Monthly Best Of on 06/28/2007




Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-

Jean-François COLONNA
www.lactamme.polytechnique.fr
jean-francois.colonna@polytechnique.edu
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France
france telecom, France Telecom R&D

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[The Y2K bug [Le bug de l'an 2000]]
[Do you believe that Real Numbers exist for a computer and that floating point computations are safe?]
[Please, visit A Virtual Space-Time Travel Machine, the place where you can find thousands of pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 06/28/2007 and last updated on 06/30/2018 14:03:35 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures:



Black dots (inside random white squares)on a square lattice
1-1586 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
2-1541 reference(s)
The random walk of photons escaping the Sun
3-595 reference(s)
The Jeener's quintuple Klein bottle
4-509 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
5-373 reference(s)
Quark and gluon structure of a nucleon
6-346 reference(s)
The random walk of photons escaping the Sun
7-344 reference(s)
Foggy Babel Tower -a tribute to Brueghel the Elder-
8-319 reference(s)
Welcome aboard a Virtual Space-Time Travel Machine
9-304 reference(s)
Artistic view of the prime numbers
10-291 reference(s)
Tridimensional display of the Riemann Zeta function inside (-10.0,+60.0)x(-35.0,+35.0) (bird's-eye view)
11-278 reference(s)
The Lorenz attractor
12-277 reference(s)
Artistic view of the Big Bang
13-266 reference(s)
Hypercube
14-229 reference(s)
Paradoxal Monument Valley at sunset
15-228 reference(s)
Bidimensional artistic view of the Verhulst dynamics
16-222 reference(s)
From Pluto to the Sun (non linear scales)
17-218 reference(s)
Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold
18-216 reference(s)
The Birth of the Universe
19-210 reference(s)
True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
20-209 reference(s)
Quantum vacuum fluctuations
21-198 reference(s)
Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
22-192 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
23-191 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
24-191 reference(s)
Synthesis of tridimensional symmetrical geometrical textures
25-189 reference(s)
Along the border of the Mandelbrot set
26-176 reference(s)
Animation of a sunrise on mountains
27-174 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)
28-174 reference(s)
Rotation about the X axis of the Lorenz attractor
29-172 reference(s)
2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
30-172 reference(s)
Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
31-171 reference(s)
Fractal synthesis of mountains with vegetation and stormy clouds
32-169 reference(s)
Quark and gluon dynamics of the nucleon
33-165 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
34-159 reference(s)
Reconstruction of a 3D structure -a cubic lattice-
35-157 reference(s)
Autostereogram with an hidden volcano
36-156 reference(s)
2 identical grey squares moving over a grey scale
37-153 reference(s)
The generalized Ulam spiral displaying 100 numbers
38-150 reference(s)
Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
39-150 reference(s)
Two multiplexed autostereograms by means of a pi/2 rotation
40-148 reference(s)
Jean-François Colonna
41-147 reference(s)
From the infinitely small to the infinitely big
42-145 reference(s)
The Earth, the Life and the Sun
43-144 reference(s)
Rotation about the X axis of the Lorenz attractor (5000 iterations), computed simultaneously on two different computers
44-136 reference(s)
The bidimensional John Conway's life game
45-136 reference(s)
16 complex Julia sets along the border of the Mandelbrot set with display of the iteration numbers
46-130 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
47-130 reference(s)
Tridimensional display of 36 eigenstates of the Hydrogen atom (bidimensional computation)
48-127 reference(s)
The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
49-125 reference(s)
Autostereogram with an hidden volcano
50-124 reference(s)
Quark and gluon structure of a nucleon
51-124 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)
52-124 reference(s)
From Pluto to the Sun -extrapolation 2- (non linear scales)
53-123 reference(s)
The Möbius strip
54-121 reference(s)
The random walk of photons escaping the Sun
55-120 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
56-119 reference(s)
Animation of a quaternionic Julia island
57-118 reference(s)
Mountains and light cloud dynamics -this sequence being periodical-
58-117 reference(s)
Isotropic random walk of 64 particles on a tridimensional square lattice
59-116 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
60-116 reference(s)
White Hole
61-116 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
62-115 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
