Monthly Best Of on 02/28/2012




A pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-

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

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[The Y2K Bug [Le bug de l'an 2000]]
[Real Numbers don't exist in Computers and Floating Point Computations aren't safe. [Les Nombres Réels n'existent dans les Ordinateurs et les Calculs Flottants ne sont pas sûrs.]]
[Please, visit A Virtual Machine for Exploring Space-Time and Beyond, the place where you can find thousands of pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 02/28/2012 and last updated on 11/14/2023 17:47:59 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The random walk of photons escaping the Sun
1-357 reference(s)		 The Lorenz attractor
2-239 reference(s)		 Autostereogram with an hidden volcano and 64 self-portraits
3-99 reference(s)		 2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
4-90 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
5-88 reference(s)		 Zoom in on the von Koch curve
6-86 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
7-86 reference(s)		 From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
8-81 reference(s)
Artistic view of the prime numbers
9-78 reference(s)		 Mystery cliffs at sunrise
10-74 reference(s)		 Mystery mountain at sunrise
11-73 reference(s)		 Mountains at sunrise
12-71 reference(s)
The foggy Babel Tower -a Tribute to Brueghel the Elder-
13-68 reference(s)		 Along the border of the Mandelbrot set
14-65 reference(s)		 Quark and gluon structure of a nucleon
15-55 reference(s)		 The random walk of photons escaping the Sun
16-54 reference(s)
From the infinitely small to the infinitely big
17-54 reference(s)		 Rotation about the X axis of the Lorenz attractor
18-51 reference(s)		 From the infinitely small to the infinitely big
19-49 reference(s)		 Three pendulums -the Red one, the Green one and the Blue one- and three magnets -white-
20-46 reference(s)
Forward tridimensional integration of the wavelet filtering of a bidimensional fractal field with cross-section
21-45 reference(s)		 Welcome aboard a Virtual Space-Time Travel Machine
22-45 reference(s)		 Quark and gluon dynamics of the nucleon
23-40 reference(s)		 Quark and gluon structure of a nucleon
24-38 reference(s)
From Pluto to the Sun (non linear scales)
25-36 reference(s)		 Autostereogram with an hidden volcano
26-33 reference(s)		 Animation of a sunrise on mountains
27-33 reference(s)		 Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
28-31 reference(s)
Intertwining
29-31 reference(s)		 The generalized Ulam spiral displaying 100 numbers
30-31 reference(s)		 Tridimensional display of the Riemann Zeta function inside [+0.1,+0.9]x[0,+50]
31-30 reference(s)		 The random walk of photons escaping the Sun
32-30 reference(s)
Along the border of the Mandelbrot set
33-29 reference(s)		 Intertwining
34-28 reference(s)		 Dynamics of the even distribution of 24 points on a sphere by means of simulated annealing
35-28 reference(s)		 A variable Archimedes spiral displaying 1000 numbers
36-28 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)
37-28 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
38-28 reference(s)		 The Solar System with a dark blue virtual planet -virtual planet point of view-
39-26 reference(s)		 Jean-François COLONNA (on 11/17/1994)with its fractal mountains
40-24 reference(s)
The Bonan-Jeener's 12-bottle before a paradoxal field
41-24 reference(s)		 Fractal synthesis of mountains with vegetation and stormy clouds
42-23 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
43-23 reference(s)		 The Syracuse conjecture for U(0)={1,2,3,4,...,262144}
44-22 reference(s)
The generalized Ulam spiral displaying 1024 numbers
45-22 reference(s)		 A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
46-22 reference(s)		 Tridimensional display of the dynamics of the bidimensional John Conway's life game
47-22 reference(s)		 Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
48-22 reference(s)
A 'fractal plane' with overhangings defined by means of three bidimensional fields
49-21 reference(s)		 Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
50-21 reference(s)		 The Solar System with a dark blue virtual planet -heliocentric point of view-
51-21 reference(s)		 The Möbius strip
52-21 reference(s)
Quantum vacuum fluctuations
53-20 reference(s)		 Autostereogram with an hidden ring and ghost bows
54-19 reference(s)		 Cloudy Monument Valley
55-19 reference(s)		 Untitled 0137 -'Jour de Lenteur', a Tribute to Yves Tanguy-
56-19 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-
57-19 reference(s)		 The Bonan-Jeener's 12-bottle before a paradoxal field
58-19 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
59-18 reference(s)		 Artistic view of the Big Bang
60-18 reference(s)
Recursive intertwining
61-18 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-
62-18 reference(s)		 Zoom in on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
63-18 reference(s)		 Tridimensional representation of a hexadimensional Calabi-Yau manifold
