Monthly Best Of on 08/28/2007




The normal field of the Klein bottle

Jean-François COLONNA
[Contact me]

www.lactamme.polytechnique.fr

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France
france telecom, France Telecom R&D

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[The Y2K Bug [Le bug de l'an 2000]]
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[Please, visit A Virtual Machine for Exploring Space-Time and Beyond, the place where you can find more than 10.000 pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 08/28/2007 and last updated on 10/03/2024 17:01:26 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

(*): Undisplayed pictures -if any- do not exist.



LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
1-2063 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
2-1387 reference(s)		Black dots (inside random white squares)on a square lattice
3-693 reference(s)		Along the border of the Mandelbrot set
4-411 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
5-403 reference(s)		The Möbius strip
6-387 reference(s)		Bidimensional artistic view of the Verhulst dynamics
7-353 reference(s)		Hypercube
8-344 reference(s)
The Lorenz attractor
9-340 reference(s)		Quark and gluon structure of a nucleon
10-325 reference(s)		The random walk of photons escaping the Sun
11-294 reference(s)		Bidimensional abstract texture with random anthropomorphic patterns
12-280 reference(s)
Welcome aboard a Virtual Space-Time Travel Machine
13-265 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
14-259 reference(s)		The foggy Babel Tower -a Tribute to Brueghel the Elder-
15-258 reference(s)		The Birth of the Universe
16-249 reference(s)
Artistic view of the prime numbers
17-233 reference(s)		The Möbius strip
18-204 reference(s)		True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
19-199 reference(s)		Tridimensional display of the Riemann Zeta function inside [-10.0,+60.0]x[-35.0,+35.0] (bird's-eye view)
20-188 reference(s)
The random walk of photons escaping the Sun
21-187 reference(s)		Quantum vacuum fluctuations
22-181 reference(s)		Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
23-171 reference(s)		Artistic view of the Big Bang
24-163 reference(s)
Autostereogram with an hidden volcano
25-163 reference(s)		Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold
26-163 reference(s)		From Pluto to the Sun (non linear scales)
27-161 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
28-156 reference(s)
Two multiplexed autostereograms by means of a pi/2 rotation
29-154 reference(s)		N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed with 2 different optimization options on the same computer (sensitivity to rounding-off errors)
30-153 reference(s)		Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
31-149 reference(s)		The trajectories of bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity
32-146 reference(s)
Animation of a sunrise on mountains
33-145 reference(s)		Computation of the Lorenz attractor on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors)
34-140 reference(s)		Rotation about the X axis of the Lorenz attractor
35-136 reference(s)		Quark and gluon dynamics of the nucleon
36-135 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
37-133 reference(s)		Synthesis of tridimensional symmetrical geometrical textures
38-131 reference(s)		2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
39-131 reference(s)		Rotation about the X axis of the Lorenz attractor (5000 iterations), computed simultaneously on two different computers
40-124 reference(s)
Fractal synthesis of mountains with vegetation and stormy clouds
41-122 reference(s)		Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms
42-122 reference(s)		Animation of a natural form
43-121 reference(s)		Reconstruction of a 3D structure -a cubic lattice-
44-119 reference(s)
Cauliflowers, seaweeds, shells,... with fog
45-117 reference(s)		Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
46-115 reference(s)		Tridimensional representation of a hexadimensional Calabi-Yau manifold
47-115 reference(s)		The generalized Ulam spiral displaying 100 numbers
48-114 reference(s)
Tridimensional display of 36 eigenstates of the Hydrogen atom (bidimensional computation)
49-114 reference(s)		Tridimensional domino effect
50-113 reference(s)		Quark and gluon structure of a nucleon
51-112 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
52-110 reference(s)
Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
53-109 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
54-108 reference(s)		Animation of a natural form
55-107 reference(s)		Psychedelic hypercube
56-107 reference(s)
Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
57-106 reference(s)		The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
58-106 reference(s)		Autostereogram with an hidden volcano
59-106 reference(s)		From the infinitely small to the infinitely big
60-106 reference(s)
The wall-paper process
61-101 reference(s)		N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors)
62-100 reference(s)		The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
63-99 reference(s)		The erection of the Babel Tower
64-98 reference(s)
Rotation about the Y (vertical)axis of a tridimensional fractal aggregate that can also be viewed as a set of 4x3 pseudo-stereograms
