Monthly Best Of on 07/28/2014




An interpolation between a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')and a tridimensional Verhulst dynamics -tridimensional cross-section-

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 07/28/2014 and last updated on 06/30/2018 14:06:35 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures:



The tridimensional Ising Model with 2-state spins, temperature=0.2, random initial conditions and an increasing number of iterations -from 100 to 4000-
1-1309 reference(s)
A tridimensional fractal manifold defined by means of three tridimensional fields
2-535 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
3-346 reference(s)
The 126.646 first digits -base 6- of 'pi' displayed as an 'absolute' tridimensional random walk
4-323 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
5-252 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
6-193 reference(s)
The random walk of photons escaping the Sun
7-158 reference(s)
Happy new year 2000
8-139 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
9-139 reference(s)
Tridimensional Hilbert Curve -iteration 3-
10-135 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
11-114 reference(s)
Reconstruction of a 3D structure -a cubic lattice-
12-111 reference(s)
Autostereogram with an hidden volcano
13-109 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
14-107 reference(s)
Bidimensional Hilbert Curve -iteration 4-
15-104 reference(s)
Hypercube
16-99 reference(s)
Autostereogram with an hidden volcano
17-96 reference(s)
Artistic view of the prime numbers
18-96 reference(s)
Sixteen interlaced torus
19-91 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
20-90 reference(s)
Zoom in on the von Koch curve
21-79 reference(s)
Autostereogram with an hidden volcano
22-77 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
23-73 reference(s)
The random walk of photons escaping the Sun
24-71 reference(s)
Quantum vacuum fluctuations
25-63 reference(s)
The generalized Ulam spiral
26-63 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
27-60 reference(s)
A dynamics of four interlaced torus defined by means of three sets of bidimensional fields
28-58 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
29-57 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)
30-56 reference(s)
Bidimensional display of the dynamics of the linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
31-55 reference(s)
The 126.646 first digits -base 6- of 'phi' -the golden ratio- displayed as an 'absolute' tridimensional random walk
32-52 reference(s)
The Lorenz attractor
33-50 reference(s)
True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
34-46 reference(s)
The Jeener's triple Klein bottle
35-46 reference(s)
An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
36-46 reference(s)
From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
37-43 reference(s)
Monument Valley at sunrise
38-39 reference(s)
Quark and gluon structure of a nucleon
39-39 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
40-39 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
41-36 reference(s)
Autostereogram with an hidden volcano
42-35 reference(s)
Tridimensional display of the Riemann Zeta function inside (+0.1,+0.9)x(0,+50)
43-34 reference(s)
Autostereogram with an hidden ring and ghost bows
44-34 reference(s)
No Title 0208
45-34 reference(s)
A set of 4x3 stereograms of a few Babel Towers
46-34 reference(s)
True colors autostereogram of a fractal landscape
47-34 reference(s)
A Peano 'fractal plane' defined by means of three bidimensional fields
48-33 reference(s)
An Archimedes spiral displaying the 100.000 first digits -base 10- of 'pi'
49-33 reference(s)
Monument Valley at sunrise
50-33 reference(s)
Rotation about the Y (vertical)axis of the 1-foil torus knot on its torus and its asociated Möbius strip, that can also be viewed as a set of 4x3 stereograms
51-33 reference(s)
Electron-positron scattering
52-32 reference(s)
Tridimensional display of the Riemann Zeta function inside (-10.0,+20.0)x(-15.0,+15.0) (bird's-eye view)
53-31 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
54-31 reference(s)
Autostereogram with an hidden volcano
55-30 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
56-30 reference(s)
2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
57-30 reference(s)
Autostereogram -using a periodical paradoxal structure as a desguise texture- with an hidden gaussian mountain
58-30 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
59-30 reference(s)
Artistic view of the Big Bang
60-29 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
61-29 reference(s)
Fractal synthesis of mountains with vegetation and stormy clouds
62-29 reference(s)
From Pluto to the Sun (non linear scales)