64-18 reference(s)
The Jeener-Klein triple bottle
65-18 reference(s)		 Autostereogram with an hidden volcano
66-17 reference(s)		 True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
67-17 reference(s)		 Tridimensional domino effect
68-17 reference(s)
Isotropic random walk of 64 particles on a bidimensional square lattice
69-17 reference(s)		 A tridimensional fractal manifold defined by means of three tridimensional fields
70-17 reference(s)		 Untitled 0142
71-17 reference(s)		 The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
72-17 reference(s)
Electron-positron scattering
73-17 reference(s)		 Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability
74-17 reference(s)		 Autostereogram with an hidden volcano
75-16 reference(s)		 Autostereogram with an hidden volcano
76-16 reference(s)
The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
77-16 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
78-16 reference(s)		 LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
79-16 reference(s)		 64 elementary bidimensional binary cellular automata with 1 white starting central point
80-16 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
81-15 reference(s)		 2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')-tridimensional cross-section-
82-15 reference(s)		 Botticelli anomaly on the Moon
83-15 reference(s)		 Autostereogram of Monument Valley
84-15 reference(s)
True colors autostereogram of a fractal landscape
85-15 reference(s)		 Mountains at sunrise
86-15 reference(s)		 Bidimensional zoom in on the Verhulst dynamics
87-15 reference(s)		 Hypercube
88-15 reference(s)
display of Ph(Zeta)inside [-50.0,+50.0]x[-50.0,+50.0]
89-14 reference(s)		 Generation of the 63x63 first Conway's surreal complex numbers
90-14 reference(s)		 Alien
91-14 reference(s)		 The pseudo-sphere
92-14 reference(s)
Paradoxal Monument Valley at sunset
93-14 reference(s)		 Foggy Monument Valley
94-14 reference(s)		 Mountains and light cloud dynamics -this sequence being periodical-
95-14 reference(s)		 Bidimensional zoom in on the Mandelbrot set with display of the arguments
96-14 reference(s)
Tridimensional visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
97-14 reference(s)		 A quaternionic Julia set -tridimensional cross-section-
98-14 reference(s)		 The Birth of the Universe
99-14 reference(s)		 The normal field of a shell (Jeener surface 1)
100-14 reference(s)
A shell (Jeener surface 1)in motion
101-14 reference(s)		 The construction process of the von Koch curve
102-13 reference(s)		 Untitled 0141
103-13 reference(s)		 Intertwining
104-13 reference(s)
Bidimensional rectangular billiard with 4 random particles, with collisions and display of their gravity center -white particle-
105-13 reference(s)		 Animation of a natural form
106-13 reference(s)		 Reconstruction of a 3D structure -a cubic lattice-
107-13 reference(s)		 Cloudy Monument Valley
108-13 reference(s)
Mountains at sunrise
109-13 reference(s)		 Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')with a 'complex' transformation in the pseudo-octonionic space -tridimensional cross-section-
110-13 reference(s)		 Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')with a 'complex' module transformation in the pseudo-octonionic space -tridimensional cross-section-
111-13 reference(s)		 Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')with a 1/O conformal transformation in the pseudo-octonionic space -tridimensional cross-section-
112-13 reference(s)
Bidimensional zoom in on the Mandelbrot set with display of the arguments
113-13 reference(s)		 Tridimensional visualization of the Mandelbrot set with mapping of the arguments
114-13 reference(s)		 Intertwining based on the geometry of the sphere
115-13 reference(s)		 The snake swallows its own tail
116-13 reference(s)
Rotation about the Y (vertical)axis of a tridimensional representation of quadridimensional Calabi-Yau manifolds that can also be viewed as a set of 4x3 stereograms -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
117-13 reference(s)		 A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
118-12 reference(s)		 Autostereogram of 8 color-multiplexed quaternionic Julia sets -tridimensional cross-sections-
119-12 reference(s)		 Tridimensional billiard with 12 -initially- still particles submitted to an attractive central field of gravity
120-12 reference(s)
The trajectories of bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity
121-12 reference(s)		 A 'spiraling plane' defined by means of three bidimensional fields
122-12 reference(s)		 From Pluto to the Sun -extrapolation 2- (non linear scales)
123-12 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
124-12 reference(s)
Different modes of representation of a tridimensional cross-section of a Quaternionic Julia set
125-12 reference(s)		 Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
126-12 reference(s)		 Untitled 0139
127-12 reference(s)		 Tridimensional display of the dynamics of the bidimensional John Conway's life game
128-12 reference(s)




