Monthly Best Of on 11/28/2007




Tridimensional integration of the anisotropic gaussian Fourier filtering of a random field with a 2.pi rotation of the kernel

Jean-François COLONNA
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www.lactamme.polytechnique.fr

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France

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(CMAP28 WWW site: this page was created on 11/28/2007 and last updated on 11/14/2023 17:47:01 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Black dots (inside random white squares)on a square lattice
1-996 reference(s)		 Bidimensional abstract texture with random anthropomorphic patterns
2-797 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
3-795 reference(s)		 Hypercube
4-531 reference(s)
The random walk of photons escaping the Sun
5-500 reference(s)		 Quantum vacuum fluctuations
6-378 reference(s)		 The foggy Babel Tower -a Tribute to Brueghel the Elder-
7-372 reference(s)		 True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
8-360 reference(s)
The random walk of photons escaping the Sun
9-357 reference(s)		 LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
10-354 reference(s)		 Quark and gluon structure of a nucleon
11-334 reference(s)		 Artistic view of the prime numbers
12-326 reference(s)
Along the border of the Mandelbrot set
13-320 reference(s)		 Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
14-316 reference(s)		 Welcome aboard a Virtual Space-Time Travel Machine
15-297 reference(s)		 Animation of a sunrise on mountains
16-289 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
17-287 reference(s)		 Artistic view of the Big Bang
18-281 reference(s)		 From Pluto to the Sun -extrapolation 2- (non linear scales)
19-259 reference(s)		 Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
20-255 reference(s)
Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
21-255 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-10.0,+60.0]x[-35.0,+35.0] (bird's-eye view)
22-252 reference(s)		 2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
23-252 reference(s)		 The Lorenz attractor
24-246 reference(s)
Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
25-244 reference(s)		 N-body problem integration (N=3)with one yellow star and two planets (the red one being very heavy and the blue one being light)
26-230 reference(s)		 Tridimensional display of 36 eigenstates of the Hydrogen atom (bidimensional computation)
27-229 reference(s)		 Fractal synthesis of mountains with vegetation and stormy clouds
28-226 reference(s)
The numerical irreversibility of the bidimensional billiard
29-220 reference(s)		 The Möbius strip
30-220 reference(s)		 Reconstruction of a 3D structure -a cubic lattice-
31-219 reference(s)		 Rotation about the X axis of the Lorenz attractor
32-215 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
33-211 reference(s)		 The Birth of the Universe
34-209 reference(s)		 World Mathematical Year 2000
35-206 reference(s)		 From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
36-202 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
37-202 reference(s)		 The Scream -a Tribute to Edvard Munch-
38-200 reference(s)		 Two multiplexed autostereograms by means of a pi/2 rotation
39-198 reference(s)		 A tridimensional fractal manifold defined by means of three tridimensional fields
40-191 reference(s)
2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-
41-191 reference(s)		 Quark and gluon dynamics of the nucleon
42-188 reference(s)		 Isotropic random walk of 64 particles on a tridimensional square lattice
43-187 reference(s)		 Synthesis of tridimensional symmetrical geometrical textures
44-187 reference(s)
The Lorenz attractor -sensitivity to initial conditions (displayed as the central point of each frame)-
45-183 reference(s)		 The bottom of the sea
46-181 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
47-179 reference(s)		 The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
48-179 reference(s)
Rotation about the X axis of the Lorenz attractor (1000 iterations), computed simultaneously on two different computers
49-178 reference(s)		 Quark and gluon structure of a nucleon
50-175 reference(s)		 16 earth-like planets initially on the same keplerian trajectory
51-175 reference(s)		 Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
52-174 reference(s)
24 evenly distributed points on a sphere by means of simulated annealing
53-165 reference(s)		 Animation of a natural form
54-164 reference(s)		 Earthquake
55-163 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)
56-161 reference(s)
Rotation about the X axis of the Lorenz attractor
57-161 reference(s)		 The random walk of photons escaping the Sun
58-160 reference(s)		 Animation of bidimensional textures by means of the self-transformation of a fractal process
59-158 reference(s)		 From Pluto to the Sun (non linear scales)
60-158 reference(s)
2.pi rotation about the Y axis of a quaternionic Julia set with motion blur -tridimensional cross-section-
61-158 reference(s)		 Autostereogram with an hidden volcano
62-157 reference(s)		 Self-transformation of a simple dynamical geometric texture
