Monthly Best Of on 02/28/2013




Intertwining based on the geometry of the sphere

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

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(CMAP28 WWW site: this page was created on 02/28/2013 and last updated on 04/15/2019 11:13:50 -CEST-)




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
1-332 reference(s)		 Monument Valley à la David Hockney
2-172 reference(s)		 Tridimensional display of the generalized Ulam spiral displaying 4096 numbers
3-167 reference(s)		 The random walk of photons escaping the Sun
4-157 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
5-141 reference(s)		 Artistic view of the prime numbers
6-130 reference(s)		 The Ulam spiral displaying 2025 numbers
7-124 reference(s)		 The generalized Ulam spiral displaying 1024 numbers
8-120 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
9-116 reference(s)		 A tridimensional fractal manifold defined by means of three tridimensional fields
10-113 reference(s)		 Autostereogram with an hidden volcano
11-106 reference(s)		 Zoom in on the von Koch curve
12-93 reference(s)
The generalized Ulam spiral
13-85 reference(s)		 From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
14-84 reference(s)		 The random walk of photons escaping the Sun
15-83 reference(s)		 Autostereogram with an hidden volcano
16-80 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
17-78 reference(s)		 A pseudo-periodical Penrose tiling of the Golden Decagon
18-76 reference(s)		 Tridimensional representation of a hexadimensional Calabi-Yau manifold
19-75 reference(s)		 64 elementary bidimensional binary cellular automata with 1 white starting central point
20-74 reference(s)
Autostereogram with an hidden volcano and 64 self-portraits
21-66 reference(s)		 Autostereogram with an hidden volcano
22-64 reference(s)		 The Lorenz attractor
23-59 reference(s)		 From the infinitely small to the infinitely big
24-55 reference(s)
Autostereogram with an hidden volcano
25-53 reference(s)		 Happy new year 2000
26-53 reference(s)		 Foggy Babel Tower -a tribute to Brueghel the Elder-
27-48 reference(s)		 Two multiplexed autostereograms by means of a pi/2 rotation
28-46 reference(s)
From Pluto to the Sun (non linear scales)
29-46 reference(s)		 Autostereogram with an hidden volcano
30-45 reference(s)		 Sixteen interlaced fractal torus
31-44 reference(s)		 True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
32-40 reference(s)
The Scream -a Tribute to Edvard Munch-
33-40 reference(s)		 Diffusion between two boxes (initial conditions: the left one is empty, the right one contains 256 particles), with collisions and display of the gravity center -white particle-
34-39 reference(s)		 Along the border of the Mandelbrot set
35-37 reference(s)		 Monument Valley à la David Hockney
36-37 reference(s)
The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
37-37 reference(s)		 Hypercube
38-36 reference(s)		 The generalized Ulam spiral displaying 100 numbers
39-35 reference(s)		 A quaternionic Julia set -tridimensional cross-section-
40-35 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
41-35 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
42-35 reference(s)		 Quantum vacuum fluctuations
43-34 reference(s)		 An interpolation between a 'double sphere' and a cylinder
44-34 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
45-33 reference(s)		 Autostereogram with an hidden ring and ghost bows
46-33 reference(s)		 The quaternionic fractal set obtained when computing the roots of Q^3=1 using Newton's method with translation along the third axis of the quaternionic space -tridimensional cross-section-
47-33 reference(s)		 Reconstruction of a 3D structure -a cubic lattice-
48-32 reference(s)
The Syracuse conjecture for U(0)={5,6,7,8,...,20} -polar coordinates display-
49-31 reference(s)		 The Syracuse conjecture for U(0)={5,6,7,8,...,20} -polar coordinates display-
50-30 reference(s)		 The same bidimensional scalar field displayed with 4 different color palettes
51-29 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-10.0,+60.0]x[-35.0,+35.0] (bird's-eye view)
52-28 reference(s)
The random walk of photons escaping the Sun
53-28 reference(s)		 24 evenly distributed points on a sphere by means of simulated annealing
54-28 reference(s)		 Fractal synthesis of mountains with vegetation and stormy clouds
55-28 reference(s)		 Quark and gluon structure of a nucleon
56-28 reference(s)
Pi rotation about the Y axis of pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-
57-28 reference(s)		 Jean-François Colonna
58-28 reference(s)		 Autostereogram of 8 color-multiplexed quaternionic Julia sets -tridimensional cross-sections-
59-27 reference(s)		 Botticelli anomaly on the Moon
60-27 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
61-27 reference(s)		 The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
62-27 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
