Epilogue
We are the days and the nightsAnd the stars,
That illuminate the darkness.We are holy beings,Recalling this truth,
We feel the Sun and the MoonIn our body
Like Dancing Spirals
The secrets of existence unfold within us.
—American Indian Wisdom
© Springer Nature Switzerland AG 2019K. Tsuji and S. C. Müller (eds.), Spirals and Vortices,The Frontiers Collection, https://doi.org/10.1007/978-3-030-05798-5
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851 (1993)4. A. Deutsch (ed.), Muster des Lebendigen (Vieweg, Braunschweig, 1994)5. J. Diamond, Guns, Germs, and Steel (W.W. Norton and Company, New York, 1999)6. I.R. Epstein, J. Pojman, An Introduction to Nonlinear Chemical Dynamics (Oxford University
Press, Oxford, 1998)7. R. Ettinghausen, O. Grabar, M. Jenkins-Madina, Islamic Art and Architecture 650-1250
(2nd ed.) (Yale University Press, Yale, 2003)8. A. Feininger, Das Antlitz der Natur (Knauer, München, 1957)9. G. Gerisch, Periodische Signale steuern die Musterbildung in Zellverbänden. Naturwis-
senschaften 58, 430–438 (1971)10. A. Goldbeter, La Vie Oscillatoire (Odile Jacob, Paris, 2010)11. H. Haberland, Amerikanische Archäologie - Geschichte, Theorie, Kulturentwicklung (Wis-
senschaftliche Buchgesellschaft, Darmstadt 1992)12. H. Haken, Synergetics - Introduction and Advanced Topics (Springer, Berlin, 2004)13. H. Haken, P.J. Plath, W.E. Ebeling, Y.M. Romanosky (eds.), Beitäge zur Geschichte der Syn-
ergetik (Springer-Spektrum, Heidelberg, 2016)14. I. Hargittai, C.A. Pickover (eds.), Spiral Symmetry (World Scientific, Hong Kong, 1992)15. M. Hauser, O. Steinbock (eds.), Emergent phenomena in spatially distributed systems - in
Honor of Stefan C. Müller. Physica D 239 (2010)16. E.S. Hedges, J.E. Myers, The Problem of Physicochemical Periodicity (Edward Arnold and
Co., London, 1926)17. A.L. Hodgkin, A.F. Huxley, A quantitative description of membrane current and its application
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2008)20. R. Kapral, K. Showalter (eds.), Chemical Waves and Patterns (Kluwer, Dordrecht, 1995)21. M. Kemp, Leonardo (C.H. Beck, München, 2004)22. R. Kessin, Dictyostelium (Cambridge University Press, Cambridge, 2001)23. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer, Heidelberg, 1984)24. H. Meinhardt, The Algorithmic Beauty of Sea Shells (Springer, Heidelberg)
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25. A.S. Mikhailov, G. Ertl, Chemical Complexity (Springer, Switzerland, 2017)26. S.C. Müller, P.J. Plath, G. Radons, A. Fuchs (eds.), Complexity and Synergetics (Springer,
Switzerland, 2018)27. J.D. Murray, Mathematical Biology I. An Introduction, 2 edn. (Springer, Heidelberg, 1993)28. G. Nicolis, I. Prigogine, Exploring Complexity (R. Piper, München, 1989)29. R.T. Paine, A. Soper, The Art and Architecture of Japan (3rd ed.), (Yale University Press
Pelican History of Art, Yale, 1981)30. J. Parisi, S.C.Müller,W. Zimmermann,APerspective Look at NonlinearMedia - FromPhysics
to Biology and Social Sciences (Springer, Berlin, Heidelberg, 1998)31. H.O. Peitgen, P.H. Richter The Beauty of Fractals (Springer, Tokyo, 1986)32. J. Ross Thermodynamics and Fluctuations Far from Equilibrium (Springer, Heidelberg, 2008)33. F.W. Schneider, A.F. Münster, Nichtlineare Dynamik in der Chemie (Spektrum Akademischer
Verlag, Oxford, 1996)34. K. Seike, M. Kudo, W. Schmidt, Japanische Gärten und Gartenteile (Ulmer, Stuttgart, 1980)35. S.H. Strogatz, Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chem-
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Glossary
Activator a substance which accelerates or stimulates a reaction.