63-157 reference(s)		 Bidimensional zoom in on the Mandelbrot set with display of the arguments
64-157 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
65-157 reference(s)		 A Tribute to Archimedes
66-156 reference(s)		 Spreading of an epidemic -color changes by means of contacts-
67-156 reference(s)		 The generalized Ulam spiral displaying 100 numbers
68-156 reference(s)
Rotation about the X axis of the Lorenz attractor (5000 iterations), computed simultaneously on two different computers
69-156 reference(s)		 Jean-François COLONNA (on 11/17/1994)with its fractal mountains
70-156 reference(s)		 N-body problem integration (N=2)displaying a perfect Keplerian orbit
71-154 reference(s)		 The iterative process used to generate bidimensional fractal fields (16 iterations)
72-154 reference(s)
Autostereogram with an hidden ring and ghost bows
73-149 reference(s)		 Tridimensional fractal structure
74-149 reference(s)		 Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold
75-148 reference(s)		 N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed with 2 slightly different sets of initial conditions (sensitivity to initial conditions)
76-146 reference(s)
Artistic view of a quadridimensional Calabi-Yau manifold
77-146 reference(s)		 Bidimensional zoom in on the Z=Gamma(Z)iteration with display of the arguments
78-145 reference(s)		 Computation of the roots of Q^3=1 using Newton's method with translation along the third axis of the quaternionic space
79-143 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
80-143 reference(s)
Bidimensional zoom in on the Verhulst dynamics
81-142 reference(s)		 The journey of an Earth-like planet (dark blue)from Pluto (grey) to the Sun (yellow)
82-141 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
83-141 reference(s)		 Self-transformation of a simple dynamical geometric texture
84-139 reference(s)
The wall-paper process
85-137 reference(s)		 Bidimensional fractal aggregates obtained by means of pasting during collisions with display of the velocity histogram
86-136 reference(s)		 A Lissajous surface
87-135 reference(s)		 Botticelli anomaly on the Moon
88-134 reference(s)
Bidimensional display of the dynamics of the linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
89-134 reference(s)		 A shell (Jeener surface 1)in motion
90-133 reference(s)		 The Eratosthene sieve displaying 100x100 numbers
91-132 reference(s)		 The first true colors autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
92-131 reference(s)
The tridimensional field defining the 'Z' coordinate of a tridimensional twisted torus-like manifold
93-130 reference(s)		 'There is a war' -a Tribute to Leonard Cohen-
94-130 reference(s)		 Alien
95-129 reference(s)		 Cauliflowers, seaweeds, shells,... with fog
96-129 reference(s)
From the infinitely small to the infinitely big
97-129 reference(s)		 The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
98-128 reference(s)		 The journey of an Earth-like planet (dark blue)from Pluto (grey) to the Sun (yellow)
99-128 reference(s)		 Along the border of the Mandelbrot set
100-124 reference(s)
Expansion of a gas inside a bidimensional circular box with display of velocity histograms
101-124 reference(s)		 Intertwining based on the geometry of the sphere
102-124 reference(s)		 An Archimedes spiral displaying 1000 numbers
103-123 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
104-121 reference(s)
Synthesis of bidimensional textures by means of the self-transformation of a fractal process
105-120 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
106-120 reference(s)		 Autostereogram with an hidden volcano
107-119 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
108-119 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
109-119 reference(s)		 Quaternionic shell fossil
110-118 reference(s)		 Animation of a natural form
111-117 reference(s)		 Animation of a quaternionic Julia island
112-117 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)
113-116 reference(s)		 Bidimensional domino effect
114-115 reference(s)		 Animation of bidimensional textures by means of the self-transformation of a fractal process
115-115 reference(s)		 Bidimensional artistic view of the Verhulst dynamics
116-115 reference(s)
Golden ring
117-114 reference(s)		 Mountains at sunrise
118-114 reference(s)		 A variable Archimedes spiral displaying 1000 numbers
119-113 reference(s)		 From Pluto to the Sun -extrapolation 1- (non linear scales)
120-113 reference(s)
Untitled 0025
121-113 reference(s)		 The normal field of a fractal surface defined by means of three bidimensional fields
122-111 reference(s)		 True colors autostereogram of a fractal landscape
123-110 reference(s)		 Artistic view of the tridimensional integration of the phase rotation of the wavelet transform of a bidimensional fractal field
124-110 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
125-110 reference(s)		 Artistic view of the trajectories of tridimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity
126-109 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
127-109 reference(s)		 A quaternionic Julia set -tridimensional cross-section-
128-109 reference(s)