2-The 128 most referenced Pages (*):

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



1-demo_14
803 reference(s)		 2-An2000.01.Fra
414 reference(s)
3-AVirtualSpaceTimeTravelMachine.Ang
353 reference(s)		 4-help.
316 reference(s)
5-Fractal.01
310 reference(s)		 6-MonodimensionalCellularAutomata.01.Fra
277 reference(s)
7-Galerie_GeneralitiesVisualization.FV
261 reference(s)		 8-ImagesDuVirtuel.01.Fra.FV
239 reference(s)
9-NDimensionalDeterministicFractalSets.01.Ang
237 reference(s)		 10-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
237 reference(s)
11-AQuoiServentLesMathematiques.01
225 reference(s)		 12-AVirtualSpaceTimeTravelMachine.Fra
221 reference(s)
13-FaireDeLaRecherche.01.vv
216 reference(s)		 14-Galerie_ParticleSystems.FV
211 reference(s)
15-Stereogrammes_AutoStereogrammes.01
209 reference(s)		 16-FloatingPointNumbers.01.Fra
206 reference(s)
17-Galerie_NewPictures.FV
205 reference(s)		 18-Galerie_ArtisticCreation.FV
201 reference(s)
19-FloatingPointNumbers.01.Ang
200 reference(s)		 20-fractal.01
197 reference(s)
21-Galerie_NumberTheory.FV
195 reference(s)		 22-ExpV_VirE.11
193 reference(s)
23-fairedelarecherche.01.vv
189 reference(s)		 24-Galerie_DeterministicFractalGeometry.FV
189 reference(s)
25-NDimensionalDeterministicFractalSets.01.Fra
187 reference(s)		 26-SurfaceProjector.01.Fra
186 reference(s)
27-AProposSite.01.Fra
185 reference(s)		 28-GenieLogiciel_VisualisationScientifique.01.vv
183 reference(s)
29-aquoiserventlesmathematiques.01
180 reference(s)		 30-SurfaceProjector.01.Ang
179 reference(s)
31-AnimFractal.01.
179 reference(s)		 32-Galerie_ArtAndScience.FV
178 reference(s)
33-MathematiquesPhysiqueFractales.02
177 reference(s)		 34-Fractal.11
177 reference(s)
35-copyright.01.
170 reference(s)		 36-Galerie_CelestialMechanics.FV
167 reference(s)
37-RealNumbers.01.Fra
161 reference(s)		 38-Autostereograms.01.
160 reference(s)
39-MonodimensionalCellularAutomata.01.Ang
158 reference(s)		 40-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
157 reference(s)
41-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
157 reference(s)		 42-IllusionConnaissance.02
156 reference(s)
43-DieuScience.01.Fra
153 reference(s)		 44-Galerie_QuantumMechanics.FV
152 reference(s)
45-NatureDesMathematiques.01.vv.Fra
151 reference(s)		 46-catalogue.11
150 reference(s)
47-stereogrammes_autostereogrammes.01
149 reference(s)		 48-Galerie_DeterministicChaos.FV
149 reference(s)
49-mail.01.vv
147 reference(s)		 50-present.01.
146 reference(s)
51-OrdinateurMathematiquesArt.01.Fra
144 reference(s)		 52-GenieLogiciel.01.Fra
144 reference(s)
53-Kepler.02.
143 reference(s)		 54-Informations_AboutPicturesAnimationsAndFiles.01.Ang
143 reference(s)
55-Galerie_TextureSynthesis.FV
143 reference(s)		 56-ImpossibleStructures.01.Fra
142 reference(s)
57-EntrelacsIntertwinings.01.Fra
142 reference(s)		 58-infinity.02.vv
141 reference(s)
59-infinity.01.vv
141 reference(s)		 60-EntrelacsIntertwinings.01.Ang
141 reference(s)
61-Galerie_Astrophysics.FV
138 reference(s)		 62-NombresEtLumiere.01.vv.Fra
137 reference(s)
63-ExpV_VirE.Fra
137 reference(s)		 64-ExpV_VirE.Ang
137 reference(s)
65-Vcatalogue.11
136 reference(s)		 66-VirtualChaos.01.Fra
