Monthly Best Of on 06/28/2008




Random intertwining

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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[Please, visit A Virtual Machine for Exploring Space-Time and Beyond, the place where you can find thousands of pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 06/28/2008 and last updated on 11/14/2023 17:47:08 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Tridimensional representation of a quadridimensional Calabi-Yau manifold
1-235 reference(s)		 Hypercube
2-115 reference(s)		 The random walk of photons escaping the Sun
3-97 reference(s)		 Quark and gluon structure of a nucleon
4-81 reference(s)
Black dots (inside random white squares)on a square lattice
5-78 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
6-68 reference(s)		 Artistic view of the prime numbers
7-59 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-10.0,+60.0]x[-35.0,+35.0] (bird's-eye view)
8-56 reference(s)
Quark and gluon dynamics of the nucleon
9-54 reference(s)		 Welcome aboard a Virtual Space-Time Travel Machine
10-46 reference(s)		 From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
11-42 reference(s)		 The Lorenz attractor
12-42 reference(s)
The foggy Babel Tower -a Tribute to Brueghel the Elder-
13-41 reference(s)		 Electron diffraction
14-41 reference(s)		 Reconstruction of a 3D structure -a cubic lattice-
15-40 reference(s)		 Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
16-39 reference(s)
The random walk of photons escaping the Sun
17-33 reference(s)		 Mountains at sunrise
18-33 reference(s)		 Vibrations 0003
19-32 reference(s)		 Botticelli anomaly on the Moon
20-31 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)
21-31 reference(s)		 From Pluto to the Sun (non linear scales)
22-31 reference(s)		 The Birth of the Universe
23-30 reference(s)		 Quark and gluon structure of a nucleon
24-29 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
25-29 reference(s)		 Tridimensional display of 36 eigenstates of the Hydrogen atom (bidimensional computation)
26-29 reference(s)		 The random walk of photons escaping the Sun
27-28 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)
28-28 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)
29-27 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
30-27 reference(s)		 Cauliflowers, seaweeds, shells,... with fog
31-26 reference(s)		 Untitled 0101
32-25 reference(s)
Fractal synthesis of mountains with vegetation and stormy clouds
33-25 reference(s)		 Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
34-25 reference(s)		 Rotation about the X axis of the Lorenz attractor
35-25 reference(s)		 From Pluto to the Sun -extrapolation 2- (non linear scales)
36-24 reference(s)
The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
37-23 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Pluto point of view-
38-23 reference(s)		 Autostereogram with an hidden volcano and 64 self-portraits
39-23 reference(s)		 64 elementary bidimensional binary cellular automata with 1 white starting central point
40-23 reference(s)
Quantum vacuum fluctuations
41-22 reference(s)		 Autostereogram with an hidden volcano
42-22 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
43-22 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
44-22 reference(s)
Artistic view of a quadridimensional Calabi-Yau manifold
45-22 reference(s)		 Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
46-21 reference(s)		 Electron-positron scattering
47-21 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
48-21 reference(s)
Untitled 0105
49-20 reference(s)		 The non linear transformation of the coordinates in the Solar System
50-20 reference(s)		 Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
51-20 reference(s)		 Jean-François COLONNA (on 11/17/1994)with its fractal mountains
52-20 reference(s)
The City and the Stars -a Tribute to Arthur C. Clarke-
53-19 reference(s)		 The first true colors autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
54-19 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
55-19 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
56-19 reference(s)
Synthesis of tridimensional symmetrical geometrical textures
57-19 reference(s)		 Animation of a sunrise on mountains
58-19 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
59-19 reference(s)		 Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
60-19 reference(s)
Tridimensional brownian motion -the colors used (magenta,red,yellow,green,cyan)are an increasing function of the time- and the 'external border' of its bidimensional projection -white-
61-19 reference(s)		 Artistic view of the Big Bang
62-18 reference(s)		 Autostereogram with an hidden volcano and fractal phenomenon
63-18 reference(s)		 Autostereogram with an hidden ring and ghost bows
64-18 reference(s)
2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-
65-18 reference(s)		 The normal field of a shell (Jeener surface 1)
66-18 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