2-The 128 most referenced Pages (*):

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



1-demo_14
1691 reference(s)		 2-AVirtualSpaceTimeTravelMachine.Ang
1099 reference(s)
3-An2000.01.Fra
893 reference(s)		 4-help.
602 reference(s)
5-Galerie_GeneralitiesVisualization.FV
412 reference(s)		 6-Fractal.01
378 reference(s)
7-FloatingPointNumbers.01.Fra
368 reference(s)		 8-ImagesDuVirtuel.01.Fra
357 reference(s)
9-ImagesDuVirtuel.01.Fra.FV
349 reference(s)		 10-AVirtualSpaceTimeTravelMachine.Fra
349 reference(s)
11-copyright.01.
341 reference(s)		 12-AQuoiServentLesMathematiques.01
339 reference(s)
13-Stereogrammes_AutoStereogrammes.01
328 reference(s)		 14-Autostereograms.01.
326 reference(s)
15-Galerie_ArtisticCreation.FV
325 reference(s)		 16-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
320 reference(s)
17-Galerie_NumberTheory.FV
299 reference(s)		 18-ExpV_VirE.11
298 reference(s)
19-mail.01.vv
291 reference(s)		 20-VisSci_SciVis.02
286 reference(s)
21-ExpV_VirE.21
281 reference(s)		 22-Galerie_Astrophysics.DIAPO.0001
280 reference(s)
23-Informations_AboutPicturesAnimationsAndFiles.01.Ang
275 reference(s)		 24-VisSci_SciVis.01
271 reference(s)
25-FloatingPointNumbers.01.Ang
270 reference(s)		 26-AProposSite.01.Fra
251 reference(s)
27-GenieLogiciel.01.Fra
248 reference(s)		 28-Galerie_DeterministicFractalGeometry.FV
248 reference(s)
29-AnimFractal.01.
247 reference(s)		 30-present.01.
242 reference(s)
31-Galerie_QuantumMechanics.FV
242 reference(s)		 32-SurfaceProjector.01.Ang
238 reference(s)
33-Galerie_TextureSynthesis.FV
232 reference(s)		 34-SurfaceProjector.01.Fra
223 reference(s)
35-RealNumbers.01.Fra
223 reference(s)		 36-Commentaires_VarieteHexaDimensionnelleCalabiYau.01
222 reference(s)
37-Galerie_ParticleSystems.FV
217 reference(s)		 38-create.03.
215 reference(s)
39-ExpV_VirE.Ang
214 reference(s)		 40-AVirtualSpaceTimeTravelMachine.Fra.FV
213 reference(s)
41-ExpV_VirE.Fra
212 reference(s)		 42-Galerie_CelestialMechanics.FV
210 reference(s)
43-EnsembleDesGaleries.DIAPO.0001
210 reference(s)		 44-Galerie_ArtAndScience.FV
209 reference(s)
45-Galerie_DeterministicChaos.FV
205 reference(s)		 46-ArtScience.11.Fra
200 reference(s)
47-AVirtualSpaceTimeTravelMachine.Ang.FV
197 reference(s)		 48-demo_14.FV
195 reference(s)
49-subject.01.
194 reference(s)		 50-An2000.02.Fra
190 reference(s)
51-catalogue.11
188 reference(s)		 52-infinity.01.vv
185 reference(s)
53-Commentaires_DefinitionTransformeeDeFourier.01
185 reference(s)		 54-MathematiquesPhysiqueFractales.01
182 reference(s)
55-Commentaires_DefinitionQuaternions.01
182 reference(s)		 56-Informations_GoodNewsAndBadNews.01.Fra
179 reference(s)
57-Galerie_Astrophysics.DIAPO.0002
178 reference(s)		 58-Commentaires_VarieteQuadriDimensionnelleCalabiYau.01
177 reference(s)
59-Commentaires_SystemeSolaire.01
176 reference(s)		 60-Galerie_NewPictures.FV
174 reference(s)
61-Commentaires_NKleinBottle.01
174 reference(s)		 62-AQuoiServentLesMathematiques.03
174 reference(s)
63-AvantPropos.01.Ang
172 reference(s)		 64-ExpV_VirE.01.Fra
171 reference(s)
65-Informations_AboutPicturesAnimationsAndFiles.01.Fra
168 reference(s)		 66-An2000.06.Fra
168 reference(s)
67-An2000.11.Fra
