Monthly Best Of on 09/28/2013




The construction process of an aperiodic Penrose tiling -1 random subdivision iteration-

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 09/28/2013 and last updated on 11/14/2023 17:48:22 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



A tridimensional fractal manifold defined by means of three tridimensional fields
1-419 reference(s)		 Fractal Notre-Dame de la Garde, Marseilles
2-306 reference(s)		 Sixteen interlaced torus
3-288 reference(s)		 Happy new year 2000
4-240 reference(s)
A fractal-fractal tree
5-217 reference(s)		 The generalized Ulam spiral
6-211 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
7-194 reference(s)		 Tridimensional representation of a hexadimensional Calabi-Yau manifold
8-185 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
9-161 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
10-160 reference(s)		 Artistic view of the prime numbers
11-157 reference(s)		 Quantum vacuum fluctuations
12-150 reference(s)
Monument Valley à la David Hockney
13-144 reference(s)		 A fractal hypercube
14-142 reference(s)		 The random walk of photons escaping the Sun
15-140 reference(s)		 Anaglyph -blue=right, red=left- of a fractal-fractal tree
16-140 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
17-110 reference(s)		 Tridimensional Hilbert Curve -iteration 3-
18-104 reference(s)		 Zoom in on the von Koch curve
19-102 reference(s)		 Autostereogram with an hidden volcano
20-101 reference(s)
Quark and gluon structure of a nucleon
21-101 reference(s)		 A set of 4x3 stereograms of a fractal hypercube
22-95 reference(s)		 From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
23-94 reference(s)		 Autostereogram with an hidden volcano and 64 self-portraits
24-92 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-
25-91 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
26-91 reference(s)		 Quantum vacuum fluctuations
27-90 reference(s)		 Fractal synthesis of mountains with vegetation and stormy clouds
28-87 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
29-87 reference(s)		 Isle of the Dead -a Tribute to Arnold Böcklin-
30-84 reference(s)		 The random walk of photons escaping the Sun
31-78 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)
32-71 reference(s)
From Pluto to the Sun (non linear scales)
33-71 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
34-69 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
35-64 reference(s)		 Autostereogram with an hidden volcano
36-64 reference(s)
Autostereogram with an hidden volcano
37-64 reference(s)		 Tridimensional display of the generalized Ulam spiral displaying 4096 numbers
38-63 reference(s)		 The Jeener-Klein triple bottle
39-62 reference(s)		 Tridimensional display of the Riemann Zeta function inside [+0.1,+0.9]x[0,+50]
40-61 reference(s)
The Syracuse conjecture for U(0)={5,6,7,8,...,20} -polar coordinates display-
41-61 reference(s)		 True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
42-61 reference(s)		 The Lorenz attractor
43-61 reference(s)		 An aperiodic Penrose tiling of the Golden Decagon
44-58 reference(s)
Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability
45-58 reference(s)		 Bidimensional Hilbert Curve -iteration 4-
46-57 reference(s)		 The foggy Babel Tower -a Tribute to Brueghel the Elder-
47-54 reference(s)		 Autostereogram with an hidden ring and ghost bows
48-50 reference(s)
The Scream -a Tribute to Edvard Munch-
49-50 reference(s)		 Autostereogram with an hidden volcano
50-48 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
51-48 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
52-48 reference(s)
Bidimensional display of the dynamics of the linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
53-47 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
54-47 reference(s)		 Rotation about the Y (vertical)axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms
55-47 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
56-46 reference(s)
Quark and gluon structure of a nucleon
57-45 reference(s)		 Autostereogram -using a periodical paradoxal structure as a desguise texture- with an hidden gaussian mountain
58-45 reference(s)		 'O temps tes pyramides' -a Tribute to Jorge Luis Borges-
59-45 reference(s)		 Artistic variation on a tridimensional fractal cross -iteration 4-
60-45 reference(s)
An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
61-45 reference(s)		 The multiplicative persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-