65-97 reference(s)		Isotropic random walk of 64 particles on a tridimensional square lattice
66-96 reference(s)		From Pluto to the Sun -extrapolation 2- (non linear scales)
67-96 reference(s)		An Archimedes spiral displaying 1000 numbers
68-95 reference(s)
Artistic view of a quadridimensional Calabi-Yau manifold
69-95 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
70-94 reference(s)		N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Pluto point of view-
71-93 reference(s)		Fractal diffusion front in a bidimensional medium obtained by means of a random walk process
72-93 reference(s)
Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms
73-92 reference(s)		Rotation about the Y (vertical)axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms
74-92 reference(s)		The numerical irreversibility of the bidimensional billiard
75-91 reference(s)		Black and white display of a tridimensional function
76-91 reference(s)
An interpolation between the Möbius strip and a 'double sphere' defined by means of three sets of bidimensional fields
77-90 reference(s)		N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)-sensitivity to initial conditions-
78-90 reference(s)		A bidimensional fern computed by means of an 'Iterated Function System' -IFS-
79-90 reference(s)		Quantum vacuum fluctuation dynamics
80-89 reference(s)
The bidimensional field defining the three coordinates of a fractal surface
81-89 reference(s)		2 identical grey squares moving over a grey scale
82-89 reference(s)		From Pluto to the Sun -extrapolation 2-
83-89 reference(s)		Quaternionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-
84-89 reference(s)
24 evenly distributed points on a sphere by means of simulated annealing
85-88 reference(s)		A dynamic 'crumpled' Klein bottle defined by means of three sets of bidimensional fields
86-88 reference(s)		Tridimensional fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
87-87 reference(s)		Mountains and light cloud dynamics -this sequence being periodical-
88-87 reference(s)
The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
89-87 reference(s)		Autostereogram with an hidden volcano and 64 self-portraits
90-87 reference(s)		The normal field of a shell (Jeener surface 1)
91-86 reference(s)		Bidimensional domino effect
92-85 reference(s)
The Eratosthene sieve displaying 100x100 numbers
93-85 reference(s)		Botticelli anomaly on the Moon
94-85 reference(s)		Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
95-85 reference(s)		Earthquake with multifractal mountains
96-85 reference(s)
Electron diffraction
97-85 reference(s)		The Jeener-Klein quintuple bottle
98-85 reference(s)		The random walk of photons escaping the Sun
99-84 reference(s)		Autostereogram with an hidden ring and ghost bows
100-83 reference(s)
The Scream -a Tribute to Edvard Munch-
101-83 reference(s)		Three pendulums -the Red one, the Green one and the Blue one- and three magnets -white-
102-83 reference(s)		Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
103-83 reference(s)		N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
104-82 reference(s)
Zoom in on light clouds
105-82 reference(s)		A shell (Jeener surface 1)in motion
106-82 reference(s)		Archimedes spirals
107-82 reference(s)		World Mathematical Year 2000
108-81 reference(s)
The random walk of photons escaping the Sun
109-81 reference(s)		Animation of a quaternionic Julia island
110-81 reference(s)		A pay slip
111-80 reference(s)		Tridimensional texture animation by means of the Generalized Product
112-80 reference(s)
A quaternionic Julia set -tridimensional cross-section-
113-80 reference(s)		Tridimensional display of the particle density of a bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle
114-79 reference(s)		Animation of bidimensional textures by means of the self-transformation of a fractal process
115-79 reference(s)		N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Jupiter point of view-
116-79 reference(s)
N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors)
117-79 reference(s)		The Lorenz attractor -sensitivity to initial conditions (displayed as the central point of each frame)-
118-79 reference(s)		The first true colors autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
119-78 reference(s)		Mountains at sunrise
120-78 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -gravity center of the 9 planets point of view-
121-78 reference(s)		From Pluto to the Sun -extrapolation 1- (non linear scales)
122-78 reference(s)		N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors)
123-78 reference(s)		N-body problem integration (N=4)with one yellow star and two planets (the red one being very heavy and the blue one and its white satellite being light)
124-78 reference(s)
Along the border of the Mandelbrot set
125-77 reference(s)		Particle collisions without energy loss in a tridimensional space with display of the velocity histogram
126-77 reference(s)		Dynamics of the even distribution of 8 points on a sphere by means of simulated annealing
127-77 reference(s)		N-body problem integration (N=10)displaying the actual Solar System with its simultaneous 2.pi rotation
128-77 reference(s)




2-The 128 most referenced Pages (*):

(*): Unclickable pages -if any- do not exist.



