Monthly Best Of on 12/28/2014




A random tridimensional fractal tree and the self-similarity

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 12/28/2014 and last updated on 06/30/2018 14:06:37 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures:



Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
1-623 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
2-480 reference(s)		 A tridimensional fractal manifold defined by means of three tridimensional fields
3-265 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
4-232 reference(s)
The random walk of photons escaping the Sun
5-216 reference(s)		 Autostereogram with an hidden volcano
6-200 reference(s)		 Happy new year 2000
7-196 reference(s)		 Zoom in on the von Koch curve
8-194 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
9-190 reference(s)		 The random walk of photons escaping the Sun
10-171 reference(s)		 Tridimensional Hilbert Curve -iteration 3-
11-166 reference(s)		 Tridimensional display of the Riemann Zeta function inside (-50.0,+50.0)x(-50.0,+50.0) (bird's-eye view)
12-165 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
13-164 reference(s)		 Tridimensional representation of a hexadimensional Calabi-Yau manifold
14-162 reference(s)		 Autostereogram with an hidden volcano
15-155 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
16-132 reference(s)
Bidimensional Hilbert Curve -iteration 4-
17-125 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
18-116 reference(s)		 Tridimensional representation of a hexadimensional Calabi-Yau manifold
19-108 reference(s)		 Reconstruction of a 3D structure -a cubic lattice-
20-102 reference(s)
Autostereogram with an hidden volcano
21-97 reference(s)		 Quantum vacuum fluctuations
22-86 reference(s)		 The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
23-85 reference(s)		 Artistic view of the prime numbers
24-75 reference(s)
Time-integration with transparencies of the bidimensional Ising Model with 2-state spins, temperature=0.2 and regular initial conditions (a chessboard)
25-73 reference(s)		 Tridimensional visualization of a conformal mapping of the Verhulst dynamics
26-71 reference(s)		 2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')-tridimensional cross-section-
27-69 reference(s)		 A bidimensional field
28-69 reference(s)
Snowy day
29-67 reference(s)		 True colors autostereogram of a fractal landscape
30-67 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
31-67 reference(s)		 An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
32-67 reference(s)
True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
33-65 reference(s)		 A Peano 'fractal plane' defined by means of three bidimensional fields
34-65 reference(s)		 Jean-François Colonna
35-64 reference(s)		 Quaternionic lion with extended arithmetics
36-63 reference(s)
Tridimensional visualization of a bidimensional turbulent flow
37-62 reference(s)		 Cauliflowers, seaweeds, shells,... with fog
38-61 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
39-60 reference(s)		 The particle trajectories during their diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus
40-60 reference(s)
Autostereogram with an hidden ring and ghost bows
41-59 reference(s)		 Fractal synthesis of mountains and clouds
42-56 reference(s)		 Mountains at sunrise
43-56 reference(s)		 A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0) with 10 iterations -tridimensional cross-section-
44-56 reference(s)
Autostereogram with an hidden volcano and 64 self-portraits
45-56 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
46-56 reference(s)		 The complement of the Menger sponge -iteration 4-
47-55 reference(s)		 Chaotic trajectory: multiple reflexions between two parallel planes for 64 different initial conditions
48-55 reference(s)
The 'Lakes' of a diffusion process obtained by means of a random walk process
49-54 reference(s)		 The tridimensional Ising Model with 2-state spins, temperature=0.4 and random initial conditions
50-53 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
51-50 reference(s)		 Fractal 3-foil torus knot
52-50 reference(s)
Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability
53-50 reference(s)		 Tridimensional spherical fractal structure
54-49 reference(s)		 Artistic view of Monument Valley at sunrise with the Great Bear
55-48 reference(s)		 Artistic view (bird's-eye view)of an hexagonal tiling of the hyperbolic Poincaré disk -iteration 4-
56-47 reference(s)
Internet
57-47 reference(s)		 A fractal-fractal tree
58-47 reference(s)		 4 evenly distributed points on a sphere -a Tetrahedron- by means of simulated annealing
59-46 reference(s)		 A fractal hypercube
60-46 reference(s)
Fractal 5-foil torus knot