63-29 reference(s)
Tridimensional display of the Riemann Zeta function inside (-50.0,+50.0)x(-50.0,+50.0) (bird's-eye view)
64-28 reference(s)
Fractal structure of a nucleon
65-28 reference(s)
The Scream -a Tribute to Edvard Munch-
66-28 reference(s)
Monument Valley à la David Hockney
67-28 reference(s)
A set of 4x3 stereograms of a fractal hypercube
68-28 reference(s)
Isle of the Dead -a Tribute to Arnold Böcklin-
69-28 reference(s)
A tridimensionally distorded pseudo-periodical Penrose tiling of the Golden Decagon
70-27 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
71-27 reference(s)
Rotation about the Y (vertical)axis of the 5-foil torus knot on its torus, that can also be viewed as a set of 4x3 stereograms
72-27 reference(s)
Rotation about the Y (vertical)axis of the 3-foil torus knot on its torus, that can also be viewed as a set of 4x3 stereograms
73-27 reference(s)
Autostereogram with an hidden volcano and 64 self-portraits
74-27 reference(s)
Along the border of the Mandelbrot set
75-26 reference(s)
Artistic view of Monument Valley at sunrise with the Great Bear
76-26 reference(s)
Paradoxal Monument Valley at sunset
77-26 reference(s)
Tridimensional visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-
78-26 reference(s)
A set of 4x3 stereograms of a tridimensional interpolation between a fractal structure and a cubic mesh
79-26 reference(s)
From the infinitely small to the infinitely big
80-26 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
81-26 reference(s)
No Title 0207
82-26 reference(s)
Autostereogram of Monument Valley
83-25 reference(s)
Quark and gluon structure of a nucleon
84-25 reference(s)
A fractal Möbius strip
85-25 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
86-25 reference(s)
Monument Valley at sunrise
87-24 reference(s)
Foggy Babel Tower -a tribute to Brueghel the Elder-
88-24 reference(s)
display of the Lyapunov exponent computed for different iteration numbers of a Julia set
89-24 reference(s)
Tridimensional fractal structure -the space-time foam?-
90-24 reference(s)
A pseudo-periodical Penrose tiling of the plane
91-23 reference(s)
An Archimedes spiral displaying 1000 numbers
92-23 reference(s)
Monument Valley à la David Hockney
93-23 reference(s)
The erosion of the Babel Tower
94-23 reference(s)
The Lorenz attractor
95-23 reference(s)
Sixteen interlaced fractal torus
96-23 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
97-23 reference(s)
Where is the Universe?
98-22 reference(s)
The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
99-22 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
100-22 reference(s)
A fractal hypercube
101-22 reference(s)
Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability
102-22 reference(s)
Quantum vacuum fluctuations
103-21 reference(s)
The non linear transformation of the coordinates in the Solar System
104-21 reference(s)
The Solar System with a dark blue virtual planet -virtual planet point of view-
105-21 reference(s)
A quaternionic Julia set -tridimensional cross-section-
106-21 reference(s)
Rotation about the Y (vertical)axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms
107-21 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
108-20 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
109-20 reference(s)
Close-up on a foggy 'MandelBox' -tridimensional cross-section-
110-20 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
111-20 reference(s)
The wall-paper process
112-20 reference(s)
A shell (Jeener surface 1)in motion
113-20 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
114-20 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
115-20 reference(s)
Recursive intertwining
116-19 reference(s)
Quark and gluon dynamics of the nucleon
117-19 reference(s)
Mountains and fog
118-19 reference(s)
Botticelli anomaly on the Moon
119-19 reference(s)
Alien spacecrafts on the Moon
120-19 reference(s)
Two identical grey rectangles in front of a grey scale
121-19 reference(s)
Rotation about the Y (vertical)axis of the 7-foil torus knot on its torus, that can also be viewed as a set of 4x3 stereograms
122-19 reference(s)
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0,1,0,0,0,0,0,0) -tridimensional cross-section-
123-19 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
124-19 reference(s)
The Goldbach conjecture -the Goldbach comet- for the even numbers from 6 to 411678
125-19 reference(s)
Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold
126-19 reference(s)
Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold
127-19 reference(s)
The Universe at the heart of a Calabi-Yau manifold
128-18 reference(s)




2-The 128 most referenced Pages:



1-demo_14
417 reference(s)
2-An2000.01.Fra
378 reference(s)
3-help.