62-44 reference(s)		 From the infinitely small to the infinitely big
63-44 reference(s)		 Autostereogram with an hidden volcano
64-42 reference(s)
A set of 4x3 stereograms of a fractal Notre-Dame de la Garde, Marseilles
65-41 reference(s)		 Reconstruction of a 3D structure -a cubic lattice-
66-40 reference(s)		 Artistic view of the Big Bang
67-38 reference(s)		 Monument Valley à la David Hockney
68-38 reference(s)
Untitled 0195
69-38 reference(s)		 Autostereogram of 8 color-multiplexed quaternionic Julia sets -tridimensional cross-sections-
70-37 reference(s)		 Tridimensional visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
71-37 reference(s)		 Jean-François COLONNA (on 11/17/1994)with its fractal mountains
72-36 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
73-36 reference(s)		 24 evenly distributed points on a sphere by means of simulated annealing
74-35 reference(s)		 Artistic variation on the generalized Ulam spiral displaying 81 numbers
75-35 reference(s)		 Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
76-35 reference(s)
Artistic variation on two quaternionic Julia/Mandelbrot sets -tridimensional cross-section-
77-35 reference(s)		 The Goldbach conjecture -the Goldbach glacier- for the even numbers from 6 to 1564
78-35 reference(s)		 A fractal aperiodic Penrose tiling
79-35 reference(s)		 Sixteen interlaced fractal torus
80-35 reference(s)
LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
81-35 reference(s)		 Birds and fishes
82-34 reference(s)		 Rotation about the Y (vertical)axis of the Jeener-Klein triple bottle that can also be viewed as a set of 4x3 stereograms
83-34 reference(s)		 Autostereogram of Monument Valley
84-33 reference(s)
Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
85-33 reference(s)		 A set of 4x3 stereograms of a tridimensional interpolation between a fractal structure and a cubic mesh
86-33 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
87-33 reference(s)		 An aperiodic Penrose tiling of the plane
88-32 reference(s)
Along the border of the Mandelbrot set
89-32 reference(s)		 The extended Borromean Rings
90-32 reference(s)		 A Peano 'fractal plane' defined by means of three bidimensional fields
91-32 reference(s)		 Sunny Monument Valley
92-32 reference(s)
Close-up on a foggy 'MandelBox' -tridimensional cross-section-
93-32 reference(s)		 Untitled 0180
94-31 reference(s)		 Bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
95-31 reference(s)		 Various bidimensional fractal crosses
96-31 reference(s)
Synthesis of bidimensional geometrical textures
97-30 reference(s)		 Fractal piano keyboard
98-30 reference(s)		 True colors autostereogram of a fractal landscape
99-30 reference(s)		 Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
100-30 reference(s)
Quark and gluon dynamics of the nucleon
101-29 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
102-29 reference(s)		 The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
103-29 reference(s)		 Hypercube
104-29 reference(s)
Tridimensional fractal structure -the space-time foam?-
105-29 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
106-29 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
107-29 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
108-28 reference(s)
Tridimensional fractal cross -iteration 5-
109-28 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
110-28 reference(s)		 Recursive intertwining
111-27 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-
112-27 reference(s)
An Archimedes spiral displaying 1000 numbers
113-27 reference(s)		 Mountains at sunrise
114-27 reference(s)		 A set of 4x3 stereograms of a fractal sphere
115-27 reference(s)		 A dynamics of a random intertwining
116-27 reference(s)
Artistic variation on a tridimensional fractal cross -iteration 2-
117-27 reference(s)		 Foggy Monument Valley
118-26 reference(s)		 From Pluto to the Sun -extrapolation 2- (non linear scales)
119-26 reference(s)		 The Möbius strip
120-26 reference(s)
The Birth of the Universe
121-26 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
122-26 reference(s)		 A fractal Möbius strip
123-26 reference(s)		 An aperiodic Penrose tiling of the plane
124-25 reference(s)
Autostereogram with an hidden volcano
125-25 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
126-25 reference(s)		 Untitled 0194
127-25 reference(s)		 A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'the children round' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
128-25 reference(s)




2-The 128 most referenced Pages (*):