135 reference(s)
67-PerteDeLAssociativite.01
135 reference(s)		 68-OrdinateursEtCalculs.01.Fra
135 reference(s)
69-Galerie_BestOf.FV
134 reference(s)		 70-MathematiquesModeleOutilArtiste.02.Ang
133 reference(s)
71-Galerie_FluidMechanics.FV
133 reference(s)		 72-RemarquesCerveau.01
132 reference(s)
73-PatrimoineHumanite.02.Fra
132 reference(s)		 74-ManyChaos.01.Ang
132 reference(s)
75-ImpossibleStructures.01.Ang
131 reference(s)		 76-Galerie_SignalProcessing.FV
129 reference(s)
77-create.03.
128 reference(s)		 78-VisitesGaleriesEnfouies.01.Fra
128 reference(s)
79-MathematiquesEtRepresentations.01.vv.Ang
127 reference(s)		 80-Fractal.02
127 reference(s)
81-ManyChaos.01.Fra
126 reference(s)		 82-HommageBenoitMandelbrot.21
126 reference(s)
83-AvantPropos.01.Fra
126 reference(s)		 84-monodimensionalcellularautomata.01.fra
125 reference(s)
85-MathematiquesEtCinematographe.01.vv
125 reference(s)		 86-ArtScience.11.Fra
125 reference(s)
87-subject.01.
124 reference(s)		 88-Galerie_NewPictures.DIAPO.0001
124 reference(s)
89-ExpV_VirE.01.Fra
124 reference(s)		 90-Commentaires_DefinitionComplexes.01
124 reference(s)
91-ImagesDuVirtuel.01.Fra
123 reference(s)		 92-ExpV_VirE.21
123 reference(s)
93-EnsembleDesGaleriesFractales.DIAPO.0001
123 reference(s)		 94-Commentaires_DefinitionTransformeeDeFourier.01
123 reference(s)
95-PerteDeLAssociativite.01.MUL3
122 reference(s)		 96-LOG_xiMc.11
122 reference(s)
97-Commentaires_DefinitionOctonions.01
122 reference(s)		 98-AvantPropos.01.Ang
122 reference(s)
99-an2000.01.fra
121 reference(s)		 100-VirtualChaos.01.Ang
121 reference(s)
101-Spheres.01
121 reference(s)		 102-QuelquesQuestionsSurLaRecherche.01.Fra
121 reference(s)
103-EnsembleDesGaleries.DIAPO.0001
121 reference(s)		 104-MathematiquesPhysiqueFractales.01
120 reference(s)
105-Informations_GoodNewsAndBadNews.01.Fra
120 reference(s)		 106-AVirtualSpaceTimeTravelMachine.Ang.FV
119 reference(s)
107-real.01.vv.
117 reference(s)		 108-demo_14.FV
117 reference(s)
109-OrdinateursEtCalculs.01.Ang
117 reference(s)		 110-MonumentValley.01.Ang
117 reference(s)
111-Galeries.01.vv
117 reference(s)		 112-Galerie_TextureSynthesis.DIAPO.0002
117 reference(s)
113-Commentaires_NKleinBottle.01
117 reference(s)		 114-VisitesGaleriesEnfouies.01.Ang
116 reference(s)
115-VisSci_SciVis.02
116 reference(s)		 116-PerteDeLAssociativite.01.ADD3
116 reference(s)
117-Galerie_NewPictures.DIAPO.0002
116 reference(s)		 118-Commentaires_VarieteQuadriDimensionnelleCalabiYau.01
116 reference(s)
119-hydrogene.61.K.
115 reference(s)		 120-PresidentRepublique.01.Fra
115 reference(s)
121-MathematiquesEtRepresentations.01.vv.Fra
115 reference(s)		 122-MOSA.JFC.F1.F2.20031207
115 reference(s)
123-Galerie_SensitivityToRoundingOffErrors.FV
115 reference(s)		 124-Galerie_DeterministicFractalGeometry.DIAPO.0002
115 reference(s)
125-Commentaires_ProblemeDesNCorps.01
115 reference(s)		 126-An2000.03.Fra
115 reference(s)
127-PourLaScience.01.Fra
114 reference(s)		 128-Galerie_SalonDAutomne.FV
114 reference(s)

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




Copyright © Jean-François COLONNA, 2012-2023.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2012-2023.