100
The Fractal Geometry of Nature, 104, 111–13
geometric intuition, 88
“How Long Is the Coast of Britain?”, 94–96
Merchant of Venice syndrome, 108
Noah and Joseph effects, 92–94
and physicists, 87
and randomness, 84
and self–similarity, 103
Mandelbrot set, 221–32, 224–25, 239–240, 306, inserts following pages 114 and 194
defined, 227
programming, 231–32
Mandell, Arnold, 278, 293, 298–99
Marat, Jean–Paul, 111
Marcus, Philip, 54–56
Marcuse, Herbert, 243
Margulis, Lynn, 279
Maryland, University of, 65
Massachusetts Institute of Technology, 11, 13, 21, 31, 103, 159, 163, 290, 321
mathematics
in biology, 60, 69, 198–200, 282, 290
complex analysis, 227
and hermeticism, 89
experimentation in, 38, 112, 218–219, 229
and Mandelbrot, 111
and numbers, 178
rigor in, 89, 183, 218, 230–31
vs. physics, 47, 52, 66, 69, 113, 118, 178
and turbulence, 121–25, 130–33, 137
Maxwell, James Clerk, 181
May, Robert, 4, 69–80, 135, 166–67, 171, 172, 182, 208, 259, 303, 321
“messianic” plea, 79, 245, 316
and period–doubling, 70–71, 172
and epidemiology, 78
McGill University, 281, 288, 290
Medawar, Sir Peter, 200
Menger sponge, 101
meterology, 3, 11–13, 21–22, 55, 168–169
Metropolis, Nicholas, 167–68, 173, 182
Mines, George, 288
mode locking, 290, 293, 294–95
models
approximation in, 15
borrowed from physics, 60, 282
“daisy world,” 279
detail vs. generalization in, 278–79
for earthquakes, 107
in economics, 20
for epidemics, 316
for galactic orbits, 146–47, 149
for heart motion, 281–83
for schizophrenia, 276–78
stability in, 48
for weather, 11–14, 16–17, 19–21, 55
Morse code, 258
Moscow University, 46
mosquitoes, 285–86
mysticism, 195
National Aeronautics and Space Administration, 54
National Center for Atmospheric Research, 250
National Institute of Mental Health, 275
National Institutes of Health, 275
National Meterological Center, 19
National Oceanic and Atmospheric Administration, 21
National Science Foundation, 46, 131, 249, 317
Navier–Stokes equation, 24
Navy (United States), 249, 275
Neumann, John von, 14, 18–19, 21
on nonlinearίty in fluids, 24
New York Academy of Sciences, 258–259, 269, 275
New York City public schools, 159
see also City College of New York
New York University, 77, 283. See also Courant Institute
Newton’s method, 217–20, 220, 227,
insert following page 114
Newton, Sir Isaac, 12–13, 15, 39, 41, 55, 118, 144–45, 164, 217, 324
and color, 164–66
Nobel Symposium, 182
noise, see errors
nonlinear dynamics, see chaos
nonlinearity, 23–24, 56, 63, 73, 80, 162, 333
as agent of stability, 193–94
in dripping faucet, 264
in fluid models, 283
in pendulum, 41–43
and problem–solving, 153, 162, 166, 250–51
in schizophrenia, 277
teaching of, 42
normal distribution, 84
Office of Naval Research, see Navy
Oppenheimer, J. Robert, 1
oscillators, see pendulums
Oxford University, 215, 306, 321
Packard, Norman, 248–51, 258–59, 270, 272
Paris Opera, 117
particle physics, 6–7, 115, 125
patterns, 5, 43, 196, 261, 308
across scale, 86
in biology, 299
formation of, 272, 308, 310, 314
generated by fractal processes, 236–239
Peitgen, Heinz–Otto, 229–31, 236, 240
