Monthly Best Of on 11/28/2014




From the Klein bottle to the Möbius strip

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

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(CMAP28 WWW site: this page was created on 11/28/2014 and last updated on 10/03/2024 17:02:55 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Zoom in on the von Koch curve
1-1457 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
2-789 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
3-511 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
4-438 reference(s)
Bidimensional Hilbert Curve -iteration 4-
5-269 reference(s)		Tridimensional Hilbert Curve -iteration 3-
6-266 reference(s)		The random walk of photons escaping the Sun
7-232 reference(s)		Tridimensional representation of a hexadimensional Calabi-Yau manifold
8-213 reference(s)
Autostereogram with an hidden volcano
9-211 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
10-199 reference(s)		64 elementary bidimensional binary cellular automata with 1 white starting central point
11-198 reference(s)		The random walk of photons escaping the Sun
12-189 reference(s)
Autostereogram with an hidden volcano
13-182 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
14-173 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
15-153 reference(s)		Happy new year 2000
16-152 reference(s)
Reconstruction of a 3D structure -a cubic lattice-
17-150 reference(s)		Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
18-146 reference(s)		The first two iterations of the construction of the von Koch curve
19-141 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
20-141 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
21-121 reference(s)		Autostereogram with an hidden volcano
22-117 reference(s)		Tridimensional filamentous fractal structure
23-114 reference(s)		A bidimensional field
24-108 reference(s)
Tridimensional visualization of a conformal mapping of the Verhulst dynamics
25-106 reference(s)		Snowy day
26-105 reference(s)		Quantum vacuum fluctuations
27-104 reference(s)		A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) with 10 iterations -tridimensional cross-section-
28-103 reference(s)
Artistic view (bird's-eye view)of an hexagonal tiling of the hyperbolic Poincaré disk -iteration 4-
29-97 reference(s)		Tridimensional visualization of a bidimensional turbulent flow
30-93 reference(s)		Cauliflowers, seaweeds, shells,... with fog
31-92 reference(s)		2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')-tridimensional cross-section-
32-89 reference(s)
Artistic view of the prime numbers
33-88 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
34-88 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
35-88 reference(s)		True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
36-87 reference(s)
The complement of the Menger Sponge -iteration 4-
37-85 reference(s)		Intertwining
38-84 reference(s)		A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) with 18 iterations -tridimensional cross-section-
39-83 reference(s)		Quaternionic lion with extended arithmetics
40-80 reference(s)
Tridimensional spherical fractal structure
41-80 reference(s)		Mystery mountain at sunrise
42-79 reference(s)		The tridimensional Ising Model with 2-state spins, temperature=0.4 and random initial conditions
43-79 reference(s)		True colors autostereogram of a fractal landscape
44-78 reference(s)
Chaotic trajectory: multiple reflexions between two parallel planes for 64 different initial conditions
45-78 reference(s)		A fractal polyhedron
46-76 reference(s)		A Peano 'fractal plane' defined by means of three bidimensional fields
47-75 reference(s)		A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.229292,-0.444326,0,0) -tridimensional cross-section-
48-75 reference(s)
A fractal-fractal tree
49-75 reference(s)		Fractal 3-foil torus knot
50-74 reference(s)		Time-integration with transparencies of the bidimensional Ising Model with 2-state spins, temperature=0.2 and regular initial conditions (a chessboard)
51-73 reference(s)		Tridimensional representation of a hexadimensional Calabi-Yau manifold
52-73 reference(s)
Bidimensional abstract texture with random anthropomorphic patterns
53-72 reference(s)		The simple case of a bidimensional scalar (fractal)field presented in four widely differing color palettes
54-70 reference(s)		An amazing cross-section inside the complement of the Menger Sponge -iteration 4-
55-69 reference(s)		Autostereogram with an hidden volcano and 64 self-portraits
56-68 reference(s)
Untitled 0174
57-68 reference(s)		Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability
58-66 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
59-65 reference(s)		Clouds
60-65 reference(s)