63-115 reference(s)
Autostereogram with an hidden ring and ghost bows
64-114 reference(s)
A variable Archimedes spiral displaying 1000 numbers
65-114 reference(s)
The non linear transformation of the coordinates in the Solar System
66-111 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
67-110 reference(s)
Cauliflowers, seaweeds, shells,... with fog
68-110 reference(s)
A pay slip
69-109 reference(s)
Animation of bidimensional symmetrical geometrical textures
70-109 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
71-109 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-
72-107 reference(s)
Along the border of the Mandelbrot set
73-105 reference(s)
Animation of a natural form
74-105 reference(s)
Quantum vacuum fluctuation dynamics
75-104 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
76-103 reference(s)
The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
77-103 reference(s)
The first true colors autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
78-102 reference(s)
Artistic view of a quadridimensional Calabi-Yau manifold
79-100 reference(s)
The irreversibility of the numerical bidimensional billiard
80-99 reference(s)
Tridimensional zoom in on the Mandelbrot set
81-98 reference(s)
2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-
82-98 reference(s)
Autostereogram with an hidden volcano and 64 self-portraits
83-98 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)
84-97 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)
85-97 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
86-96 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
87-94 reference(s)
From Mars to the Sun
88-93 reference(s)
The Lorenz attractor
89-93 reference(s)
Alien
90-92 reference(s)
Mountains at sunrise
91-92 reference(s)
From 'geocentrism' to 'heliocentrism'
92-92 reference(s)
Rotation about the X axis of the Lorenz attractor (1000 iterations), computed simultaneously on two different computers
93-92 reference(s)
The Lorenz attractor -sensitivity to initial conditions (displayed as the central point of each frame)-
94-90 reference(s)
Quaternionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-
95-90 reference(s)
Tridimensional display of the particle density of a bidimensional crenellated billiard
96-88 reference(s)
Animation of a natural form
97-88 reference(s)
Botticelli anomaly on the Moon
98-88 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Pluto point of view-
99-88 reference(s)
A quaternionic Julia set -tridimensional cross-section-
100-88 reference(s)
Electron diffraction
101-88 reference(s)
Rotation about the Y (vertical)axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms
102-88 reference(s)
The Scream -a Tribute to Edvard Munch-
103-86 reference(s)
First clouds on the Moon
104-86 reference(s)
Rotation about the Y (vertical)axis of the CMAP logo that can also be viewed as a set of 4x3 stereograms
105-86 reference(s)
Autostereogram with an hidden volcano and an animated disguise texture
106-85 reference(s)
Erosion in Monument Valley with fog
107-85 reference(s)
N-body problem integration (N=10)displaying the actual Solar System with its simultaneous 2.pi rotation, our Earth being at the origin of the coordinates
108-85 reference(s)
A shell (Jeener surface 1)in motion
109-85 reference(s)
Cross-sections inside a tridimensional fractal aggregate
110-84 reference(s)
An Archimedes spiral displaying 1000 numbers
111-84 reference(s)
A dynamic fractal surface (four iterations)defined by means of three sets of bidimensional fields
112-84 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
113-84 reference(s)
Bidimensional display of the dynamics of the linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
114-84 reference(s)
The iterative process used to generate bidimensional fractal fields (16 iterations)
115-84 reference(s)
Tridimensional display (bird's-eye view)of the density of particles during a bidimensional diffusion process
116-84 reference(s)
Translation along the fourth axis of a quaternionic Julia set -tridimensional cross-sections-
117-83 reference(s)
The random walk of photons escaping the Sun
118-82 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
119-82 reference(s)
The bidimensional field defining the three coordinates of a fractal surface
120-82 reference(s)
Black and white display of a tridimensional function
121-82 reference(s)
Tridimensional display (bird's-eye view)of the density of particles during a bidimensional diffusion process
122-82 reference(s)
Tridimensional texture animation by means of the Generalized Product
123-81 reference(s)
From Pluto to the Sun -extrapolation 1- (non linear scales)
124-81 reference(s)
An arbitrary surface (Jeener surface 2)in motion
125-81 reference(s)
The normal field of a shell (Jeener surface 1)
126-81 reference(s)
N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)-sensitivity to initial conditions-
127-80 reference(s)
Extended life game
128-80 reference(s)