63-27 reference(s)		 Tridimensional display of the Riemann Zeta function inside [+0.1,+0.9]x[0,+50]
64-26 reference(s)
Universe or Multiverse -The fractal Universe-?
65-26 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
66-26 reference(s)		 Quaternionic butterfly with extended arithmetics -a tribute to Laurent Schwartz-
67-26 reference(s)		 A shell (Jeener surface 1)in motion
68-26 reference(s)
Rotation about the Y (vertical)axis of the Jeener's triple Klein bottle that can also be viewed as a set of 4x3 stereograms
69-26 reference(s)		 The Jeener's triple Klein bottle
70-26 reference(s)		 The self-similarity of the von Koch curve displayed by means of a zoom in with a ratio that is equal to 3
71-25 reference(s)		 Quark and gluon structure of a nucleon
72-25 reference(s)
2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
73-25 reference(s)		 Rotation about the Y (vertical)axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms
74-25 reference(s)		 Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
75-24 reference(s)		 Artistic view of the Big Bang
76-24 reference(s)
Close-up on a foggy 'MandelBox' -tridimensional cross-section-
77-24 reference(s)		 Autostereogram -using periodical light clouds as desguise texture- with a hidden gaussian mountain
78-24 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
79-24 reference(s)		 An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
80-24 reference(s)
Intertwining
81-23 reference(s)		 True colors autostereogram of a fractal landscape
82-23 reference(s)		 Tridimensional visualization of the Mandelbrot set with mapping of the arguments -the Mont Saint Michel-
83-23 reference(s)		 Autostereogram -using a periodical paradoxal structure as a desguise texture- with an hidden gaussian mountain
84-23 reference(s)
Artistic view of a pyramidal Menger sponge computed by means of an 'Iterated Function System' -IFS-
85-23 reference(s)		 The normal field of a fractal surface defined by means of three bidimensional fields
86-22 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)
87-22 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)
88-22 reference(s)
Paradoxal Monument Valley at sunset
89-21 reference(s)		 Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
90-21 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
91-20 reference(s)		 The Syracuse conjecture for U(0)={5,6,7,8,...,20} -tridimensional display-
92-20 reference(s)
Tridimensional visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-
93-20 reference(s)		 Tridimensional Self-Portrait
94-20 reference(s)		 Tridimensional Hilbert Curve -iteration 3-
95-20 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
96-20 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
97-20 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
98-20 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
99-20 reference(s)		 The construction process of the von Koch curve
100-19 reference(s)
Quantum vacuum fluctuations
101-19 reference(s)		 Monument Valley à la David Hockney
102-19 reference(s)		 Autostereogram of Monument Valley
103-19 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)
104-19 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'the children round' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
105-19 reference(s)		 Rotation about the X axis of the Lorenz attractor (5000 iterations), computed simultaneously on two different computers
106-19 reference(s)		 A quaternionic Julia set -tridimensional cross-section-
107-19 reference(s)		 Tridimensional display of the inflationary Universe
108-19 reference(s)
Fractal intertwining
109-19 reference(s)		 Sixty-four interlaced fractal torus
110-19 reference(s)		 Snowy Rocky Mountains
111-19 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
112-19 reference(s)
Along the border of the Mandelbrot set
113-18 reference(s)		 7-foil torus knot on its torus
114-18 reference(s)		 The tridimensional Ising Model with 2-state spins, temperature=0.2, random initial conditions and an increasing number of iterations -from 100 to 4000-
115-18 reference(s)		 Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
116-18 reference(s)
Double impossible staircase
117-18 reference(s)		 The Syracuse conjecture for U(0)={1,2,3,4,...,128} -monodimensional display-
118-17 reference(s)		 Intertwining
119-17 reference(s)		 A variable Archimedes spiral displaying 1000 numbers
120-17 reference(s)
An arbitrary surface (Jeener surface 2)in motion
121-17 reference(s)		 A shell (Jeener surface 1)
122-17 reference(s)		 Intertwining based on the geometry of a Möbius strip
123-17 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
124-17 reference(s)
The ABC conjecture
125-17 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
126-16 reference(s)		 Artistic view of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0) -a Tribute to José Hernández- -tridimensional cross-section-
127-16 reference(s)		 The Birth of the Universe
128-16 reference(s)