ADP, AMP see ATP.
Allosteric The term allostery comes from the Greek allos “other”, and stereos “solid(object)”. This is in reference to the fact that the regulatory site of a protein (calledallosteric site) is different from its active site.
Anoxia an absence or deficiency of oxygen reaching the tissues.
ATP (adenosine triphosphate) a complex organic chemical which is used for intra-cellular energy transfer. When consumed in metabolic processes, it converts to eitherADP (adenosine diphospate) or AMP (adenosine monophosphate).
Attractor points, loops (limit cycles), surfaces (tori), and other geometrical subsets(chaotic and fractal), where a dynamical system reaches (or approximates) stableconfiguration or its “death”. For example, the center bottom position of a dampedpendulum is a point attractor: the pendulum is losing energy (energy dissipation) dueto friction time by time and finally it stops at the bottom.
Autocatalysis a catalysis of a reaction by one of its own products.
Avatar a word in Hinduism, means incarnation.
Belousov–Zhabotinsky (BZ) Reaction one of chemical reactions occurring alongthe laws of non-equilibrium thermodynamics, showing chemical oscillations. Theoscillatory behavior is observed temporally and/or spatially. The essential ele-ments in this oscillator are the autocatalytic species HBrO2 as activator, bromide asinhibitor, and a catalyst/color indicator. Under excitable conditions it forms propa-gating concentration waves.
Brewster Angle an incident angle at which a particular polarized light is transmittedwithout reflection.
Carolingian script combining characteristics of cursive and half uncial, developedin France in the 8th century (when the Carolingian dynasty governed).
© Springer Nature Switzerland AG 2019K. Tsuji and S. C. Müller (eds.), Spirals and Vortices,The Frontiers Collection, https://doi.org/10.1007/978-3-030-05798-5
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282 Glossary
Cellular Automaton a discrete model studied typically in complexity science andtheoretical biology. It consists of a regular grid of cells, each in one of a finite numberof states, such as “on” and “off‘’. For each cell, a set of cells called its neighborhoodis defined relative to the specified cell in discrete time steps.
Chemotaxis movement of cells or organisms due to gradient of chemical agents (seealso phototaxis).
Conservative System incompressible flux in phase space, phase space volume is con-served. For example, trajectories of harmonic oscillator or planet movement aroundthe Sun. (↔ dissipative system).
Convection thermally or chemically produced upward or downward movement offluids (liquids or gases).
CNS (central nervous system) the part of the nervous system consisting of the brainand spinal cord.
Craniotomy the surgical removal of part of the bone from the skull to expose thebrain.
Deterministic a deterministic system is a system inwhich no randomness is involvedin the development of future states of the system. A deterministic model will alwaysproduce the same output from a given initial state.
Dissipative System phase space volume contracts in time. For example, dampedoscillator. (↔ conservative system).
Dolmen a prehistoric monument consisting of two or more stones supporting ahorizontal stone slab.
Exoskeleton an external skeleton or supportive covering an animal (↔ endoskele-ton).
Feigenbaum Scenario a mathematical scenario to cause deterministic chaos fromorder by period doubling.
Fractal infinitely repeating similar pattern (self-similar pattern) at increasing smallerscales, usually due to its non-integer dimension.
Gabel (Wimperg in German) the vertical triangular portion of a wall between theedges of intersecting roof pitches, often used in the architecture of churches.
Geoglyph a large mark or motif produced on the ground, formed by stones, stonefragments, live trees, gravel, or earth.
Heaviside Function a step function, whose value is zero for negative argument andone for positive argument.
Inhibitor a substance that interferes with a chemical process or reaction, e.g., bysuppressing growth.
Ischemia an inadequate blood supply to an organ or part of the body, especially theheart muscles.