67-18 reference(s)		 Rotation about the Y (vertical)axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms
68-18 reference(s)
Along the border of the Mandelbrot set
69-17 reference(s)		 A dynamic 'crumpled' Klein bottle defined by means of three sets of bidimensional fields
70-17 reference(s)		 The Eratosthene sieve displaying 100x100 numbers
71-17 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)
72-17 reference(s)
The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
73-17 reference(s)		 Animation of a quaternionic Julia island
74-17 reference(s)		 2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
75-17 reference(s)		 Bidimensional display of the dynamics of the linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
76-17 reference(s)
Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
77-16 reference(s)		 True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
78-16 reference(s)		 A Tribute to Archimedes
79-16 reference(s)		 Tridimensional display of cross-sections inside a tridimensional fractal aggregate
80-16 reference(s)
Fractal synthesis of the light cloud dynamics -this sequence being periodical-
81-16 reference(s)		 From Pluto to the Sun -extrapolation 1- (non linear scales)
82-16 reference(s)		 N-body problem integration (N=9)with a simultaneous 2.pi rotation of the observer
83-16 reference(s)		 The Möbius strip
84-16 reference(s)
The Lorenz attractor -sensitivity to initial conditions (displayed as the central point of each frame)-
85-16 reference(s)		 16 complex Julia sets
86-16 reference(s)		 Rotation about the Y (vertical)axis of the CMAP logo that can also be viewed as a set of 4x3 stereograms
87-16 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
88-16 reference(s)
16 complex Julia sets along the border of the Mandelbrot set with display of the iteration numbers
89-15 reference(s)		 Autostereogram with an hidden volcano
90-15 reference(s)		 Animation of a natural form
91-15 reference(s)		 Texture animation by means of Fourier filtering of a random walk process
92-15 reference(s)
The set of bidimensional fields defining the 'Z' coordinate of an interpolation between the Bonan-Jeener-Klein triple bottle and a 'double sphere'
93-15 reference(s)		 The set of bidimensional fields defining the 'X' coordinate of an interpolation between the Möbius strip and a 'double sphere'
94-15 reference(s)		 The same bidimensional scalar field displayed with 4 different color palettes
95-15 reference(s)		 The journey of an Earth-like planet (dark blue)from Pluto (grey) to the Sun (yellow)
96-15 reference(s)
An arbitrary surface (Jeener surface 2)in motion
97-15 reference(s)		 Rotation about the X axis of the Lorenz attractor (5000 iterations), computed simultaneously on two different computers
98-15 reference(s)		 2.pi rotation about the Y axis of a quaternionic Julia set with motion blur -tridimensional cross-section-
99-15 reference(s)		 Texture animation by means of Fourier interpolation
100-15 reference(s)
Periodical earthquake with multifractal mountains
101-15 reference(s)		 Texture animation by means of the generalized Fourier filtering process
102-15 reference(s)		 Intertwining based on the geometry of the sphere
103-15 reference(s)		 Artistic view of the Klein bottle
104-15 reference(s)
Untitled 0102
105-14 reference(s)		 Autostereogram with an hidden volcano
106-14 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
107-14 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
108-14 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
109-14 reference(s)		 Bidimensional domino effect
110-14 reference(s)		 Alien
111-14 reference(s)		 Animation of a natural form
112-14 reference(s)
Animation of bidimensional symmetrical geometrical textures
113-14 reference(s)		 26 evenly distributed points on a sphere by means of simulated annealing displayed upon the (PHI,TETA)plane
114-14 reference(s)		 An interpolation between a 'double sphere' and a torus
115-14 reference(s)		 Untitled 0106
116-14 reference(s)
An interpolation between the Möbius strip and a 'double sphere' defined by means of three sets of bidimensional fields
117-14 reference(s)		 The set of bidimensional fields defining the 'Z' coordinate of a dynamic 'crumpled' Klein bottle
118-14 reference(s)		 Texture animation by means of inertia momentum computation
119-14 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Earth point of view-
120-14 reference(s)
From Pluto to the Sun
121-14 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
122-14 reference(s)		 Rotation about the X axis of the Lorenz attractor (1000 iterations), computed simultaneously on two different computers
123-14 reference(s)		 Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
124-14 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
125-14 reference(s)		 Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold
126-14 reference(s)		 Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold
127-14 reference(s)		 Tridimensional billiard with 12 -initially- still particles submitted to an attractive central field of gravity
128-13 reference(s)