2-The 128 most referenced Pages:



1-demo_14
2600 reference(s)
2-AVirtualSpaceTimeTravelMachine.Ang
1288 reference(s)
3-An2000.01.Fra
1111 reference(s)
4-help.
731 reference(s)
5-mail.01.vv
564 reference(s)
6-ImagesDuVirtuel.01.Fra
513 reference(s)
7-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
453 reference(s)
8-Stereogrammes_AutoStereogrammes.01
452 reference(s)
9-copyright.01.
451 reference(s)
10-Galerie_GeneralitiesVisualization.FV
449 reference(s)
11-Fractal.01
435 reference(s)
12-ExpV_VirE.11
434 reference(s)
13-Galerie_CelestialMechanics.FV
425 reference(s)
14-AVirtualSpaceTimeTravelMachine.Fra
415 reference(s)
15-Galerie_ArtisticCreation.FV
414 reference(s)
16-FloatingPointNumbers.01.Fra
408 reference(s)
17-present.01.
393 reference(s)
18-Autostereograms.01.
367 reference(s)
19-Informations_AboutPicturesAnimationsAndFiles.01.Ang
359 reference(s)
20-ArtScience.11.Fra
352 reference(s)
21-AProposSite.01.Fra
352 reference(s)
22-Galerie_TextureSynthesis.FV
346 reference(s)
23-GenieLogiciel.01.Fra
345 reference(s)
24-Galerie_NumberTheory.FV
343 reference(s)
25-FloatingPointNumbers.01.Ang
339 reference(s)
26-demo_14.FV
317 reference(s)
27-ImagesDuVirtuel.01.Fra.FV
313 reference(s)
28-AVirtualSpaceTimeTravelMachine.Fra.FV
312 reference(s)
29-Galerie_QuantumMechanics.FV
309 reference(s)
30-Galerie_NewPictures.FV
309 reference(s)
31-AQuoiServentLesMathematiques.01
306 reference(s)
32-Galerie_ParticleSystems.FV
302 reference(s)
33-Galerie_DeterministicFractalGeometry.FV
297 reference(s)
34-Galerie_ArtAndScience.FV
296 reference(s)
35-ExpV_VirE.21
294 reference(s)
36-LOG_xiMc.11
291 reference(s)
37-SurfaceProjector.01.Ang
290 reference(s)
38-Galerie_DeterministicChaos.FV
285 reference(s)
39-AnimFractal.01.
285 reference(s)
40-ExpV_VirE.Fra
277 reference(s)
41-SurfaceProjector.01.Fra
276 reference(s)
42-RealNumbers.01.Fra
271 reference(s)
43-Galerie_Astrophysics.DIAPO.0002
270 reference(s)
44-An2000.02.Fra
264 reference(s)
45-create.03.
258 reference(s)
46-Kepler.02.
254 reference(s)
47-Commentaires_SystemeSolaire.01
248 reference(s)
48-Galerie_SignalProcessing.FV
242 reference(s)
49-Commentaires_DefinitionQuaternions.01
238 reference(s)
50-Commentaires_NKleinBottle.01
233 reference(s)
51-AvantPropos.01.Ang
230 reference(s)
52-An2000.05.Fra
223 reference(s)
53-An2000.01.Ang
223 reference(s)
54-ExpV_VirE.01.Fra
220 reference(s)
55-VirtualChaos.01.Fra
219 reference(s)
56-Commentaires_VarieteQuadriDimensionnelleCalabiYau.01
219 reference(s)
57-ArtOrdinateur.01
216 reference(s)
58-Galerie_FromTheInfinitelySmallToTheInfinitelyBig.FV
215 reference(s)
59-Commentaires_EspaceLyapunovComplexe.01
214 reference(s)
60-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis
213 reference(s)
61-MonumentValley.01.Ang
209 reference(s)
62-ArtScience.01
209 reference(s)
63-RemarquesCerveau.01
206 reference(s)
64-An2000.04.Fra
204 reference(s)
65-AVirtualSpaceTimeTravelMachine.Ang.FV
204 reference(s)
66-Commentaires_DefinitionComplexes.01
203 reference(s)
67-Galerie_AnthropomorphicPatterns.FV
200 reference(s)