Glossary 283
Laminar Flow streamline flow in which a fluid flows in parallel layers, with nodisruption between the layers (↔ turbulence).
Luciferase an oxidative enzyme which acts on luciforin. Resulting excited stateintermediate emits light upon decaying to its ground state which produces biolumi-nescence.
Mean Field Theory Mean field theory studies the behavior of large and complexstochasticmodels by studying a simplermodel. Suchmodels consider a large numberof small individual components which interact with each other. The effect of all theother individuals on any given individual is approximated by a single averaged effect,thus reducing a many-body problem to a one-body problem.
Metamorphosis change into a different physical or biological form.
Morphogenesis the biological process that causes an organism to develop its shape,for example, control of cell growth and cellular differentiation.
Nacre iridescent inner layer of some shellfish, known as “mother of pearl”.
NAD (nicotinamide adenine dinucleotide) a coenzyme existing in all living cellsin two forms: an oxidized and reduced form NAD+ and NADH, respectively, func-tioning for electron transfer in cells.
NGC (New General Catalogue) a catalogue of 7840 deep-sky objects, includinggalaxies, star clusters, emission nebulae and absorption nebulae.
Non-equilibrium In thermodynamic equilibrium there are no net macroscopic flowsof matter or of energy, either within a system or between systems. In non-equilibriumsystems, by contrast, there are net flows of matter or energy. The role of entropy hasto be considered.
Nonlinear Dynamics a field of physics that studies systems governed by equationsmore complex than the linear aX + b form. Nonlinear systems, such as the weatheror neurons, often appear unpredictable, but still they are not random.
Normal Velocity In mathematics, given a velocity vector at a point on a curve, thatvector can be decomposed uniquely as a sum of two vectors, one tangent to the curve,called the tangential component of the vector, and another one perpendicular to thecurve, called the normal component of the vector.
Phototaxis movements of cells or organisms due to light gradient (see also chemo-taxis).
Proboscis a sucking organ of insects or some other invertebrates, or a flexible con-spicuously long snout of some mammals.
Refractory unresponsive to stimuli, a resting state.
Self-Organization a process where some form of overall order arises from localinteractions between parts of an initially disordered system. The process is oftenspontaneous structuration out of a homogeneous initial state, triggered by random
284 Glossary
fluctuations and amplified by positive feedback. Examples are: crystallization, ther-mal convection of fluids, chemical oscillation, animal swarming, neural networks,and others.
Self-Similarity for objects being exactly or approximately similar to a part of itself.
Stochastic a system that is randomly determined; variables proceed by probabilities,or guesswork.
Swarm Intelligence the collective behavior of decentralized, self-organized systemssuch as insect, bird or fish colonies.
Tetanic Stimulation awayof stimulationof a neuronwith a high frequency repetition(like tetanus suffering).
Thermodynamic Equilibrium a state of a physical system in which it is in mechan-ical, chemical and thermal equilibrium and in which there is no tendency for spon-taneous change.
Trade Wind a wind blowing almost continuously from the northeast in the NorthernHemisphere and from the southeast in theSouthernHemisphere, acting as the steeringflow for tropical storms. They have been used for sailing ships to cross the world’soceans for centuries.
Trajectory indicates in phase space the progression or line of development of theevolving system.
Tropopause the boundary region between the troposphere (the lowest layer of theatmosphere) and stratosphere (the layer above the troposphere).
Turbulence any pattern of fluid motion characterized by chaotic changes in pressureand flow velocity (↔ laminar flow). Turbulence is commonly observed in everydayphenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from achimney.Most fluid flows occurring in nature and created in engineering applicationsare turbulent.
Turing Patterns patterns appearing in nature (biological organisms as well as othernatural systems, like sand patterns formed by wind). Stripes and spots arising natu-rally out of a homogeneous, uniform state, introduced by Alan Turing in 1952, dueto reaction-diffusion coupling of a fast activator and slow inhibitor.
Visual Cortex a part of the cerebral cortex that processes visual information.