341 reference(s)
4-Galerie_Tributes.FV
325 reference(s)
5-FloatingPointNumbers.01.Fra
269 reference(s)
6-AVirtualSpaceTimeTravelMachine.Ang
262 reference(s)
7-Stereogrammes_AutoStereogrammes.01
251 reference(s)
8-Fractal.01
243 reference(s)
9-Galerie_NewPictures.FV
234 reference(s)
10-AVirtualSpaceTimeTravelMachine.Fra
231 reference(s)
11-Galerie_NumberTheory.FV
227 reference(s)
12-RealNumbers.01.Fra
223 reference(s)
13-mail.01.vv
217 reference(s)
14-Galerie_DeterministicFractalGeometry.FV
214 reference(s)
15-Galerie_GeneralitiesVisualization.FV
210 reference(s)
16-UlamSpiral.01.Fra
202 reference(s)
17-MorePages.
200 reference(s)
18-FaireDeLaRecherche.01.vv
197 reference(s)
19-copyright.01.
194 reference(s)
20-MathematiquesPhysiqueFractales.02
192 reference(s)
21-AQuoiServentLesMathematiques.01
191 reference(s)
22-GenieLogiciel_VisualisationScientifique.01.vv
189 reference(s)
23-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
187 reference(s)
24-Autostereograms.01.
187 reference(s)
25-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
185 reference(s)
26-AProposSite.01.Fra
183 reference(s)
27-Galerie_CelestialMechanics.FV
181 reference(s)
28-DuModeleALImage.02.Fra
176 reference(s)
29-Galerie_ArtAndScience.FV
174 reference(s)
30-catalogue.11
170 reference(s)
31-Galerie_BestOf.FV
170 reference(s)
32-ExpV_VirE.11
170 reference(s)
33-SurfaceProjector.01.Fra
169 reference(s)
34-GoldenTriangle.01.Fra
169 reference(s)
35-Fractal.11
169 reference(s)
36-Galerie_Astrophysics.FV
168 reference(s)
37-Galerie_TextureSynthesis.FV
167 reference(s)
38-OrdinateurMathematiquesArt.01.Fra
166 reference(s)
39-NDimensionalDeterministicFractalSets.01.Ang
166 reference(s)
40-ImagesDuVirtuel.01.Fra.FV
164 reference(s)
41-IllusionConnaissance.02
162 reference(s)
42-Galerie_ParticleSystems.FV
162 reference(s)
43-DieuScience.01.Fra
162 reference(s)
44-AnimFractal.01.
162 reference(s)
45-MonodimensionalCellularAutomata.01.Fra
161 reference(s)
46-LOG_xiMc.11
161 reference(s)
47-ImpossibleStructures.01.Ang
161 reference(s)
48-SurfaceProjector.01.Ang
160 reference(s)
49-Galerie_QuantumMechanics.FV
160 reference(s)
50-infinity.02.vv
159 reference(s)
51-NatureDesMathematiques.01.vv.Fra
158 reference(s)
52-Galerie_ArtisticCreation.FV
158 reference(s)
53-EntrelacsIntertwinings.01.Ang
158 reference(s)
54-FloatingPointNumbers.01.Ang
157 reference(s)
55-NDimensionalDeterministicFractalSets.01.Fra
156 reference(s)
56-EntrelacsIntertwinings.01.Fra
156 reference(s)
57-UlamSpiral.01.Ang
155 reference(s)
58-ImpossibleStructures.01.Fra
154 reference(s)
59-Galerie_DeterministicChaos.FV
154 reference(s)
60-OrdinateursEtCalculs.01.Fra
153 reference(s)
61-MonodimensionalCellularAutomata.01.Ang
153 reference(s)
62-LesApprentisDieux.01
153 reference(s)
63-EnsembleDesGaleriesFractales.DIAPO.0001
151 reference(s)
64-Kepler.02.