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



1-catalogue.11
3070 reference(s)		 2-demo_14
475 reference(s)
3-An2000.01.Fra
448 reference(s)		 4-help.
348 reference(s)
5-AQuoiServentLesMathematiques.01
347 reference(s)		 6-Fractal.01
336 reference(s)
7-Stereogrammes_AutoStereogrammes.01
294 reference(s)		 8-FloatingPointNumbers.01.Fra
294 reference(s)
9-FaireDeLaRecherche.01.vv
272 reference(s)		 10-RealNumbers.01.Fra
261 reference(s)
11-AVirtualSpaceTimeTravelMachine.Ang
261 reference(s)		 12-fractal.01
254 reference(s)
13-AVirtualSpaceTimeTravelMachine.Fra
253 reference(s)		 14-UlamSpiral.01.Fra
248 reference(s)
15-Galerie_ArtAndScience.FV
235 reference(s)		 16-Galerie_DeterministicFractalGeometry.FV
229 reference(s)
17-aquoiserventlesmathematiques.01
223 reference(s)		 18-Galerie_NewPictures.FV
223 reference(s)
19-MathematiquesPhysiqueFractales.02
222 reference(s)		 20-MonodimensionalCellularAutomata.01.Fra
221 reference(s)
21-Galerie_NumberTheory.FV
217 reference(s)		 22-ExpV_VirE.11
217 reference(s)
23-ComplexiteStructurelle.01
215 reference(s)		 24-Galerie_ArtisticCreation.FV
214 reference(s)
25-mail.01.vv
212 reference(s)		 26-GenieLogiciel_VisualisationScientifique.01.vv
211 reference(s)
27-AProposSite.01.Fra
211 reference(s)		 28-Galerie_GeneralitiesVisualization.FV
210 reference(s)
29-Galerie_CelestialMechanics.FV
207 reference(s)		 30-ImagesDuVirtuel.01.Fra.FV
203 reference(s)
31-copyright.01.
198 reference(s)		 32-MorePages.
197 reference(s)
33-Autostereograms.01.
197 reference(s)		 34-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
194 reference(s)
35-Galerie_ParticleSystems.FV
192 reference(s)		 36-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
192 reference(s)
37-DieuScience.01.Fra
192 reference(s)		 38-SurfaceProjector.01.Fra
190 reference(s)
39-MathematiquesPhysiqueFractales.22
187 reference(s)		 40-Galerie_QuantumMechanics.FV
187 reference(s)
41-NatureDesMathematiques.01.vv.Fra
186 reference(s)		 42-NDimensionalDeterministicFractalSets.01.Fra
186 reference(s)
43-ManyChaos.01.Fra
184 reference(s)		 44-SurfaceProjector.01.Ang
183 reference(s)
45-Galerie_DeterministicChaos.FV
182 reference(s)		 46-Fractal.11
182 reference(s)
47-fairedelarecherche.01.vv
181 reference(s)		 48-NombresEtLumiere.01.vv.Fra
181 reference(s)
49-NDimensionalDeterministicFractalSets.01.Ang
181 reference(s)		 50-UlamSpiral.01.Ang
179 reference(s)
51-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
179 reference(s)		 52-demo
178 reference(s)
53-Kepler.02.
178 reference(s)		 54-Galerie_TextureSynthesis.FV
177 reference(s)
55-Galerie_BestOf.FV
177 reference(s)		 56-Fractal.03
176 reference(s)
57-Informations_GoodNewsAndBadNews.01.Fra
174 reference(s)		 58-EnsembleDesGaleries.DIAPO.0001
174 reference(s)
59-realnumbers
173 reference(s)		 60-EntrelacsIntertwinings.01.Ang
173 reference(s)
61-AvantPropos.01.Fra
173 reference(s)		 62-AvantPropos.01.Ang
172 reference(s)
63-GenieLogiciel.01.Fra
171 reference(s)		 64-an2000
170 reference(s)
65-ImpossibleStructures.01.Ang
170 reference(s)		 66-ExpV_VirE.Ang