2-The 128 most referenced Pages (*):

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



1-demo_14
700 reference(s)		 2-An2000.01.Fra
456 reference(s)
3-Fractal.01
442 reference(s)		 4-help.
421 reference(s)
5-AQuoiServentLesMathematiques.01
369 reference(s)		 6-AVirtualSpaceTimeTravelMachine.Ang
346 reference(s)
7-FloatingPointNumbers.01.Fra
335 reference(s)		 8-MathematiquesPhysiqueFractales.02
334 reference(s)
9-aquoiserventlesmathematiques.01
319 reference(s)		 10-Stereogrammes_AutoStereogrammes.01
302 reference(s)
11-fractal.01
293 reference(s)		 12-RealNumbers.01.Fra
290 reference(s)
13-FaireDeLaRecherche.01.vv
260 reference(s)		 14-GenieLogiciel_VisualisationScientifique.01.vv
258 reference(s)
15-Galerie_ArtisticCreation.FV
248 reference(s)		 16-Galerie_NumberTheory.FV
239 reference(s)
17-MonodimensionalCellularAutomata.01.Fra
222 reference(s)		 18-Galerie_GeneralitiesVisualization.FV
220 reference(s)
19-catalogue.11
215 reference(s)		 20-mail.01.vv
214 reference(s)
21-GenieLogiciel.01.Fra
212 reference(s)		 22-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
212 reference(s)
23-ImagesDuVirtuel.01.Fra.FV
210 reference(s)		 24-copyright.01.
209 reference(s)
25-ExpV_VirE.11
209 reference(s)		 26-Galerie_NewPictures.FV
207 reference(s)
27-OrdinateursEtCalculs.01.Fra
205 reference(s)		 28-subject.01.
203 reference(s)
29-SurfaceProjector.01.Fra
203 reference(s)		 30-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
202 reference(s)
31-DieuScience.01.Fra
202 reference(s)		 32-AVirtualSpaceTimeTravelMachine.Fra
201 reference(s)
33-GoldenTriangle.01.Fra
198 reference(s)		 34-NatureDesMathematiques.01.vv.Fra
196 reference(s)
35-FloatingPointNumbers.01.Ang
196 reference(s)		 36-SurfaceProjector.01.Ang
194 reference(s)
37-Galerie_ArtAndScience.FV
194 reference(s)		 38-OrdinateurMathematiquesArt.01.Fra
193 reference(s)
39-AnimFractal.01.
193 reference(s)		 40-AProposSite.01.Fra
193 reference(s)
41-UlamSpiral.01.Fra
192 reference(s)		 42-Galerie_DeterministicFractalGeometry.FV
186 reference(s)
43-UlamSpiral.01.Ang
185 reference(s)		 44-Autostereograms.01.
185 reference(s)
45-Galerie_DeterministicChaos.FV
183 reference(s)		 46-Galerie_ParticleSystems.FV
182 reference(s)
47-fairedelarecherche.01.vv
181 reference(s)		 48-Galerie_QuantumMechanics.FV
181 reference(s)
49-infinity.01.vv
180 reference(s)		 50-create.03.
180 reference(s)
51-Fractal.11
180 reference(s)		 52-EnsembleDesGaleries.DIAPO.0001
180 reference(s)
53-NombresEtLumiere.01.vv.Fra
179 reference(s)		 54-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
179 reference(s)
55-Galerie_BestOf.FV
178 reference(s)		 56-NDimensionalDeterministicFractalSets.01.Ang
177 reference(s)
57-Kepler.02.
177 reference(s)		 58-Galerie_CelestialMechanics.FV
176 reference(s)
59-NDimensionalDeterministicFractalSets.01.Fra
175 reference(s)		 60-Informations_AboutPicturesAnimationsAndFiles.01.Ang
174 reference(s)
61-ManyChaos.01.Ang
173 reference(s)		 62-Galerie_SensitivityToRoundingOffErrors.FV
172 reference(s)
63-ExpV_VirE.21
172 reference(s)		 64-EnsembleDesGaleriesFractales.DIAPO.0001
172 reference(s)
65-RemarquesCerveau.01
