Monthly Best Of on 10/28/2007




A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.451358,0.296439,0,0) -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 10/28/2007 and last updated on 06/30/2018 14:03:35 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures:



Black dots (inside random white squares)on a square lattice
1-963 reference(s)
Bidimensional abstract texture with random anthropomorphic patterns
2-884 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
3-838 reference(s)
LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
4-487 reference(s)
Hypercube
5-466 reference(s)
Along the border of the Mandelbrot set
6-449 reference(s)
The random walk of photons escaping the Sun
7-441 reference(s)
The random walk of photons escaping the Sun
8-381 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
9-375 reference(s)
Foggy Babel Tower -a tribute to Brueghel the Elder-
10-360 reference(s)
The bottom of the sea
11-358 reference(s)
Artistic view of the prime numbers
12-321 reference(s)
Welcome aboard a Virtual Space-Time Travel Machine
13-286 reference(s)
True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
14-255 reference(s)
Quantum vacuum fluctuations
15-240 reference(s)
Paradoxal Monument Valley at sunset
16-239 reference(s)
Animation of a sunrise on mountains
17-237 reference(s)
Quark and gluon structure of a nucleon
18-236 reference(s)
Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
19-232 reference(s)
The Lorenz attractor
20-227 reference(s)
The Birth of the Universe
21-222 reference(s)
Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
22-217 reference(s)
Bidimensional artistic view of the Verhulst dynamics
23-206 reference(s)
Tridimensional display of the Riemann Zeta function inside (-10.0,+60.0)x(-35.0,+35.0) (bird's-eye view)
24-204 reference(s)
Reconstruction of a 3D structure -a cubic lattice-
25-203 reference(s)
Synthesis of tridimensional symmetrical geometrical textures
26-193 reference(s)
2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
27-189 reference(s)
Fractal synthesis of mountains with vegetation and stormy clouds
28-185 reference(s)
The irreversibility of the numerical bidimensional billiard
29-178 reference(s)
From Pluto to the Sun -extrapolation 2- (non linear scales)
30-173 reference(s)
Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
31-171 reference(s)
Tridimensional display of 36 eigenstates of the Hydrogen atom (bidimensional computation)
32-171 reference(s)
From the infinitely small to the infinitely big
33-167 reference(s)
Quark and gluon structure of a nucleon
34-166 reference(s)
The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
35-165 reference(s)
Animation of a natural form
36-164 reference(s)
Isotropic random walk of 64 particles on a tridimensional square lattice
37-157 reference(s)
Jean-François Colonna
38-157 reference(s)
Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold
39-155 reference(s)
Artistic view of the Big Bang
40-154 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
41-149 reference(s)
Autostereogram with an hidden volcano
42-148 reference(s)
Two multiplexed autostereograms by means of a pi/2 rotation
43-148 reference(s)
The Scream -a Tribute to Edvard Munch-
44-147 reference(s)
Animation of a natural form
45-146 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
46-146 reference(s)
From Pluto to the Sun (non linear scales)
47-144 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
48-144 reference(s)
World Mathematical Year 2000
49-143 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
50-140 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)
51-139 reference(s)
Quark and gluon dynamics of the nucleon
52-137 reference(s)
Rotation about the X axis of the Lorenz attractor
53-136 reference(s)
A Tribute to Archimedes
54-134 reference(s)
N-body problem integration (N=3)with one yellow star and two planets (the red one being very heavy and the blue one being light)
55-133 reference(s)
Rotation about the X axis of the Lorenz attractor (5000 iterations), computed simultaneously on two different computers
56-133 reference(s)
Computation of the Lorenz attractor on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors)
57-133 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
58-132 reference(s)
The Lorenz attractor -sensitivity to initial conditions (displayed as the central point of each frame)-
59-128 reference(s)
24 evenly distributed points on a sphere by means of simulated annealing
60-126 reference(s)
Rotation about the X axis of the Lorenz attractor (1000 iterations), computed simultaneously on two different computers
61-124 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
62-124 reference(s)
The random walk of photons escaping the Sun
63-121 reference(s)
16 earth-like planets initially on the same keplerian trajectory
64-120 reference(s)
2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-
65-120 reference(s)
Cauliflowers, seaweeds, shells,... with fog