2-The 128 most referenced Pages (*):

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



1-demo_14
615 reference(s)		 2-An2000.01.Fra
190 reference(s)
3-AVirtualSpaceTimeTravelMachine.Ang
186 reference(s)		 4-Galerie_NumberTheory.FV
99 reference(s)
5-help.
92 reference(s)		 6-SurfaceProjector.01.Ang
88 reference(s)
7-Galerie_GeneralitiesVisualization.FV
85 reference(s)		 8-Autostereograms.01.
85 reference(s)
9-ImagesDuVirtuel.01.Fra
84 reference(s)		 10-Galerie_DeterministicFractalGeometry.FV
83 reference(s)
11-Fractal.01
83 reference(s)		 12-Galerie_ArtisticCreation.FV
81 reference(s)
13-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
74 reference(s)		 14-FloatingPointNumbers.01.Fra
74 reference(s)
15-FloatingPointNumbers.01.Ang
74 reference(s)		 16-Galerie_TextureSynthesis.FV
73 reference(s)
17-Galerie_ArtAndScience.FV
72 reference(s)		 18-AVirtualSpaceTimeTravelMachine.Ang.FV
72 reference(s)
19-GenieLogiciel.01.Fra
71 reference(s)		 20-AnimFractal.01.
70 reference(s)
21-Stereogrammes_AutoStereogrammes.01
68 reference(s)		 22-ExpV_VirE.Ang
67 reference(s)
23-ExpV_VirE.11
67 reference(s)		 24-copyright.01.
66 reference(s)
25-Galerie_DeterministicChaos.FV
66 reference(s)		 26-SurfaceProjector.01.Fra
65 reference(s)
27-ImagesDuVirtuel.01.Fra.FV
65 reference(s)		 28-Galerie_QuantumMechanics.FV
65 reference(s)
29-VisSci_SciVis.01
64 reference(s)		 30-Kepler.02.
64 reference(s)
31-Galerie_CelestialMechanics.FV
61 reference(s)		 32-ExpV_VirE.21
61 reference(s)
33-An2000.05.Fra
61 reference(s)		 34-AProposSite.01.Fra
61 reference(s)
35-MonumentValley.01.Fra
60 reference(s)		 36-Informations_AboutPicturesAnimationsAndFiles.01.Ang
60 reference(s)
37-Galerie_ParticleSystems.FV
60 reference(s)		 38-AQuoiServentLesMathematiques.01
60 reference(s)
39-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis
58 reference(s)		 40-AVirtualSpaceTimeTravelMachine.Fra
58 reference(s)
41-Galerie_Astrophysics.DIAPO.0001
56 reference(s)		 42-Commentaires_NKleinBottle.01
56 reference(s)
43-subject.01.
55 reference(s)		 44-RealNumbers.01.Fra
54 reference(s)
45-AVirtualSpaceTimeTravelMachine.Fra.FV
54 reference(s)		 46-MathematiquesPhysiqueFractales.01
53 reference(s)
47-Informations_GoodNewsAndBadNews.01.Fra
53 reference(s)		 48-RemarquesCerveau.01
52 reference(s)
49-demo_14.FV
51 reference(s)		 50-Galerie_FromTheInfinitelySmallToTheInfinitelyBig.FV
51 reference(s)
51-Galerie_SalonDAutomne.FV
50 reference(s)		 52-ExpV_VirE.01.Ang
50 reference(s)
53-VirtualChaos.01.Fra
49 reference(s)		 54-PatrimoineHumanite.02.Fra
49 reference(s)
55-Galerie_SignalProcessing.FV
49 reference(s)		 56-Galerie_GeneralitiesVisualization
49 reference(s)
57-Galerie_CollaborativeWorks..FV
49 reference(s)		 58-Galerie_Astrophysics.FV
49 reference(s)
59-ExpV_VirE.Fra
49 reference(s)		 60-Commentaires_VarieteQuadriDimensionnelleCalabiYau.01
49 reference(s)
61-An2000.06.Fra
49 reference(s)		 62-AQuoiServentLesMathematiques.03
49 reference(s)
63-VisitesGaleriesEnfouies.01.Ang
48 reference(s)		 64-VisSci_SciVis.02
48 reference(s)
65-ManyChaos.01.Ang
48 reference(s)		 66-ExpV_VirE.01.Fra
48 reference(s)