pendulums, 39, 41–44, 49, 60, 169–170, 174, 234, 292–93, 315
Aristotle and Galileo on, 40–42
double, 230
nonlinearity in, 42–43
and schizophrenia, 276
spherical, 43
strange attractor of, 143
perception, 163
period–doubling, 71, 73, 76, 171–72, 176–77, 204, 206, 211, 215, 265, 305
found in experiment, 204–6, 207
in heart cells, 290
in schizophrenia, 276
phase space, 49–52, 50, 134–39, 136–137, 144, 149, 206, 227, 230, 246, 261, 269, 299
infinite dimensional, 136–37, 271
reconstruction of, 265–66, 316
phase transitions, 126–28, 160–61, 236, 298
of beer glasses, 245
condensed matter, 126
experiment vs. theory, 125–26
Grand Unified Theory of, 7
mentors and protégés in, 244, 249
Newtonian, 6
and turbulence, 121–25, 130–33, 137
radios vs. chemistry sets, 132
reductionism in, 185
teaching of, 42, 56, 67–68, 244, 250
without chaos, 67
complexity in, 279–80
dynamical diseases, 292
eyes, 275–78
lungs, 108–9
see also blood vessels; brain; heart; immune system
pinball, 233–34
planets, 14
Poincaré, Jules Henri, 46–47, 88, 123, 145, 166, 181, 264, 321–22
and many–body problem, 145
Poincaré conjecture, 46
Poincaré map, 142–44, 143, 146, 150, 290, 316
Pomeau, Yves, 149
population, see ecology
predictability, 7–8, 14, 18, 21, 253, 268
and aperiodicity, 22
Princeton University, 4, 69, 146, 285
quadratic difference equation, see logistic difference equation
quantum mechanics, 6–7, 118, 161. 184–85. 250, 314
quarks, 5
rain, 18
randomness, 3, 5, 8, 21–22, 68, 73, 84, 122, 236–39, 251–52, 257, 261, 306
and complexity, 314
in constructing fractals, 236–39
debate over, in ecology, 77–78
and determinism, 250–52
hidden structure in, 22
and information theory, 252, 261
from simple models, 79
and weather forecasting, 21–22
Rayleigh, Lord, 128
Red Spot of Jupiter, 53–56, insert following page 114
reductionism, 5, 14, 115, 165, 185, 201, 210, 279, 304
redundancy, 256
relativity, 6–7, 14, 121, 162, 226
renormalization group theory, 161–62, 172, 179–80, 268–69
Reynolds, Osborne, 128
Richardson, Lewis F., 94–95
Richter, Peter, 229–30, 236, 240
Ricker, W. E., 63
Rössler attractor, see strange attractors roulette, 248
Royal McBee computer, 11–12, 15–16, 19
Rubin, Jerry, 45
Ruelle, David, 4, 131–34, 138–39, 149–50, 152–53, 182, 194, 216, 259, 261, 307
childhood, 132–33
on heart dynamics, 280–81
invents strange attractors, 133–34, 138–39
meets Lorenz, 141
on turbulence, 133
Ruysdael, Jacob van, 186
Santa Catalina mountains, 316
Sarkovskii, A. N., 74
scaling, 86, 90, 103, 107, 115–16, 172–73, 175, 179, 186
in economics, 86
in phase transitions, 161
in turbulence, 162
Schaffer, William M., 15, 315–17
schizophrenia, 275–78, 292, 298
Scholz, Christopher, 103–7
Schrier, Alvin, 290–91
Schrödinger, Erwin, 299–300
Schwenk, 197
Schwinger, Julian, 161
science
causality in, 201–2
communication in, 31, 38, 181–82, 184, 196, 252, 275
financing of, 249
in Soviet Union, 76
and mysticism, 195
“normal,” 36–37
peer review in, 131, 180–81, 195
revolution in, 36–39, 111, 315
seeing the unexpected in, 35
traditional beliefs in, 14–15, 44, 64–65, 85, 92–93, 123–24, 303–306