66-116 reference(s)
The generalized Ulam spiral displaying 100 numbers
67-116 reference(s)
The wall-paper process
68-115 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
69-115 reference(s)
N-body problem integration (N=2)displaying a perfect Keplerian orbit
70-112 reference(s)
Earthquake
71-111 reference(s)
Rotation about the Y (vertical)axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms
72-111 reference(s)
Autostereogram with an hidden volcano
73-109 reference(s)
A tridimensional fractal manifold defined by means of three tridimensional fields
74-109 reference(s)
Rotation about the X axis of the Lorenz attractor
75-109 reference(s)
Tridimensional fractal structure
76-109 reference(s)
Artistic view of a quadridimensional Calabi-Yau manifold
77-108 reference(s)
The first true colors autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
78-107 reference(s)
Bidimensional zoom in on the Mandelbrot set with display of the arguments
79-107 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
80-107 reference(s)
The Möbius strip
81-106 reference(s)
The random walk of photons escaping the Sun
82-105 reference(s)
The Eratosthene sieve displaying 100x100 numbers
83-105 reference(s)
Animation of bidimensional textures by means of the self-transformation of a fractal process
84-105 reference(s)
N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed with 2 slightly different sets of initial conditions (sensitivity to initial conditions)
85-105 reference(s)
Bidimensional zoom in on the Verhulst dynamics
86-105 reference(s)
Bidimensional display of the dynamics of the linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
87-105 reference(s)
16 complex Julia sets along the border of the Mandelbrot set with display of the iteration numbers
88-103 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
89-103 reference(s)
Self-transformation of a simple dynamical geometric texture
90-103 reference(s)
A pay slip
91-102 reference(s)
Animation of bidimensional textures by means of the self-transformation of a fractal process
92-102 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
93-102 reference(s)
Spreading of an epidemic -color changes by means of contacts-
94-101 reference(s)
2 identical grey squares moving over a grey scale
95-101 reference(s)
The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
96-101 reference(s)
The iterative process used to generate bidimensional fractal fields (16 iterations)
97-101 reference(s)
Rotation about the Y (vertical)axis of the CMAP logo that can also be viewed as a set of 4x3 stereograms
98-101 reference(s)
Alien
99-100 reference(s)
Animation of bidimensional symmetrical geometrical textures
100-100 reference(s)
A variable Archimedes spiral displaying 1000 numbers
101-100 reference(s)
Botticelli anomaly on the Moon
102-100 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
103-100 reference(s)
2.pi rotation about the Y axis of a quaternionic Julia set with motion blur -tridimensional cross-section-
104-100 reference(s)
Along the border of the Mandelbrot set
105-99 reference(s)
Computation of the roots of Q^3=1 using Newton's method with translation along the third axis of the quaternionic space
106-99 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
107-99 reference(s)
Bidimensional zoom in on the Z=Gamma(Z)iteration with display of the arguments
108-98 reference(s)
A shell (Jeener surface 1)in motion
109-98 reference(s)
Rotation about X and Y axes of the Boy surface
110-96 reference(s)
An Archimedes spiral displaying 1000 numbers
111-94 reference(s)
Mountains at sunrise
112-94 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -gravity center of the 9 planets point of view-
113-94 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
114-94 reference(s)
Bidimensional domino effect
115-93 reference(s)
The journey of an Earth-like planet (dark blue)from Pluto (grey) to the Sun (yellow)
116-93 reference(s)
Self-transformation of a simple dynamical geometric texture
117-92 reference(s)
Mountains and light cloud dynamics -this sequence being periodical-
118-92 reference(s)
Artistic view of the tridimensional integration of the phase rotation of the wavelet transform of a bidimensional fractal field
119-92 reference(s)
Non euclidian distance
120-92 reference(s)
The non linear transformation of the coordinates in the Solar System
121-91 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Pluto point of view-
122-91 reference(s)
Periodical earthquake with multifractal mountains
123-90 reference(s)
Intertwining based on the geometry of the sphere
124-90 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
125-89 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
126-89 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
127-88 reference(s)
The erosion of the Babel Tower
128-88 reference(s)




2-The 128 most referenced Pages:



1-demo_14
1710 reference(s)
2-AVirtualSpaceTimeTravelMachine.Ang
1052 reference(s)
3-An2000.01.Fra
879 reference(s)
4-help.