:= a mathematical symbol meaning “is defined to be equal to”
Index
AAblation, 212–214Actin-myosin cytoskeleton, 199Activator, 50, 52, 145, 146, 148, 159–162,
164, 165, 168, 169, 172, 228, 231,241–244, 266, 268, 269
Adenosine Diphosphate (ADP), 226, 227Adenosine Triphosphate (ATP), 61Adenylyl cyclase, 196, 200ACA, 196, 201, 203Aggregation stream, 194, 201–203A-line, 130Allosteric, 226Ammonite, v, 50, 51Amoebae, x, 33, 61, 141, 193, 194, 217, 244Amun, 12Anchoring, 211Anti-clothoid, 105Arabesque, 25, 26, 83Arrhythmia, 211–214, 239, 244, 245, 249,
266Arrhythmia disappearance, 214Atomic-Force Microscopy (AFM), 44, 45Atria, 210–212Atrial Fibrillation (AF), x, 211, 244, 245Attractor, 114, 119Auger
shell, 50snail, 50
Aurora, 33, 35–37Autocatalysis, 281Autocatalytic
feedback, 196reproduction, 157
BBach/Johann Sebastian Bach, x, 113Ban Chiang, 13, 14Barkley model, 242, 260, 261Barred spiral galaxy, 34Basso continuo, 123Bauhaus, 71, 72Belousov–Zhabotinsky reaction (BZ reac-
tion), x, 60, 150, 157, 159–165, 167,168, 171, 172, 213, 243, 249
Bernward’s column, 18, 19Biological pattern formation, 254Biomineralization, 45Birth-death process, 253Bistable
condition, 242, 243system, 218, 242
Blackbuck, 51, 141Book of Gospels, 21Book of Kells, 11Boundary curvature, 268Brass instrument, 84Briggs–Rauscher reaction, 159Brusselator, 242, 243Buddha, 17, 20, 21Buoyant, 39
CCalcium wave, x, 225, 228, 244Cantalloc aqueduct, 16Cardiac arrhythmias, 213, 239, 245, 249, 266Cardiac contraction, 209Carolingian, 21Cell-cell signalling, 193, 195
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286 Index
Cellular Automaton (CA), x, 219, 253, 254Celt, 9–11Celtic
art, 9, 11knot, 11spiral, 10
Central Nervous System (CNS), 229, 230Chameleon, 51, 52, 141Chaotic pattern, 184, 212Chemical wave, 147, 158, 227Chemo-attractant, 61, 193, 195, 196, 217,
244Chemotaxis, 195, 197, 204Chichen Itza, 15Chicken retina, 229, 230Chirality, 8, 10, 106, 151, 152, 163, 214, 215Chiral orientation, 60Chiribiquete National Park, 4Chloride-Iodide-Malonic-Acid (CIMA)
reaction, 243Chlorine-dioxide-iodine-malonic acid reac-
tion, 161Chloroplast, 58Circular helix, 106, 107Clarke/Harry Clarke, 67, 80, 86Clothoid, 103, 105Coda, 118Collective cell migration, 254Collision, 36, 151, 226Colloidal particle, 130, 137Compact Disc (CD), 67, 85Complex Ginzburg–Landau Equation
(CGLE), 245Compound eye, 60Concentric circle, viii, 3, 4, 32, 43, 79, 162,
230Conical helix, 93, 107Conservative system, 282Convection, 32, 38CO2 oscillation, 178CO-oxidation, 175–177, 179–181, 183, 187,
188Core of the spiral wave, 213Counter-rotating spiral wave, 165Cretaceous–Palegogene extinction event, 50Critical curvature, 163Critical droplet fraction, 167Crystal growth, 43, 44, 130CyclicAMP (cAMP), 61, 195–205, 217, 244Cyclone, 38–40, 141
DDash waves, 168, 169Da Vinci/Leonardo da Vinci, 56, 59, 72, 75,