An amazing cross-section inside the Menger Sponge -iteration 4- with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
61-65 reference(s)		Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
62-65 reference(s)		A pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
63-65 reference(s)		Untitled 0186
64-65 reference(s)
A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
65-64 reference(s)		Artistic view of Monument Valley at sunrise with the Great Bear
66-64 reference(s)		Artistic variation on 3-foil and 5-foil torus knots
67-64 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 4- with a O^2conformal transformation in the octonionic space -tridimensional cross-section-
68-63 reference(s)
A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
69-62 reference(s)		Autostereogram with an hidden volcano
70-61 reference(s)		A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -10.000 digits, -base 10- into 050330... -12.849 digits, -base 6-
71-61 reference(s)		Painted Desert
72-61 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
73-61 reference(s)		Intertwining
74-60 reference(s)		Untitled 0063
75-60 reference(s)		4 evenly distributed points on a sphere -a Tetrahedron- by means of simulated annealing
76-60 reference(s)
A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
77-60 reference(s)		Autostereogram with an hidden ring and ghost bows
78-59 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
79-58 reference(s)		Intertwining
80-57 reference(s)
Autostereogram of Monument Valley
81-57 reference(s)		Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')with a 1/Z conformal transformation in the complex plane -tridimensional cross-section-
82-57 reference(s)		The Lorenz attractor
83-55 reference(s)		Exhibition at the Ecole Polytechnique -09/2013-
84-55 reference(s)
Tridimensional display of the Riemann Zeta function inside [+0.1,+0.9]x[0,+50]
85-54 reference(s)		The generalized Ulam spiral
86-54 reference(s)		Autostereogram -using a periodical paradoxal structure as a desguise texture- with an hidden gaussian mountain
87-54 reference(s)		An aperiodic Penrose tiling of the Golden Decagon
88-53 reference(s)
A bidimensional field
89-53 reference(s)		Jean-François COLONNA
90-53 reference(s)		Fractal 5-foil torus knot
91-51 reference(s)		The 'Lakes' of a diffusion process obtained by means of a random walk process
92-50 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)
93-49 reference(s)		Exhibition at the Ecole Polytechnique -09/2013-
94-49 reference(s)		A bidimensional field
95-48 reference(s)		Tridimensional display of the generalized Ulam spiral displaying 4096 numbers
96-48 reference(s)
Internet
97-48 reference(s)		Tridimensional visualization of the Verhulst dynamics
98-48 reference(s)		The Scream -a Tribute to Edvard Munch-
99-47 reference(s)		Sixteen interlaced fractal torus
100-46 reference(s)
Fractal 5-foil torus knot
101-45 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
102-45 reference(s)		The bidimensional Ising Model with 2-state spins, a centred gaussian temperature field (minimum=0.035,maximum=0.6)and random initial conditions
103-44 reference(s)		A fractal Klein bottle
104-44 reference(s)
The Bonan-Jeener-Klein triple bottle
105-44 reference(s)		Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
106-42 reference(s)		Birds and fishes
107-42 reference(s)		The particle trajectories during their diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus
108-42 reference(s)
Fractal structure of a nucleon
109-41 reference(s)		Untitled 0204 -a Tribute to Francis Crick, Rosalind Franklin and James Watson-
110-41 reference(s)		Autostereogram with an hidden volcano
111-40 reference(s)		Planet
112-40 reference(s)
The foggy Babel Tower -a Tribute to Brueghel the Elder-
113-40 reference(s)		Octonionic archimedian spirals with extended arithmetics
114-40 reference(s)		From Pluto to the Sun
115-40 reference(s)		An aperiodic Penrose tiling of the plane
116-39 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
117-39 reference(s)		Quark and gluon structure of a nucleon
118-39 reference(s)		Tridimensional fractal structure -the space-time foam?-
119-39 reference(s)		The normal field of a shell (Jeener surface 1)
120-39 reference(s)
An Archimedes spiral displaying the 100.000 first digits -base 10- of 'pi'
121-38 reference(s)		A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
122-38 reference(s)		A fractal hypercube
123-38 reference(s)		Mountains at sunrise
124-37 reference(s)
The bidimensional Ising Model after 1000 iterations, with 2-state spins, random initial conditions and for a temperature equal to the critical temperature
125-36 reference(s)		N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
126-35 reference(s)		The Lorenz attractor
127-35 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
128-34 reference(s)