582 reference(s)
5-Galerie_GeneralitiesVisualization.FV
376 reference(s)
6-AQuoiServentLesMathematiques.01
357 reference(s)
7-AVirtualSpaceTimeTravelMachine.Fra
351 reference(s)
8-FloatingPointNumbers.01.Fra
347 reference(s)
9-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
326 reference(s)
10-ImagesDuVirtuel.01.Fra
323 reference(s)
11-Galerie_ArtisticCreation.FV
320 reference(s)
12-Autostereograms.01.
320 reference(s)
13-ExpV_VirE.21
316 reference(s)
14-Stereogrammes_AutoStereogrammes.01
315 reference(s)
15-Fractal.01
314 reference(s)
16-ImagesDuVirtuel.01.Fra.FV
310 reference(s)
17-ExpV_VirE.11
296 reference(s)
18-VisSci_SciVis.01
295 reference(s)
19-Galerie_NumberTheory.FV
288 reference(s)
20-copyright.01.
277 reference(s)
21-FloatingPointNumbers.01.Ang
273 reference(s)
22-Informations_AboutPicturesAnimationsAndFiles.01.Ang
261 reference(s)
23-Galerie_DeterministicFractalGeometry.FV
256 reference(s)
24-ExpV_VirE.Ang
256 reference(s)
25-Galerie_TextureSynthesis.FV
248 reference(s)
26-RealNumbers.01.Fra
245 reference(s)
27-AProposSite.01.Fra
244 reference(s)
28-Galerie_QuantumMechanics.FV
238 reference(s)
29-Galerie_ParticleSystems.FV
238 reference(s)
30-mail.01.vv
237 reference(s)
31-GenieLogiciel.01.Fra
229 reference(s)
32-SurfaceProjector.01.Ang
227 reference(s)
33-Galerie_ArtAndScience.FV
227 reference(s)
34-AnimFractal.01.
227 reference(s)
35-SurfaceProjector.01.Fra
218 reference(s)
36-AVirtualSpaceTimeTravelMachine.Fra.FV
212 reference(s)
37-demo_14.FV
209 reference(s)
38-Galerie_DeterministicChaos.FV
204 reference(s)
39-Galerie_CelestialMechanics.FV
203 reference(s)
40-present.01.
198 reference(s)
41-Commentaires_VarieteHexaDimensionnelleCalabiYau.01
195 reference(s)
42-MathematiquesPhysiqueFractales.01
194 reference(s)
43-ExpV_VirE.Fra
194 reference(s)
44-Commentaires_DefinitionQuaternions.01
194 reference(s)
45-DuModeleALImage.01.Fra
192 reference(s)
46-AVirtualSpaceTimeTravelMachine.Ang.FV
190 reference(s)
47-An2000.02.Fra
189 reference(s)
48-VisSci_SciVis.02
187 reference(s)
49-Galerie_SignalProcessing.FV
187 reference(s)
50-Commentaires_NKleinBottle.01
186 reference(s)
51-ArtScience.11.Fra
183 reference(s)
52-EnsembleDesGaleries.DIAPO.0001
181 reference(s)
53-AvantPropos.01.Ang
177 reference(s)
54-Galerie_FromTheInfinitelySmallToTheInfinitelyBig.FV
176 reference(s)
55-Galerie_Astrophysics.DIAPO.0001
176 reference(s)
56-ExpV_VirE.01.Fra
176 reference(s)
57-Commentaires_DefinitionComplexes.01
176 reference(s)
58-Informations_AboutPicturesAnimationsAndFiles.01.Fra
175 reference(s)
59-Commentaires_SystemeSolaire.01
175 reference(s)
60-An2000.05.Fra
175 reference(s)
61-create.03.