170 reference(s)
67-infinity.01.vv
169 reference(s)		 68-demo14
169 reference(s)
69-FloatingPointNumbers.01.Ang
169 reference(s)		 70-genielogiciel
168 reference(s)
71-Informations_AboutPicturesAnimationsAndFiles.01.Ang
168 reference(s)		 72-ImpossibleStructures.01.Fra
168 reference(s)
73-nombresreels
167 reference(s)		 74-logiciel
167 reference(s)
75-demo.14
167 reference(s)		 76-IllusionConnaissance.02
167 reference(s)
77-OrdinateursEtCalculs.01.Fra
166 reference(s)		 78-GoldenTriangle.01.Ang
166 reference(s)
79-MonodimensionalCellularAutomata.01.Ang
165 reference(s)		 80-GoldenTriangle.01.Fra
165 reference(s)
81-Galerie_SignalProcessing.FV
165 reference(s)		 82-EnsembleDesGaleriesFractales.DIAPO.0001
165 reference(s)
83-EntrelacsIntertwinings.01.Fra
164 reference(s)		 84-AnimFractal.01.
164 reference(s)
85-create.03.
161 reference(s)		 86-ManyChaos.01.Ang
160 reference(s)
87-LOG_xiMc.11
160 reference(s)		 88-Galerie_SensitivityToRoundingOffErrors.FV
159 reference(s)
89-subject.01.
157 reference(s)		 90-VisitesGaleriesEnfouies.01.Fra
157 reference(s)
91-OrdinateurMathematiquesArt.01.Fra
157 reference(s)		 92-AVirtualSpaceTimeTravelMachine.Fra.FV
157 reference(s)
93-infinity.02.vv
156 reference(s)		 94-VisitesGaleriesEnfouies.01.Ang
156 reference(s)
95-Spheres.01
156 reference(s)		 96-RemarquesCerveau.01
156 reference(s)
97-Galerie_FluidMechanics.FV
156 reference(s)		 98-OrdinateursEtCalculs.01.Ang
153 reference(s)
99-PerteDeLAssociativite.01
152 reference(s)		 100-MathematiquesPhysiqueFractales.01
152 reference(s)
101-An2000.01.Ang
152 reference(s)		 102-MathematiquesEtCinematographe.01.vv
150 reference(s)
103-Galerie_Astrophysics.FV
149 reference(s)		 104-An2000.04.Fra
149 reference(s)
105-MathematiquesModeleOutilArtiste.02.Ang
148 reference(s)		 106-VirtualChaos.01.Ang
147 reference(s)
107-MathematiquesEtRepresentations.01.vv.Ang
147 reference(s)		 108-Fractal.02
147 reference(s)
109-ExpV_VirE.21
146 reference(s)		 110-MathematiquesPhysiqueFractales.12
142 reference(s)
111-Galerie_Tributes.FV
142 reference(s)		 112-Galerie_QuantumMechanics
142 reference(s)
113-VirtualChaos.01.Fra
140 reference(s)		 114-Vcatalogue.11
136 reference(s)
115-present.01.
134 reference(s)		 116-AQuoiServentLesMathematiques.02
132 reference(s)
117-MonumentValley.01.Ang
131 reference(s)		 118-Galerie_FromTheInfinitelySmallToTheInfinitelyBig.FV
131 reference(s)
119-ExpV_VirE.01.Fra
131 reference(s)		 120-ImagesDuVirtuel.01.Fra
129 reference(s)
121-PatrimoineHumanite.02.Fra
128 reference(s)		 122-Informations_AboutPicturesAnimationsAndFiles.01.Fra
128 reference(s)
123-Commentaires_VarieteQuadriDimensionnelleCalabiYau.01
128 reference(s)		 124-MathematiquesPhysiqueFractales.02.27
127 reference(s)
125-ExpV_VirE.01.Ang
126 reference(s)		 126-Commentaires_NKleinBottle.01
126 reference(s)
127-Commentaires_ModeleIsingBiDimensionnel.01
126 reference(s)		 128-ArtScience.11.Fra
126 reference(s)

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




Copyright © Jean-François COLONNA, 2013-2023.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2013-2023.