2-The 128 most referenced Pages (*):

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



1-demo_14
719 reference(s)		2-An2000.01.Fra
432 reference(s)
3-GenieLogiciel_VisualisationScientifique.01.vv
376 reference(s)		4-Stereogrammes_AutoStereogrammes.01
359 reference(s)
5-FloatingPointNumbers.01.Fra
356 reference(s)		6-FaireDeLaRecherche.01.vv
345 reference(s)
7-Fractal.01
337 reference(s)		8-help.
330 reference(s)
9-Galerie_Tributes.FV
325 reference(s)		10-AVirtualSpaceTimeTravelMachine.Ang
315 reference(s)
11-AQuoiServentLesMathematiques.01
289 reference(s)		12-RealNumbers.01.Fra
274 reference(s)
13-MathematiquesPhysiqueFractales.02
239 reference(s)		14-UlamSpiral.01.Fra
238 reference(s)
15-Galerie_DeterministicFractalGeometry.FV
233 reference(s)		16-AVirtualSpaceTimeTravelMachine.Fra
227 reference(s)
17-AProposSite.01.Fra
226 reference(s)		18-ExpV_VirE.11
223 reference(s)
19-Galerie_NumberTheory.FV
222 reference(s)		20-Galerie_NewPictures.FV
220 reference(s)
21-mail.01.vv
212 reference(s)		22-Galerie_CelestialMechanics.FV
208 reference(s)
23-SurfaceProjector.01.Fra
207 reference(s)		24-Galerie_GeneralitiesVisualization.FV
206 reference(s)
25-AnimFractal.01.
204 reference(s)		26-EntrelacsIntertwinings.01.Fra
203 reference(s)
27-NDimensionalDeterministicFractalSets.01.Fra
202 reference(s)		28-MorePages.
202 reference(s)
29-MonodimensionalCellularAutomata.01.Fra
200 reference(s)		30-GoldenTriangle.01.Fra
199 reference(s)
31-Fractal.11
199 reference(s)		32-Galerie_ArtisticCreation.FV
196 reference(s)
33-EnsembleDesGaleries.DIAPO.0001
196 reference(s)		34-FloatingPointNumbers.01.Ang
195 reference(s)
35-copyright.01.
193 reference(s)		36-SurfaceProjector.01.Ang
193 reference(s)
37-Galerie_ArtAndScience.FV
193 reference(s)		38-NDimensionalDeterministicFractalSets.01.Ang
192 reference(s)
39-DieuScience.01.Fra
192 reference(s)		40-Kepler.02.
190 reference(s)
41-EntrelacsIntertwinings.01.Ang
189 reference(s)		42-ImagesDuVirtuel.01.Fra.FV
185 reference(s)
43-OrdinateursEtCalculs.01.Fra
184 reference(s)		44-Galerie_Astrophysics.FV
184 reference(s)
45-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
183 reference(s)		46-ImagesDuVirtuel.01.Fra
182 reference(s)
47-GenieLogiciel.01.Fra
181 reference(s)		48-Galerie_BestOf.FV
180 reference(s)
49-Autostereograms.01.
180 reference(s)		50-catalogue.11
179 reference(s)
51-NatureDesMathematiques.01.vv.Fra
179 reference(s)		52-LOG_xiMc.11
179 reference(s)
53-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
179 reference(s)		54-Fractal.03
179 reference(s)
55-Galerie_QuantumMechanics.FV
177 reference(s)		56-DuModeleALImage.02.Fra
176 reference(s)
57-UlamSpiral.01.Ang
175 reference(s)		58-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
175 reference(s)
59-AvantPropos.01.Fra
175 reference(s)		60-ManyChaos.01.Fra
174 reference(s)
61-Galerie_ParticleSystems.FV
174 reference(s)		62-AvantPropos.01.Ang
173 reference(s)
63-LesApprentisDieux.01
172 reference(s)		64-ImpossibleStructures.01.Ang
172 reference(s)
65-Galerie_SensitivityToRoundingOffErrors.FV