67-Commentaires_DefinitionTransformeeDeFourier.01
48 reference(s)		 68-Commentaires_DefinitionComplexes.01
48 reference(s)
69-An2000.01.Ang
48 reference(s)		 70-create.03.
47 reference(s)
71-Galerie_NewPictures.FV
47 reference(s)		 72-EnsembleDesGaleries.DIAPO.0001
47 reference(s)
73-ArtScience.11.Fra
47 reference(s)		 74-mail.01.vv
46 reference(s)
75-infinity.01.vv
46 reference(s)		 76-Galerie_QuantumMechanics
46 reference(s)
77-Commentaires_ProblemeDesNAimants.01
46 reference(s)		 78-Commentaires_DefinitionQuaternions.01
46 reference(s)
79-PerteDeLAssociativite.01
45 reference(s)		 80-MonumentValley.01.Ang
45 reference(s)
81-Galerie_FluidMechanics.FV
45 reference(s)		 82-Commentaires_EnsembleMandelbrotComplexe.01
45 reference(s)
83-An2000.02.Fra
45 reference(s)		 84-present.01.
44 reference(s)
85-display
44 reference(s)		 86-ManyChaos.01.Fra
44 reference(s)
87-Galerie_CollaborativeWorks.
44 reference(s)		 88-Galerie_AnthropomorphicPatterns.FV
44 reference(s)
89-Commentaires_SystemeSolaire.01
44 reference(s)		 90-Commentaires_SurfaceDeBoy.01
44 reference(s)
91-Commentaires_JeenerMobiusManifold.01
44 reference(s)		 92-Commentaires_EspaceLyapunovComplexe.01
44 reference(s)
93-Galerie_SensitivityToRoundingOffErrors.FV
43 reference(s)		 94-Galerie_QuantumMechanics.DIAPO.0001
43 reference(s)
95-Galerie_DeterministicChaos
43 reference(s)		 96-Galerie_BestOf.FV
43 reference(s)
97-AvantPropos.01.Ang
43 reference(s)		 98-ArtScience.01
43 reference(s)
99-An2000.03.Fra
43 reference(s)		 100-Informations_AboutPicturesAnimationsAndFiles.01.Fra
42 reference(s)
101-Galerie_ArtAndScience.DIAPO.0001
42 reference(s)		 102-DuModeleALaPriseDeDecision.01.Fra
42 reference(s)
103-Commentaires_KleinBottle.01
42 reference(s)		 104-AvantPropos.01.Fra
42 reference(s)
105-ArtScience.11.Ang.DIAPO.0001
42 reference(s)		 106-An2000.11.Fra
42 reference(s)
107-VirtualChaos.01.Ang
41 reference(s)		 108-IllusionConnaissance.01
41 reference(s)
109-Galerie_ArtisticCreation.DIAPO.0001
41 reference(s)		 110-Commentaires_FluideInstationnaireBiDimensionnelIdeal.01
41 reference(s)
111-Commentaires_DoubleJeenerBottle.01
41 reference(s)		 112-ArtOrdinateur.01
41 reference(s)
113-AQuoiServentLesMathematiques.02
41 reference(s)		 114-Vcatalogue.11
40 reference(s)
115-ImpossibleStructures.01.Ang
40 reference(s)		 116-Galeries.01.vv
40 reference(s)
117-Galerie_SignalProcessing
40 reference(s)		 118-Galerie_NumberTheory.DIAPO.0001
40 reference(s)
119-Galerie_NewPictures.DIAPO.0001
40 reference(s)		 120-Galerie_DeterministicFractalGeometry
40 reference(s)
121-Galerie_BestOf
40 reference(s)		 122-Commentaires_VarieteHexaDimensionnelleCalabiYau.01
40 reference(s)
123-Commentaires_NKleinBottle.02
40 reference(s)		 124-Commentaires_ModeleIsingBiDimensionnel.01
40 reference(s)
125-An2000.04.Fra
40 reference(s)		 126-stereogra.01.c.
39 reference(s)
127-Galerie_TextureSynthesis
39 reference(s)		 128-Galerie_NumberTheory
39 reference(s)

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




Copyright © Jean-François COLONNA, 2008-2023.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2008-2023.