61-46 reference(s)		 Exhibition at the Ecole Polytechnique -09/2013-
62-46 reference(s)		 Exhibition at the Ecole Polytechnique -09/2013-
63-46 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
64-45 reference(s)
The Scream -a Tribute to Edvard Munch-
65-45 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-
66-45 reference(s)		 The Bonan-Jeener's triple Klein bottle
67-45 reference(s)		 Foggy Babel Tower -a tribute to Brueghel the Elder-
68-44 reference(s)
Artistic view of 'from Pluto to the Sun' -extrapolation 1- (non linear scales)
69-44 reference(s)		 A pseudo-periodical Penrose tiling of the Golden Decagon
70-43 reference(s)		 Intertwining
71-43 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
72-43 reference(s)
The generalized Ulam spiral
73-43 reference(s)		 The 12.723 first digits -base 6- of 'pi' displayed as an 'absolute' tridimensional random walk
74-43 reference(s)		 Painted Desert
75-43 reference(s)		 Octonionic archimedian spirals with extended arithmetics
76-43 reference(s)
The simple case of a bidimensional scalar (fractal)field presented in four widely differing color palettes
77-43 reference(s)		 An amazing cross-section inside the complement of the Menger sponge -iteration 4-
78-43 reference(s)		 An amazing cross-section inside the Menger sponge -iteration 4- with a OxO conformal transformation in the Octonionic space -tridimensional cross-section-
79-43 reference(s)		 Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
80-43 reference(s)
No Title 0174
81-43 reference(s)		 No Title 0186
82-43 reference(s)		 Planet
83-42 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
84-42 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
85-42 reference(s)		 Autostereogram of Monument Valley
86-41 reference(s)		 Quark and gluon structure of a nucleon
87-41 reference(s)		 From Pluto to the Sun (non linear scales)
88-40 reference(s)
Quantum vacuum fluctuation dynamics
89-39 reference(s)		 Fractal structure of a nucleon
90-39 reference(s)		 Pi/2 rotation about the X axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')-tridimensional cross-section-
91-39 reference(s)		 Sixteen interlaced fractal torus
92-39 reference(s)
Tridimensional display of the Riemann Zeta function inside (+0.1,+0.9)x(0,+50)
93-38 reference(s)		 Intertwining
94-38 reference(s)		 A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0) with 18 iterations -tridimensional cross-section-
95-38 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
96-38 reference(s)
A bidimensional field
97-37 reference(s)		 No Title 0063
98-37 reference(s)		 Tridimensional display of the generalized Ulam spiral displaying 4096 numbers
99-37 reference(s)		 A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-
100-37 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)
101-37 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
102-37 reference(s)		 Hypercube
103-37 reference(s)		 Tridimensional fractal structure -the space-time foam?-
104-37 reference(s)
Autostereogram with an hidden volcano
105-36 reference(s)		 The Klein bottle
106-36 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-
107-36 reference(s)		 No Title 0222
108-36 reference(s)
A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-
109-36 reference(s)		 Autostereogram -using a periodical paradoxal structure as a desguise texture- with an hidden gaussian mountain
110-36 reference(s)		 Autostereogram with an hidden volcano
111-35 reference(s)		 The Lorenz attractor
112-35 reference(s)
A pseudo-periodical Penrose tiling of the plane
113-34 reference(s)		 Intertwining
114-34 reference(s)		 The Lorenz attractor
115-34 reference(s)		 A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.229292,-0.444326,0,0) -tridimensional cross-section-
116-34 reference(s)
2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
117-34 reference(s)		 No Title 0204
118-34 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
119-34 reference(s)		 Paradoxal Monument Valley at sunset
120-33 reference(s)
From Pluto to the Sun
121-33 reference(s)		 From the infinitely small to the infinitely big
122-33 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
123-33 reference(s)		 A punched paper tape
124-32 reference(s)
A pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
125-32 reference(s)		 A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) with a rotation about the X axis -tridimensional cross-section-
126-32 reference(s)		 An Archimedes spiral displaying the 100.000 first digits -base 10- of 'pi'
127-31 reference(s)		 Tridimensional filamentous fractal structure
128-31 reference(s)




2-The 128 most referenced Pages:



1-demo_14
501 reference(s)		 2-An2000.01.Fra
379 reference(s)
3-Stereogrammes_AutoStereogrammes.01
343 reference(s)		 4-help.