1-demo_14
1934 reference(s)		2-AVirtualSpaceTimeTravelMachine.Ang
1004 reference(s)
3-An2000.01.Fra
870 reference(s)		4-help.
551 reference(s)
5-Galerie_GeneralitiesVisualization.FV
454 reference(s)		6-copyright.01.
414 reference(s)
7-Stereogrammes_AutoStereogrammes.01
399 reference(s)		8-ImagesDuVirtuel.01.Fra
398 reference(s)
9-Autostereograms.01.
371 reference(s)		10-Informations_AboutPicturesAnimationsAndFiles.01.Ang
361 reference(s)
11-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
353 reference(s)		12-Galerie_NumberTheory.FV
351 reference(s)
13-ExpV_VirE.11
341 reference(s)		14-AVirtualSpaceTimeTravelMachine.Fra
340 reference(s)
15-mail.01.vv
333 reference(s)		16-FloatingPointNumbers.01.Fra
331 reference(s)
17-Galerie_ArtisticCreation.FV
329 reference(s)		18-Fractal.01
327 reference(s)
19-GenieLogiciel.01.Fra
325 reference(s)		20-Galerie_ParticleSystems.FV
300 reference(s)
21-Galerie_TextureSynthesis.FV
295 reference(s)		22-ImagesDuVirtuel.01.Fra.FV
293 reference(s)
23-Galerie_QuantumMechanics.FV
287 reference(s)		24-FloatingPointNumbers.01.Ang
284 reference(s)
25-AProposSite.01.Fra
276 reference(s)		26-AVirtualSpaceTimeTravelMachine.Fra.FV
272 reference(s)
27-SurfaceProjector.01.Ang
271 reference(s)		28-present.01.
268 reference(s)
29-Galerie_ArtAndScience.FV
266 reference(s)		30-ExpV_VirE.Fra
266 reference(s)
31-Galerie_DeterministicFractalGeometry.FV
264 reference(s)		32-LOG_xiMc.11
259 reference(s)
33-Galerie_DeterministicChaos.FV
256 reference(s)		34-Galerie_CelestialMechanics.FV
254 reference(s)
35-AnimFractal.01.
253 reference(s)		36-demo_14.FV
251 reference(s)
37-ExpV_VirE.21
251 reference(s)		38-EnsembleDesGaleries.DIAPO.0001
250 reference(s)
39-Commentaires_NKleinBottle.01
247 reference(s)		40-Commentaires_DefinitionQuaternions.01
247 reference(s)
41-RealNumbers.01.Fra
246 reference(s)		42-Galerie_NewPictures.FV
240 reference(s)
43-Kepler.02.
237 reference(s)		44-create.03.
232 reference(s)
45-SurfaceProjector.01.Fra
231 reference(s)		46-An2000.02.Fra
231 reference(s)
47-ExpV_VirE.01.Fra
227 reference(s)		48-infinity.01.vv.DIAPO.0001
226 reference(s)
49-Informations_AboutPicturesAnimationsAndFiles.01.Fra
225 reference(s)		50-Commentaires_VarieteQuadriDimensionnelleCalabiYau.01
223 reference(s)
51-AvantPropos.01.Ang
222 reference(s)		52-AVirtualSpaceTimeTravelMachine.Ang.FV
217 reference(s)
53-MathematiquesPhysiqueFractales.01
214 reference(s)		54-Galerie_SignalProcessing.FV
213 reference(s)
55-Galerie_CelestialMechanics
213 reference(s)		56-AQuoiServentLesMathematiques.01
210 reference(s)
57-VirtualChaos.01.Fra
202 reference(s)		58-Galeries.01.vv
202 reference(s)
59-Galerie_AnthropomorphicPatterns.DIAPO.0001
202 reference(s)		60-MonumentValley.01.Ang
201 reference(s)
61-ArtScience.11.Fra
200 reference(s)		62-AQuoiServentLesMathematiques.03
199 reference(s)
63-RemarquesCerveau.01
197 reference(s)		64-Galerie_DeterministicFractalGeometry.DIAPO.0001
196 reference(s)
65-ExpV_VirE.01.Ang
195 reference(s)		66-Commentaires_DefinitionTransformeeDeFourier.01
195 reference(s)
67-subject.01.
194 reference(s)		68-Galerie_NewPictures