171 reference(s)		 66-MonodimensionalCellularAutomata.01.Ang
171 reference(s)
67-ImpossibleStructures.01.Fra
171 reference(s)		 68-IllusionConnaissance.02
170 reference(s)
69-Galerie_TextureSynthesis.FV
168 reference(s)		 70-infinity.02.vv
167 reference(s)
71-VirtualChaos.01.Fra
167 reference(s)		 72-PerteDeLAssociativite.01
166 reference(s)
73-Galerie_Astrophysics.FV
166 reference(s)		 74-EntrelacsIntertwinings.01.Fra
166 reference(s)
75-EntrelacsIntertwinings.01.Ang
166 reference(s)		 76-PatrimoineHumanite.02.Fra
165 reference(s)
77-GoldenTriangle.01.Ang
165 reference(s)		 78-VirtualChaos.01.Ang
163 reference(s)
79-ImpossibleStructures.01.Ang
163 reference(s)		 80-Galerie_FluidMechanics.FV
163 reference(s)
81-MathematiquesPhysiqueFractales.01
161 reference(s)		 82-MathematiquesModeleOutilArtiste.02.Ang
161 reference(s)
83-Fractal.02
160 reference(s)		 84-realnumbers
159 reference(s)
85-MathematiquesEtCinematographe.01.vv
159 reference(s)		 86-VisitesGaleriesEnfouies.01.Fra
158 reference(s)
87-LOG_xiMc.11
158 reference(s)		 88-nombresreels
157 reference(s)
89-demo
157 reference(s)		 90-an2000
157 reference(s)
91-logiciel
156 reference(s)		 92-genielogiciel
156 reference(s)
93-demo14
156 reference(s)		 94-demo.14
156 reference(s)
95-Galerie_SignalProcessing.FV
156 reference(s)		 96-ExpV_VirE.Ang
156 reference(s)
97-Spheres.01
155 reference(s)		 98-OrdinateursEtCalculs.01.Ang
155 reference(s)
99-ManyChaos.01.Fra
152 reference(s)		 100-AvantPropos.01.Fra
152 reference(s)
101-VisitesGaleriesEnfouies.01.Ang
151 reference(s)		 102-MathematiquesEtRepresentations.01.vv.Ang
151 reference(s)
103-Informations_AboutPicturesAnimationsAndFiles.01.Fra
148 reference(s)		 104-AvantPropos.01.Ang
148 reference(s)
105-ExpV_VirE.Fra
147 reference(s)		 106-Commentaires_DefinitionComplexes.01
146 reference(s)
107-present.01.
145 reference(s)		 108-MathematiquesPhysiqueFractales.12
145 reference(s)
109-QuelquesQuestionsSurLaRecherche.01.Fra
144 reference(s)		 110-Commentaires_Cube.01
141 reference(s)
111-VisSci_SciVis.02
138 reference(s)		 112-Commentaires_ProblemeDesNCorps.01
137 reference(s)
113-Commentaires_EnsembleMandelbrotComplexe.01
135 reference(s)		 114-Commentaires_ModeleIsingTriDimensionnel.01
134 reference(s)
115-An2000.01.Ang
131 reference(s)		 116-Commentaires_ModeleIsingBiDimensionnel.01
129 reference(s)
117-Commentaires_FluideInstationnaireBiDimensionnelIdeal.01
129 reference(s)		 118-HommageBenoitMandelbrot.21
128 reference(s)
119-Commentaires_KleinBottle.02
128 reference(s)		 120-ExpV_VirE.01.Fra
127 reference(s)
121-Commentaires_NKleinBottle.01
127 reference(s)		 122-AQuoiServentLesMathematiques.03
127 reference(s)
123-Commentaires_DefinitionTransformeeDeFourier.01
126 reference(s)		 124-ArtScience.11.Fra
126 reference(s)
125-EnsembleDesGaleries.DIAPO.0002
125 reference(s)		 126-EnsembleDesGaleries.DIAPO.0004
124 reference(s)
127-Commentaires_DefinitionQuaternions.01
124 reference(s)		 128-EnsembleDesGaleries.DIAPO.0006
123 reference(s)

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Copyright (c) Jean-François Colonna, 2013-2019.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2013-2019.