306 reference(s)
5-Galerie_Tributes.FV
304 reference(s)		 6-Fractal.01
292 reference(s)
7-FloatingPointNumbers.01.Fra
283 reference(s)		 8-GenieLogiciel_VisualisationScientifique.01.vv
279 reference(s)
9-AQuoiServentLesMathematiques.01
246 reference(s)		 10-AVirtualSpaceTimeTravelMachine.Ang
243 reference(s)
11-FaireDeLaRecherche.01.vv
228 reference(s)		 12-RealNumbers.01.Fra
225 reference(s)
13-UlamSpiral.01.Fra
223 reference(s)		 14-MathematiquesPhysiqueFractales.02
223 reference(s)
15-AVirtualSpaceTimeTravelMachine.Fra
218 reference(s)		 16-mail.01.vv
201 reference(s)
17-AnimFractal.01.
200 reference(s)		 18-Galerie_GeneralitiesVisualization.FV
198 reference(s)
19-Galerie_DeterministicFractalGeometry.FV
197 reference(s)		 20-fractal.01
187 reference(s)
21-copyright.01.
187 reference(s)		 22-Galerie_NumberTheory.FV
187 reference(s)
23-AProposSite.01.Fra
184 reference(s)		 24-Galerie_NewPictures.FV
183 reference(s)
25-ExpV_VirE.11
183 reference(s)		 26-NDimensionalDeterministicFractalSets.01.Fra
182 reference(s)
27-GoldenTriangle.01.Fra
181 reference(s)		 28-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
181 reference(s)
29-FloatingPointNumbers.01.Ang
170 reference(s)		 30-EntrelacsIntertwinings.01.Fra
169 reference(s)
31-DieuScience.01.Fra
169 reference(s)		 32-MathematiquesPhysiqueFractales.22
167 reference(s)
33-LOG_xiMc.11
165 reference(s)		 34-ExpV_VirE.21
164 reference(s)
35-catalogue.11
161 reference(s)		 36-DuModeleALImage.02.Fra
160 reference(s)
37-Fractal.11
159 reference(s)		 38-MonodimensionalCellularAutomata.01.Fra
157 reference(s)
39-Galerie_ArtAndScience.FV
157 reference(s)		 40-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
156 reference(s)
41-NombresEtLumiere.01.vv.Fra
155 reference(s)		 42-NDimensionalDeterministicFractalSets.01.Ang
155 reference(s)
43-Galerie_ArtisticCreation.FV
155 reference(s)		 44-Autostereograms.01.
155 reference(s)
45-GenieLogiciel.01.Fra
153 reference(s)		 46-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
153 reference(s)
47-Galerie_Astrophysics.FV
153 reference(s)		 48-SurfaceProjector.01.Fra
152 reference(s)
49-OrdinateursEtCalculs.01.Fra
152 reference(s)		 50-MorePages.
152 reference(s)
51-Informations_GoodNewsAndBadNews.01.Fra
152 reference(s)		 52-Galerie_CelestialMechanics.FV
152 reference(s)
53-subject.01.
151 reference(s)		 54-OrdinateurMathematiquesArt.01.Fra
151 reference(s)
55-SurfaceProjector.01.Ang
150 reference(s)		 56-EnsembleDesGaleriesFractales.DIAPO.0001
150 reference(s)
57-ExpV_VirE.Ang
149 reference(s)		 58-Galerie_QuantumMechanics.FV
148 reference(s)
59-ImagesDuVirtuel.01.Fra.FV
147 reference(s)		 60-PatrimoineHumanite.02.Fra
146 reference(s)
61-ManyChaos.01.Fra
146 reference(s)		 62-EntrelacsIntertwinings.01.Ang
145 reference(s)
63-NatureDesMathematiques.01.vv.Fra
144 reference(s)		 64-MonodimensionalCellularAutomata.01.Ang
144 reference(s)
65-GoldenTriangle.01.Ang
144 reference(s)		 66-AvantPropos.01.Fra
144 reference(s)
67-RemarquesCerveau.01
143 reference(s)		 68-Galerie_BestOf.FV
143 reference(s)
69-UlamSpiral.01.Ang
142 reference(s)		 70-Galerie_DeterministicChaos.FV
142 reference(s)
71-Fractal.03
142 reference(s)		 72-realnumbers
141 reference(s)
73-infinity.01.vv
141 reference(s)		 74-demo
141 reference(s)
75-Kepler.02.