68-Commentaires_DefinitionTransformeeDeFourier.01
199 reference(s)
69-DuModeleALImage.01.Fra
198 reference(s)
70-MonumentValley.01.Fra
197 reference(s)
71-ManyChaos.01.Fra
197 reference(s)
72-Galerie_FluidMechanics.FV
197 reference(s)
73-Galerie_SalonDAutomne.FV
196 reference(s)
74-VisSci_SciVis.01
195 reference(s)
75-Galeries.01.vv
195 reference(s)
76-Informations_AboutPicturesAnimationsAndFiles.01.Fra
194 reference(s)
77-An2000.06.Fra
194 reference(s)
78-AQuoiServentLesMathematiques.02
191 reference(s)
79-Galerie_CelestialMechanics
190 reference(s)
80-ExpV_VirE.Ang
190 reference(s)
81-An2000.03.Fra
190 reference(s)
82-Galerie_SensitivityToRoundingOffErrors.FV
188 reference(s)
83-Galerie_ParticleSystems
188 reference(s)
84-Commentaires_ProblemeDesNAimants.01
188 reference(s)
85-An2000.11.Fra
187 reference(s)
86-Galerie_Astrophysics.FV
185 reference(s)
87-catalogue.11
184 reference(s)
88-subject.01.
183 reference(s)
89-Galerie_NewPictures.DIAPO.0001
182 reference(s)
90-infinity.01.vv
181 reference(s)
91-Vcatalogue.11
181 reference(s)
92-Spheres.01
181 reference(s)
93-Galerie_CollaborativeWorks..FV
181 reference(s)
94-Galerie_BestOf.FV
181 reference(s)
95-EnsembleDesGaleries.DIAPO.0001
181 reference(s)
96-Galerie_CollaborativeWorks.
178 reference(s)
97-PerteDeLAssociativite.01
177 reference(s)
98-Informations_GoodNewsAndBadNews.01.Fra
177 reference(s)
99-ExpV_VirE.01.Ang
177 reference(s)
100-Galerie_ArtisticCreation.DIAPO.0001
176 reference(s)
101-VisitesGaleriesEnfouies.01.Ang
175 reference(s)
102-Galerie_NewPictures
175 reference(s)
103-FaireDeLaRecherche.01.vv
175 reference(s)
104-Commentaires_KleinBottle.01
175 reference(s)
105-Galerie_Astrophysics.DIAPO.0003
174 reference(s)
106-Galerie_Astrophysics.DIAPO.0001
174 reference(s)
107-Commentaires_EnsembleMandelbrotComplexe.01
174 reference(s)
108-AvantPropos.01.Fra
174 reference(s)
109-relativity.01.
173 reference(s)
110-ManyChaos.01.Ang
173 reference(s)
111-Galerie_QuantumMechanics.DIAPO.0001
172 reference(s)
112-real.01.vv.
171 reference(s)
113-Commentaires_EnsembleJuliaComplexe.01
171 reference(s)
114-Galerie_QuantumMechanics
169 reference(s)
115-Galerie_ArtAndScience.DIAPO.0001
169 reference(s)
116-Commentaires_FluideInstationnaireBiDimensionnelIdeal.01
169 reference(s)
117-PatrimoineHumanite.02.Fra
168 reference(s)
118-infinity.01.vv.DIAPO.0001
167 reference(s)
119-VirtualChaos.01.Ang
167 reference(s)
120-Galerie_DeterministicChaos
167 reference(s)
121-Commentaires_ProblemeDesNCorps.01
167 reference(s)
122-Galerie_DeterministicFractalGeometry
165 reference(s)
123-Commentaires_JeenerMobuisManifold.01
165 reference(s)
124-Galerie_GeneralitiesVisualization
164 reference(s)
125-hydrogene.61.K.
163 reference(s)
126-DuReelAuVirtuel.01.Fra
162 reference(s)
127-IllusionConnaissance.01
160 reference(s)
128-Galerie_DeterministicChaos.DIAPO.0001
160 reference(s)

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




Copyright (c) Jean-François Colonna, 2007-2018.
Copyright (c) France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2007-2018.