167 reference(s)		 68-LOG_xiMc.11
166 reference(s)
69-DuModeleALImage.01.Fra
165 reference(s)		 70-Commentaires_EspaceLyapunovComplexe.01
164 reference(s)
71-An2000.01.Ang
164 reference(s)		 72-Commentaires_DefinitionComplexes.01
163 reference(s)
73-An2000.05.Fra
162 reference(s)		 74-Galerie_SignalProcessing.FV
161 reference(s)
75-Commentaires_ModeleIsingBiDimensionnel.01
161 reference(s)		 76-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis
159 reference(s)
77-Galerie_Astrophysics.DIAPO.0003
158 reference(s)		 78-Kepler.02.
156 reference(s)
79-Galerie_FromTheInfinitelySmallToTheInfinitelyBig.FV
156 reference(s)		 80-ArtOrdinateur.01
156 reference(s)
81-AQuoiServentLesMathematiques.02
153 reference(s)		 82-Galerie_SalonDAutomne.FV
152 reference(s)
83-An2000.04.Fra
150 reference(s)		 84-Galerie_SensitivityToRoundingOffErrors.FV
148 reference(s)
85-Galerie_NewPictures.DIAPO.0001
148 reference(s)		 86-VirtualChaos.01.Fra
147 reference(s)
87-FaireDeLaRecherche.01.vv
146 reference(s)		 88-RemarquesCerveau.01
145 reference(s)
89-Galerie_Astrophysics.FV
145 reference(s)		 90-ManyChaos.01.Fra
143 reference(s)
91-Commentaires_KleinBottle.01
143 reference(s)		 92-MonumentValley.01.Fra
141 reference(s)
93-ArtScience.01
141 reference(s)		 94-Spheres.01
140 reference(s)
95-Galerie_CollaborativeWorks..FV
140 reference(s)		 96-EnsembleDesGaleries.DIAPO.0038
140 reference(s)
97-Galerie_FluidMechanics.FV
139 reference(s)		 98-Commentaires_EnsembleMandelbrotComplexe.01
139 reference(s)
99-Vcatalogue.11
138 reference(s)		 100-Galerie_DeterministicChaos
138 reference(s)
101-Galerie_BestOf.FV
138 reference(s)		 102-Commentaires_RacinesTroisiemesUniteComplexes.01
138 reference(s)
103-Galerie_BestOf.DIAPO.0001
137 reference(s)		 104-infinity.01.vv.DIAPO.0001
136 reference(s)
105-Commentaires_FluideInstationnaireBiDimensionnelIdeal.01
136 reference(s)		 106-Galeries.01.vv
135 reference(s)
107-Galerie_QuantumMechanics.DIAPO.0001
135 reference(s)		 108-EnsembleDesGaleries.DIAPO.0002
135 reference(s)
109-Galerie_FluidMechanics.DIAPO.0001
134 reference(s)		 110-ExpV_VirE.01.Ang
134 reference(s)
111-Commentaires_RacinesNIemesUniteComplexes.01
134 reference(s)		 112-ArtScience.11.Ang.DIAPO.0001
133 reference(s)
113-An2000.03.Fra
133 reference(s)		 114-stereogra.01.c.
132 reference(s)
115-Galerie_NumberTheory.DIAPO.0001
131 reference(s)		 116-avirtualspacetimetravelmachine.ang
130 reference(s)
117-MonumentValley.01.Ang
130 reference(s)		 118-Galerie_DeterministicFractalGeometry.DIAPO.0001
130 reference(s)
119-Galerie_NewPictures
129 reference(s)		 120-ImpossibleStructures.01.Ang
128 reference(s)
121-Galerie_TextureSynthesis
128 reference(s)		 122-Commentaires_ProblemeDesNCorps.01
128 reference(s)
123-ManyChaos.01.Ang
127 reference(s)		 124-EnsembleDesGaleries.DIAPO.0003
127 reference(s)
125-Commentaires_StructuresVivantesRecursives.01
127 reference(s)		 126-Commentaires_ProblemeDesNAimants.01
127 reference(s)
127-Galerie_GeneralitiesVisualization
126 reference(s)		 128-hydrogene.61.K.
125 reference(s)

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




Copyright © Jean-François COLONNA, 2007-2023.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2007-2023.