141Deluge, 76Deterministic PDE model, 253, 254Deterministic transport step, 255Dictyostelium discoideum/Dictyostelium/
Dictyostelids, 157, 193–195, 253Diffusion coefficient, 52, 55, 130, 136, 147,
158, 161–163, 165, 167, 168, 172,266
Digital Video Disc (DVD), 67, 85Discontinuously propagating waves, 168,
169, 172Discrete dynamical system, 254Discrete excitable model, 219Dislocation, 44, 267, 271Dispersion relation, 148, 162, 172, 263Dissipative system, 239Dissolution, 158Doguu, 8, 9, 28Dolmen, 6, 10Dürer/Albrecht Dürer, x, 91, 92, 102
EEffector, 226Eikonal equation, 163, 220, 267, 269, 272,
275Electric conductivity, 167Electroencephalography (EEG), 233Electrolyte, 130, 132, 134, 135, 138Ellipso-Microsopy for Surface Imaging
(EMSI), 186, 187Entropy, 171, 239Epidemiological spreading, 253Epilepsy, x, 229, 233, 234Epileptic
neocortex, 225, 233seizure, 233, 234
Ertl/Gerhard Ertl, 176, 178, 249Erythema, 218, 220–222Escherichia Coli, 244Evangeliar, 21Excitability limit, 265, 271Excitable
medium/media, x, 37, 74, 114, 142,149, 157, 161–163, 213, 217–219, 222,228–230, 240–242, 244, 245, 253, 254,256–261, 265, 266, 269, 270, 275
system, 141, 145–147, 205, 209, 210,215, 218, 220
Index 287
Excitation wave, 141, 147, 148, 150, 162,164, 210, 211, 213, 218, 230, 232,248, 266, 273
Exoskeleton, 48Eyewall, 39
FFibonacci numbers, 33, 48, 53, 56, 63, 64,
103Filament, 195, 240, 246, 247Finite difference equation, 259Firefly, 60FitzHugh–Nagumo model, 241, 242Flagella, 51, 58Fluorescence Resonance Energy Transfer
(FRET), 199Fortification illusion, 231–233Fractal, 57, 91, 110, 111Fraser/James Fraser, 79, 80Free boundary approach, 268Frieze, 19, 69, 70, 141Frog oocyte, 228Fruiting body, 194, 195, 203, 204
GGabel, 282Galaxy/galaxies, v, viii, 33–35, 45, 65, 77,
101, 141, 181, 183Gastropod, 48–50Gelatin, 131–134Genetic predisposition, 218Geoglyph, 16Geographic Tongue (GT), 217–221Geomagnetic field, 35Ggantija, 7Ginzburg–Landau equation, 245Global
coupling, 181feedback, 175, 183–185
Glycolyticoscillation, x, 226pathway, 228
Gobekli Tepe, 3Goethe/JohannWolfgangvonGoethe, ix, 31,
33, 46, 47Golden
angle, 33, 48, 54, 55cut, 54, 63, 64
Gothic, 23, 25Gotland, 19, 20Great Mosque, 22, 23
HHaber-Bosch process, 176Harmonic oscillator, 142, 143Harmony, 71, 113–115, 117Heart, x, 157, 158, 161, 171, 209–213, 218,
223, 244, 245, 249, 266Heart atria, 210–212Heaviside function, 282Helix, x, 21, 33, 45, 51, 58, 59, 65, 79, 84,
92, 93, 100, 106, 107, 116, 122, 130,132, 138, 139
Helix Pteron, 59Herodot, 7Heterogeneous catalysis, 175–177, 186, 249Hexagonal pattern, viiiHieroglyph, 14Hildegard von Bingen, 25Hiroshige, 80, 81Hodkin–Huxley model, 241Hopf instability, 240Hurricane, viii, x, 21, 38, 39, 45, 61, 65, 67,
101Hurricane eye, 21, 39
IImmobile species, 141, 256, 262Inflammatory skin, 218Inhibition by oxygen, 165Inhibitor, 50, 52, 56, 145, 147, 150, 159–
161, 168, 169, 172, 200, 231, 233,241–244, 266, 272