172 reference(s)		66-ImpossibleStructures.01.Fra
171 reference(s)
67-GoldenTriangle.01.Ang
171 reference(s)		68-EnsembleDesGaleriesFractales.DIAPO.0001
171 reference(s)
69-IllusionConnaissance.02
170 reference(s)		70-an2000
169 reference(s)
71-Galerie_DeterministicChaos.FV
169 reference(s)		72-NombresEtLumiere.01.vv.Fra
168 reference(s)
73-demo14
167 reference(s)		74-Informations_AboutPicturesAnimationsAndFiles.01.Ang
167 reference(s)
75-demo
166 reference(s)		76-VirtualChaos.01.Ang
166 reference(s)
77-OrdinateurMathematiquesArt.01.Fra
166 reference(s)		78-MathematiquesModeleOutilArtiste.02.Ang
166 reference(s)
79-realnumbers
165 reference(s)		80-nombresreels
165 reference(s)
81-logiciel
165 reference(s)		82-MonodimensionalCellularAutomata.01.Ang
165 reference(s)
83-MathematiquesPhysiqueFractales.22
165 reference(s)		84-Galerie_TextureSynthesis.FV
165 reference(s)
85-genielogiciel
164 reference(s)		86-OrdinateursEtCalculs.01.Ang
164 reference(s)
87-demo.14
163 reference(s)		88-create.03.
163 reference(s)
89-ExpV_VirE.Ang
163 reference(s)		90-infinity.02.vv
161 reference(s)
91-infinity.01.vv
161 reference(s)		92-Galerie_SignalProcessing.FV
159 reference(s)
93-Galerie_FluidMechanics.FV
159 reference(s)		94-VirtualChaos.01.Fra
158 reference(s)
95-QuelquesQuestionsSurLaRecherche.01.Fra
158 reference(s)		96-MathematiquesEtCinematographe.01.vv
158 reference(s)
97-Informations_GoodNewsAndBadNews.01.Fra
158 reference(s)		98-VisitesGaleriesEnfouies.01.Fra
157 reference(s)
99-subject.01.
156 reference(s)		100-RemarquesCerveau.01
156 reference(s)
101-Fractal.02
156 reference(s)		102-VisitesGaleriesEnfouies.01.Ang
154 reference(s)
103-PatrimoineHumanite.02.Fra
154 reference(s)		104-PerteDeLAssociativite.01
153 reference(s)
105-MathematiquesEtRepresentations.01.vv.Ang
151 reference(s)		106-ManyChaos.01.Ang
148 reference(s)
107-ExpV_VirE.21
146 reference(s)		108-Spheres.01
145 reference(s)
109-fairedelarecherche.01.vv
141 reference(s)		110-MathematiquesPhysiqueFractales.01
141 reference(s)
111-present.01.
138 reference(s)		112-fractal.01
138 reference(s)
113-Commentaires_NKleinBottle.01
136 reference(s)		114-Informations_AboutPicturesAnimationsAndFiles.01.Fra
134 reference(s)
115-ExpV_VirE.Fra
130 reference(s)		116-ExpV_VirE.01.Fra
130 reference(s)
117-ComplexiteStructurelleClassements.01
130 reference(s)		118-Galerie_GeneralitiesVisualization.DIAPO.0094
129 reference(s)
119-ArtEtMathematiques.01
129 reference(s)		120-Vcatalogue.11
128 reference(s)
121-Commentaires_VarieteQuadriDimensionnelleCalabiYau.01
128 reference(s)		122-Galerie_TextureSynthesis.DIAPO.0001
127 reference(s)
123-An2000.04.Fra
126 reference(s)		124-demo_14.FV
125 reference(s)
125-MonumentValley.01.Ang
125 reference(s)		126-Commentaires_RacinesTroisiemesUniteComplexes.01
125 reference(s)
127-HommageBenoitMandelbrot.21
124 reference(s)		128-Commentaires_SurfaceDeBoy.01
124 reference(s)

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




Copyright © Jean-François COLONNA, 2014-2024.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2014-2024.