second law, see thermodynamics
self–organization, 55, 252, 261, 308, 314
self–similarity, 103, 115–16, 227
in turbulence, 162
Shakespeare, William, 258, 320
Shannon. Claude, 255–57
Shaw, Christopher, 259
Shaw, Robert Stetson, 243–50, 252–253, 258–72, 293
and dripping faucet, 262–66, 269
Shlesinger, Michael, 5
Sierpiński carpet and gasket, 100, 101, 237
Smale, Stephen, 4, 45–53, 61, 70, 76, 89, 118, 132, 171, 182, 208, 247
antiwar protests, 45
conjecture on chaos, 45, 47–48, 66
horseshoe, 51–52, 51, 76, 132–33, 149
stability in the sense of, 47–48
Smith, J. Maynard, 64
smoke, 5
snowflakes, 114, 272, 309–14, 312–313
stability of, 145
spectrum diagram, 205–6, 206, 207
Spiegel, Edward A., 244–45
through feedback, 61–62, 193–94, 292
Stanford Linear Accelerator Center, 263
Stanford University, 269
stars, 4
state space, see phase space
Stein, Paul, 167–68, 173–74, 182
Steiner, Rudolf, 197
Stevens, Wallace, 196
Stewart, H. Bruce, 306, 334–35
stock market, 85, 93, 152, 271, 307
strange attractors, 4, 133–35, 137–38, 140–44, 143, 152, 209, 246, 252, 254, 258, 262, 266, 269, 271, 320
in climate, 307
in epidemics, 316
in experiment, 265–66
fractal nature of, 139, 141, 152
measuring, 253–55
named by Ruelle and Takens, 133–134
of Feigenbaum, 175
of Lorenz, 28, 30, 139–41, 140, 149, 153, 218, 244–47, 269, insert following page 114
of Rössler, 141
of Ueda, 141
supercomputers, 1, 7, 19, 123, 137
surface tension, 311
Swift, Jonathan, 103
Swinney, Harry L., 126–27, 150, 152, 194, 203, 209, 266, 270, 317
Symmer, Robert, 111
Systron–Donner computer, see computers, analog
Takens, Floris, 133, 138–39, 141 and reconstructing phase space, 266
Taylor, Sir Geoffrey Ingram, 130
Tellus, 169
Texas, University of, 266, 285
thermodynamics, second law of, 257–258, 307, 308
as metaphor, 308
Thompson, D’Arcy Wentworth, 198–202
Tolstoy, Leo, 38
topology, 45–46, 50, 52, 198, 253
and dynamical systems, 47
of biological rhythms, 286, 289, 292
traffic, 5
transistor, 7
turbulence, 2, 4, 7, 39, 121–25, 130–133, 137–38, 162, 198, 203, 307
and information, 261
in heart valves, 282–83
on Jupiter, 53
Landau picture of, 123–25, 130–33, 137, 180, 194
modeling, with computers, 137
onset of, 122–23, 170, 174–75, 192, 194
Turner, Joseph Mallord William, 186
Ueda’s attractor, see strange attractors
universality, 5, 172–81, 187, 196, 215, 236
apparent lack of, 153
consequences for science, 179–81, 183, 268–69
discovered by Feigenbaum, 172–75
theory for, 175–79
and perception, 166
unpredictability, 44, 253, 258, 261, 319
Updike, John, 53
van der Pol, Balthasar, 49, 51, 332
van Gogh, Vincent, 186
Vatican, 53
Virchow, Rudolf, 111
Virginia Polytechnic Institute, 159
Voyager, see satellites
war, 5
Water Resources Bulletin, 197
Watson, James, 111
and strange attractors, 152
control and modification, 18–19
forecasting, 13
Weaver, Warren, 257
White, Robert, 21
Wilson, Kenneth, 160–62
Winfree, Arthur, 284–86, 288–89, 291–92, 307
Xerox Palo Alto Research Center, 269, 275
Yale University, 306
Yorke, James, 65–69, 182, 259, 270–271, 317
and fractal basin boundaries, 233–235
recognition of chaos, 73–76