Initiation, 138, 149, 165, 223, 226Instability, 42, 74, 157, 169, 172, 201, 240,
243, 245Interdiffusion, 162Interface, 165, 248Intracellular calcium, 228, 244Involute of a circle, 86, 92, 95, 104, 105Ionic, 24, 25, 27Iridogorgiids/iridogorgia, 57, 58, 65, 111Irregular dynamics, 246–248Ischemia, 229Isocline, 143Isotope dilution fluorography, 199Itten/Johannes Itten, 67, 71, 72, 86, 141
KKandinsky/Wassily Kandinsky, 69, 71, 72Karakusa, 82, 83Karman vortex street, 40–42KEE-model, 179Kimono, 67, 82, 83Kinematics, x, 37, 265–268, 275
288 Index
Kink eliminating effect, 220Klee/Paul Klee, 67, 69, 71–75, 141Klimt/Gustav Klimt, 26, 67, 69, 70, 86, 141Kukulkan, 15, 16Kush, 12
LLamellar, 166Laminar, 42Laocoön, 26–28La Ola, 222Lattice
hexagonal, 255, 258square, 255
Lattice-Gas Cellular Automaton (LGCA),219, 253, 255–261
Lesion, 219Lesional
evolution, 219formation, 219
Lichen, 33, 56, 57Liesegang
band, 138pattern, 138ring, 136structure, x, 45, 130, 131, 133, 135, 136,139, 228
Liesegang/R.E. Liesegang, viii, x, 45, 129–131, 133–139, 158
Linear A/Linear B, 14Lipid monolayer, 244Lituus, 92, 98, 99Loopy line, 149, 151–153Lotka–Volterra model, 159Loxodrome, 108, 109L2 phase, 166, 167Luciferase, 61Lyme disease, 221
MMaelstrom/Maelström, 67Mandelbrot set, 110Mars, 33, 37, 45Maya, 15, 28Meandering, 3, 5, 149, 230, 231, 245, 246,
261, 263Mean-field theory, 259Mean return time, 261, 262Medicago, 59Megalithic/Megalithic art, 3, 5–7, 74Melody, 114, 117, 119Merging of dashes, 169Metabolic rhythm, 225
Metamorphosis, ix, 33, 46Mexican wave, 222Microemulsion, x, 165–168, 244Migraine, 229, 231–233Migraine aura, 231Milky Way, 33, 34, 183Min protein, 244Mirror symmetry, 48Mixing operator, 256, 258Mollusc, 44, 48–50Monolayer (ML), 166, 178, 244Morphogenesis, 161, 171, 195, 204, 239,
241, 249Mound, 5, 8, 44, 193–195, 201–204Multicellular aggregates, 193, 195Mussorgski, 124Mutant, 200–203
NNacre, 44, 48NAD/NADH, 226–228Nanostructure, 45Nanotube, 33, 45, 46Naqa, 12, 13, 28Nara, 20, 21Naruto whirlpool, 80, 81Nazca lines, 16, 17Neolithic period, 3Newgrange, 3, 5, 6Newton, 46, 47Nitmiluk National Park, 4Nodal point, 32, 33Node, 146, 209, 254–259, 261No-flux boundary, 270Non-equilibrium, v, 157, 283Nonlinear dynamics, 74, 141, 218, 233, 234,
245Nonlinear stability analysis, 263Nordic art, 19, 72Nordic symbol, 19Normal velocity, 163, 267, 268, 270Nucleation, 130, 136–138Nuclei, 44, 137, 138Nullcline, 144–146, 260, 270Nutritional state, 203
OObstacle, 40–42, 154, 163–165, 210, 211,
266, 267Œuvre, 69, 92Open reactor, 243, 244, 249Optogenetic, 213, 214
Index 289
Ordinary Differential Equation (ODE), 142,241
Oregonator, 243Oscillating
center/centre, 199chemical reaction, 157–159
Oscillator, 114, 196, 205Oscillatory
condition, 242, 245media, 270
Ostwald/Wilhelm Ostwald, 130, 158, 175
PPacemaker, 162, 209Paper chromatography, viiParastichies, 52–54Partial Differential Equation (PDE), 160,