150 reference(s)
65-subject.01.
149 reference(s)
66-ExpV_VirE.Ang
149 reference(s)
67-demo.14
148 reference(s)
68-realnumbers
147 reference(s)
69-an2000
147 reference(s)
70-RemarquesCerveau.01
147 reference(s)
71-Fractal.03
147 reference(s)
72-EnsembleDesGaleries.DIAPO.0001
147 reference(s)
73-nombresreels
146 reference(s)
74-genielogiciel
146 reference(s)
75-fractal.01
146 reference(s)
76-demo14
146 reference(s)
77-demo
146 reference(s)
78-OrdinateursEtCalculs.01.Ang
146 reference(s)
79-logiciel
145 reference(s)
80-create.03.
145 reference(s)
81-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
145 reference(s)
82-MathematiquesEtCinematographe.01.vv
145 reference(s)
83-infinity.01.vv
143 reference(s)
84-Informations_AboutPicturesAnimationsAndFiles.01.Ang
143 reference(s)
85-GenieLogiciel.01.Fra
143 reference(s)
86-AvantPropos.01.Ang
143 reference(s)
87-MathematiquesPhysiqueFractales.22
142 reference(s)
88-MathematiquesModeleOutilArtiste.02.Ang
142 reference(s)
89-GoldenTriangle.01.Ang
142 reference(s)
90-Galerie_SignalProcessing.FV
142 reference(s)
91-aquoiserventlesmathematiques.01
141 reference(s)
92-ManyChaos.01.Ang
140 reference(s)
93-VirtualChaos.01.Ang
139 reference(s)
94-NombresEtLumiere.01.vv.Fra
139 reference(s)
95-MathematiquesEtRepresentations.01.vv.Ang
139 reference(s)
96-Spheres.01
138 reference(s)
97-AvantPropos.01.Fra
138 reference(s)
98-QuelquesQuestionsSurLaRecherche.01.Fra
137 reference(s)
99-Galerie_FluidMechanics.FV
135 reference(s)
100-PerteDeLAssociativite.01
133 reference(s)
101-Galerie_SensitivityToRoundingOffErrors.FV
133 reference(s)
102-ManyChaos.01.Fra
132 reference(s)
103-VisitesGaleriesEnfouies.01.Ang
131 reference(s)
104-VisitesGaleriesEnfouies.01.Fra
129 reference(s)
105-VirtualChaos.01.Fra
127 reference(s)
106-ExpV_VirE.21
127 reference(s)
107-Fractal.02
126 reference(s)
108-present.01.
125 reference(s)
109-PatrimoineHumanite.02.Fra
123 reference(s)
110-fairedelarecherche.01.vv
121 reference(s)
111-Vcatalogue.11
120 reference(s)
112-Informations_AboutPicturesAnimationsAndFiles.01.Fra
119 reference(s)
113-ImagesDuVirtuel.01.Fra
116 reference(s)
114-Informations_GoodNewsAndBadNews.01.Fra
114 reference(s)
115-ArtEtMathematiques.01
113 reference(s)
116-ExpV_VirE.01.Fra
112 reference(s)
117-demo_14.FV
111 reference(s)
118-ArtScience.11.Fra
108 reference(s)
119-An2000.02.Fra
108 reference(s)
120-ExpV_VirE.Fra
107 reference(s)
121-ExpV_VirE.01.Ang
107 reference(s)
122-MathematiquesPhysiqueFractales.01
105 reference(s)
123-EnsembleDesGaleriesFractales.DIAPO.0003
105 reference(s)
124-Informations_GoodNewsAndBadNews.01.Ang
104 reference(s)
125-Galerie_ImagesDesMathematiques.FV
104 reference(s)
126-Galerie_FromTheInfinitelySmallToTheInfinitelyBig.FV
104 reference(s)
127-Commentaires_NKleinBottle.01
103 reference(s)
128-EnsembleDesGaleriesFractales.DIAPO.0002
102 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.