173 reference(s)
62-Commentaires_DefinitionTransformeeDeFourier.01
172 reference(s)
63-LOG_xiMc.11
166 reference(s)
64-An2000.11.Fra
164 reference(s)
65-An2000.06.Fra
164 reference(s)
66-Commentaires_VarieteQuadriDimensionnelleCalabiYau.01
163 reference(s)
67-Galerie_NewPictures.FV
162 reference(s)
68-An2000.01.Ang
161 reference(s)
69-Informations_GoodNewsAndBadNews.01.Fra
159 reference(s)
70-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis
158 reference(s)
71-Commentaires_EnsembleMandelbrotComplexe.01
158 reference(s)
72-AQuoiServentLesMathematiques.03
157 reference(s)
73-Galerie_DeterministicChaos
154 reference(s)
74-Galerie_SalonDAutomne.FV
153 reference(s)
75-An2000.04.Fra
153 reference(s)
76-infinity.01.vv
152 reference(s)
77-Galerie_NewPictures
152 reference(s)
78-Galerie_NewPictures.DIAPO.0001
151 reference(s)
79-Galerie_QuantumMechanics
150 reference(s)
80-Vcatalogue.11
149 reference(s)
81-Galerie_Astrophysics.FV
149 reference(s)
82-ArtOrdinateur.01
149 reference(s)
83-MonumentValley.01.Fra
146 reference(s)
84-Commentaires_EspaceLyapunovComplexe.01
146 reference(s)
85-ExpV_VirE.01.Ang
143 reference(s)
86-Commentaires_ModeleIsingBiDimensionnel.01
143 reference(s)
87-Commentaires_RacinesNIemesUniteComplexes.01
142 reference(s)
88-subject.01.
141 reference(s)
89-VirtualChaos.01.Fra
141 reference(s)
90-ArtScience.01
141 reference(s)
91-RemarquesCerveau.01
140 reference(s)
92-Galerie_FluidMechanics.FV
140 reference(s)
93-catalogue.11
139 reference(s)
94-FaireDeLaRecherche.01.vv
139 reference(s)
95-Commentaires_RacinesTroisiemesUniteComplexes.01
139 reference(s)
96-Galerie_QuantumMechanics.DIAPO.0001
138 reference(s)
97-Galerie_CollaborativeWorks..FV
138 reference(s)
98-Galerie_SensitivityToRoundingOffErrors.FV
137 reference(s)
99-AQuoiServentLesMathematiques.02
137 reference(s)
100-Spheres.01
136 reference(s)
101-MonumentValley.01.Ang
136 reference(s)
102-ManyChaos.01.Fra
136 reference(s)
103-Kepler.02.
136 reference(s)
104-Galerie_BestOf.FV
136 reference(s)
105-Galerie_GeneralitiesVisualization
135 reference(s)
106-Galerie_BestOf.DIAPO.0001
135 reference(s)
107-Galerie_ArtAndScience
135 reference(s)
108-An2000.03.Fra
135 reference(s)
109-infinity.01.vv.DIAPO.0001
133 reference(s)
110-Galerie_CelestialMechanics
133 reference(s)
111-Galeries.01.vv
132 reference(s)
112-Galerie_NumberTheory.DIAPO.0001
132 reference(s)
113-Galerie_FluidMechanics
132 reference(s)
114-ManyChaos.01.Ang
131 reference(s)
115-ImpossibleStructures.01.Ang
130 reference(s)
116-Commentaires_StructuresVivantesRecursives.01
130 reference(s)
117-Commentaires_ProblemeDesNCorps.01
130 reference(s)
118-Commentaires_KleinBottle.01
130 reference(s)
119-Commentaires_SurfaceDeBoy.01
129 reference(s)
120-Commentaires_ProblemeDesNAimants.01
129 reference(s)
121-Commentaires_FluideInstationnaireBiDimensionnelIdeal.01
129 reference(s)
122-ArtScience.11.Ang.DIAPO.0001
129 reference(s)
123-Galerie_FluidMechanics.DIAPO.0001
127 reference(s)
124-Galerie_AnthropomorphicPatterns.FV
127 reference(s)
125-DuReelAuVirtuel.01.Fra
127 reference(s)
126-PerteDeLAssociativite.01
126 reference(s)
127-Galerie_CelestialMechanics.DIAPO.0001
126 reference(s)
128-AvantPropos.01.Fra
126 reference(s)

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




Copyright (c) Jean-François Colonna, 2007-2018.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2007-2018.