241, 253, 254Pedagogical Sketch Book, 74Percolation transition, 168Peroxidase-oxidase reaction, 228Phaistos disc, 14, 15Phase
diagram, 166, 261plane, 141–143plot, 114, 116–121, 124portrait, 113, 114, 116, 117, 269, 270space, 218, 257, 258, 261
Phosphofructokinase (PFK), 226, 228Photoemission Electron Microscope
(PEEM), x, 179Photosensitive catalyst, 152Phyllotaxis, 33, 47, 52, 53Piece-wise turning, 121Pigment, 49, 58, 60Pitch, 33, 45, 46, 49, 53, 59, 94, 95, 107, 110,
114–116, 119, 139, 152, 153Platinum/Pt(110), 175–177, 180, 182, 183,
187, 188, 266Poe/Edgar Allan Poe, 67, 80, 86Polar ice cap, 37Post-interaction configuration, 255, 258Post-nucleation
model, 130, 135Precipitation, 39, 130, 131, 133, 134, 136,
138, 158, 220, 221Prelude, 68, 113–115, 117–119, 123, 124Prespore, 203, 204Prestalk, 203, 204Proboscis, 51, 52, 141Projection, 55, 107, 116, 121–123, 232Propagating wave, 37, 148, 158, 163, 168,
169, 172, 211, 220, 223, 266
Pseudo-color, 150, 151, 153, 154, 164Pseudopod, 195, 196, 198Pulsatile induced gene expression, 199Pyruvate Kinase (PK), 226
QQuasi-quiescent center, 40Queen conch, 48, 49
RRadial direction, 54, 240, 245, 268Random walk, 196, 253Rash, 217, 220, 221Reaction-diffusion
equation, 136, 147, 161, 239pattern, 50, 240, 266, 268system, 130, 157, 160, 171, 187, 239–241, 243–245, 249, 266
Reentrant/reentry, 149, 248Reflection Anisotropy Microscope (RAM),
186, 187Refractory, 146–148, 162, 163, 198, 210,
230, 256, 257, 262Renaissance, 3, 4, 23, 25–27, 72, 75, 76, 92Reynolds number, 42Rhythm, x, 77, 117, 152, 225, 228, 234Ringworm, 221Ripples, 169Rock arts, 3, 4Romanesque, 18, 19, 23, 25Rotating
excitation source, 212spiral, x, 19, 47, 141, 142, 151, 152, 163–165, 181, 209, 211–214, 217, 225, 226,229–231, 240, 245, 249, 265, 268, 272–275
Rotationalcenter, 267, 268frequency, 267, 275
Rotation wave, 203Runge/Friedlieb Ferdinand Runge, vii, viii,
x, 130, 158
SSamarkand, 25, 26Samarra, 22, 23, 28Sanchi, 17, 28Sanjusangen-do, 81, 82Scanning TunnelingMicroscopy (STM), 44,
45Schiller/Friedrich von Schiller, 68
290 Index
School of fish, 61Screw dislocation, 44, 267, 271Scroll, 83, 84, 105, 203, 204, 239, 240, 244,
246, 247, 249Scroll wave, 203, 204, 239, 240, 244, 246,
247Scyths, 7Seahorse, 51, 52, 111Seashell, 48–50, 141, 183Self-induced criticality, 201Self-organization, 171, 226, 265Self-similarity, 101Self-sustained pattern, 186Self-sustained wave, 265, 275Serpent, 3, 15–17, 19, 26Shock wave, 43Sinus node, 209Slug, 193–195, 203–205Snail, viii, 31, 32, 48–51, 59, 92, 101, 141Snow storm, 79, 141Solar wind, 35, 36Spatially chaotic pattern, 212Spatiotemporal chaos, 242, 243, 245Spatiotemporal pattern, 187, 233Spectral color of sunlight, 78Spiral
acoustic, x, 68, 113, 114, 124algebraic, 91, 95, 97–99anti, 270Archimedean, x, 85, 86, 92–95, 102, 105,107, 109, 110, 151, 219, 267