194 reference(s)
69-Commentaires_EspaceLyapunovComplexe.01
194 reference(s)		70-An2000.05.Fra
194 reference(s)
71-catalogue.11
193 reference(s)		72-Galerie_NumberTheory.DIAPO.0001
193 reference(s)
73-An2000.11.Fra
192 reference(s)		74-Galerie_GeneralitiesVisualization
190 reference(s)
75-relativity.01.
189 reference(s)		76-Informations_GoodNewsAndBadNews.01.Fra
189 reference(s)
77-Galerie_FromTheInfinitelySmallToTheInfinitelyBig.FV
188 reference(s)		78-Commentaires_KleinBottle.01
187 reference(s)
79-ManyChaos.01.Fra
186 reference(s)		80-Galerie_DeterministicChaos
186 reference(s)
81-ExpV_VirE.Ang
186 reference(s)		82-An2000.01.Ang
185 reference(s)
83-Galerie_TextureSynthesis.DIAPO.0001
184 reference(s)		84-Galerie_ParticleSystems
184 reference(s)
85-Galerie_SalonDAutomne.FV
183 reference(s)		86-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis
183 reference(s)
87-Galerie_BestOf.FV
183 reference(s)		88-stereogra.01.c.
182 reference(s)
89-Commentaires_DefinitionComplexes.01
182 reference(s)		90-ArtScience.01
182 reference(s)
91-MonumentValley.01.Fra
181 reference(s)		92-Galerie_Astrophysics.DIAPO.0001
181 reference(s)
93-Galerie_Astrophysics
181 reference(s)		94-DuReelAuVirtuel.01.Fra
181 reference(s)
95-Galerie_TextureSynthesis
180 reference(s)		96-An2000.04.Fra
179 reference(s)
97-Galerie_NewPictures.DIAPO.0001
178 reference(s)		98-DuModeleALImage.01.Fra
178 reference(s)
99-An2000.06.Fra
178 reference(s)		100-Galerie_SensitivityToRoundingOffErrors
177 reference(s)
101-Galerie_FluidMechanics.FV
177 reference(s)		102-Galerie_CollaborativeWorks.
177 reference(s)
103-Commentaires_SystemeSolaire.01
177 reference(s)		104-Commentaires_SurfaceDeBoy.01
177 reference(s)
105-Commentaires_FluideInstationnaireBiDimensionnelIdeal.01
177 reference(s)		106-real.01.vv.
176 reference(s)
107-Galerie_DeterministicFractalGeometry
176 reference(s)		108-An2000.03.Fra
175 reference(s)
109-Galerie_QuantumMechanics
174 reference(s)		110-Galerie_BestOf.DIAPO.0001
174 reference(s)
111-Commentaires_StructuresVivantesRecursives.01
174 reference(s)		112-infinity.01.vv
173 reference(s)
113-Vcatalogue.11
173 reference(s)		114-Galerie_FluidMechanics.DIAPO.0001
173 reference(s)
115-Galerie_AnthropomorphicPatterns.FV
173 reference(s)		116-Commentaires_ProblemeDesNAimants.01
173 reference(s)
117-Commentaires_EnsembleMandelbrotComplexe.01
173 reference(s)		118-Spheres.01
172 reference(s)
119-Galerie_Astrophysics.DIAPO.0002
172 reference(s)		120-Galerie_SensitivityToRoundingOffErrors.FV
171 reference(s)
121-Galerie_QuantumMechanics.DIAPO.0001
171 reference(s)		122-Galerie_DeterministicChaos.DIAPO.0001
171 reference(s)
123-Galerie_CelestialMechanics.DIAPO.0001
171 reference(s)		124-Galerie_ArtAndScience.DIAPO.0001
171 reference(s)
125-VisSci_SciVis.01
169 reference(s)		126-Commentaires_NKleinBottle.02
168 reference(s)
127-LumiereVirtuelleParadoxale.01
167 reference(s)		128-ArtOrdinateur.01
167 reference(s)

And now, enjoy visiting A Virtual Space-Time Travel Machine.




Copyright © Jean-François COLONNA, 2007-2024.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2007-2024.