141 reference(s)		 76-Galerie_SensitivityToRoundingOffErrors.FV
141 reference(s)
77-nombresreels
140 reference(s)		 78-logiciel
140 reference(s)
79-genielogiciel
140 reference(s)		 80-demo14
140 reference(s)
81-demo.14
140 reference(s)		 82-an2000
140 reference(s)
83-PerteDeLAssociativite.01
140 reference(s)		 84-LesApprentisDieux.01
140 reference(s)
85-Galerie_SignalProcessing.FV
140 reference(s)		 86-present.01.
139 reference(s)
87-Informations_AboutPicturesAnimationsAndFiles.01.Ang
139 reference(s)		 88-Galerie_ParticleSystems.FV
139 reference(s)
89-infinity.02.vv
137 reference(s)		 90-ImpossibleStructures.01.Fra
137 reference(s)
91-AvantPropos.01.Ang
136 reference(s)		 92-create.03.
135 reference(s)
93-IllusionConnaissance.02
135 reference(s)		 94-Galerie_TextureSynthesis.FV
135 reference(s)
95-fairedelarecherche.01.vv
134 reference(s)		 96-VisitesGaleriesEnfouies.01.Fra
132 reference(s)
97-QuelquesQuestionsSurLaRecherche.01.Fra
132 reference(s)		 98-Fractal.02
132 reference(s)
99-EnsembleDesGaleries.DIAPO.0001
132 reference(s)		 100-MathematiquesModeleOutilArtiste.02.Ang
131 reference(s)
101-MathematiquesEtRepresentations.01.vv.Ang
131 reference(s)		 102-Galerie_FluidMechanics.FV
131 reference(s)
103-VirtualChaos.01.Ang
129 reference(s)		 104-MathematiquesPhysiqueFractales.01
129 reference(s)
105-MathematiquesEtCinematographe.01.vv
129 reference(s)		 106-ImpossibleStructures.01.Ang
129 reference(s)
107-VisitesGaleriesEnfouies.01.Ang
128 reference(s)		 108-ManyChaos.01.Ang
126 reference(s)
109-VirtualChaos.01.Fra
125 reference(s)		 110-Spheres.01
125 reference(s)
111-Informations_AboutPicturesAnimationsAndFiles.01.Fra
123 reference(s)		 112-OrdinateursEtCalculs.01.Ang
120 reference(s)
113-aquoiserventlesmathematiques.01
118 reference(s)		 114-Galerie_ImagesDesMathematiques.FV
118 reference(s)
115-Commentaires_NKleinBottle.01
114 reference(s)		 116-ArtEtMathematiques.01
111 reference(s)
117-catalogue.11..m4.
110 reference(s)		 118-ExpV_VirE.01.Fra
110 reference(s)
119-Commentaires_FluideInstationnaireBiDimensionnelIdeal.01
110 reference(s)		 120-Informations_GoodNewsAndBadNews.01.Ang
109 reference(s)
121-AQuoiServentLesMathematiques.03
109 reference(s)		 122-Galeries.01.vv
108 reference(s)
123-expv_vire.11
107 reference(s)		 124-HommageBenoitMandelbrot.21
106 reference(s)
125-ExpV_VirE.Fra
106 reference(s)		 126-Commentaires_VarieteQuadriDimensionnelleCalabiYau.01
106 reference(s)
127-Commentaires_DefinitionQuaternions.01
106 reference(s)		 128-PerteDeLAssociativite.01.MUL3
105 reference(s)

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Copyright (c) Jean-François Colonna, 2014-2018.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2014-2018.