band, 132blossoms, 72, 73breakup, 242, 245, 246, 260, 262core, 153, 163, 170, 215, 240, 245, 265,275
Cornu, 92, 103, 104counter-rotating, 47, 151, 163–165, 214,221
drift, 151Dürer, 102Euler, 103false, 69, 79, 80Fermat, 92, 97, 98Fibonacci, 102, 103fractal, 110galaxy, viii, 34, 35, 181, 183Galilean, 92, 97, 98golden, 101–103hyperbolic, 92, 96logarithmic, 34, 83, 92, 99–102, 107,108, 110
meandering, 231, 263multi-armed, 33, 201parabolic, 92, 97pseudo, 91, 92, 99, 104rotating/rigidly rotating, x, 151, 231,265, 268, 272–275
tendency, 46, 47tip, 149, 150, 152, 163, 164, 230, 231,271, 272, 274
twisted, 22, 270wave, x, 37, 40, 60, 61, 150, 153, 157,161–165, 169, 171, 172, 176, 185, 193,199, 200, 204, 205, 209–215, 217, 218,223, 225, 229, 230, 233, 243, 244, 246,253, 258, 260, 263, 265–270, 272–275
wave in cardiac tissue, 209, 210, 215, 247Spirogyra, 57, 58, 65Splitting of dashes, 169, 170Spore, 193–195SpreadingDepression (SD), x, 225, 229–233Staircase, 18, 23, 67, 84, 85, 113, 118, 121,
123, 124Starry Night, 77, 78, 141State dependent anisotropy, 181Stationary rotation, 211Stochastic
birth, 257death, 257interaction step, 255LGCA, 254, 258, 261
Stonehenge, 5, 7Streaming instability, 201Stupa, 17Supercell, 39, 40Supersaturation, 44, 45, 130, 137Superthreshold
perturbation, 146, 241stimulus, 265
Surface reaction, x, 175, 183, 185, 186, 188,243
Swarm intelligence, 61
TTarget pattern, 4, 148, 149, 157, 159, 161,
162, 164, 171, 172, 175, 180, 181,219, 230, 243
Tarxien tempel, 6, 7Taste bud, 218Taucher/der Taucher, 68Theodorus, 109, 110Thermodynamic equilibrium, 171, 217, 239Three comma-shaped figure, 81, 82
Index 291
Three-Dimensional (3D)expression, 113, 116, 121, 123, 124presentation, 122spiral, 79, 106, 108
Time delayed global feedback, 185Todaiji temple, 20Tongue, x, 51, 217–219Tornado, viii, x, 31, 32, 39, 40, 67, 78Trade wind, 38Trajan’s column, 18, 19Trajectory, 94, 98, 105, 114, 116, 121, 143,
146, 149, 163, 230, 231, 258, 269,270, 274, 275
Traveling wave, 244Triskele, 10, 19, 33Tropopause, 39Turbulence, 33, 40, 42, 141, 157, 175, 183–
185, 245Turing instability, 240, 243Turing pattern, 161, 168, 172, 242, 244, 249,
261Turner/Joseph M.W. Turner, 67, 78, 79, 86,
141Twister, 39
UUkiyo-e, 67, 80, 81
VVan Gogh/Vincent van Gogh, 67, 76, 77, 81,
141Ventricle, 210–212Ventricular fibrillation, x, 212, 245Viscosity, 167Visual cortical orientation map, 233Volume droplet fraction, 167Vortex/voltices, 19–21, 36, 38, 39, 41–43,
61, 67, 72, 239Vortex wheel, 19, 20, 72
WWake turbulence, 42Water-in-oil emulsion, 165, 172Wave
curvature, 172front, 148, 151, 162–164, 168–172, 198,201, 203, 210, 221, 229, 230, 266–272,274, 275
propagation, 157, 158, 162, 163, 165,171, 172, 196, 199–202, 210, 212, 229,231, 275
Wave front, 210, 266–268, 272, 274, 275Well-tempered clavier, 113, 114, 124
YYin-Yang pattern, 265, 274
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