Monthly Best Of on 02/28/2010




A bijection

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 02/28/2010 and last updated on 06/30/2018 14:04:35 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures:



Happy new year 2000
1-1807 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
2-364 reference(s)
The random walk of photons escaping the Sun
3-340 reference(s)
Welcome aboard a Virtual Space-Time Travel Machine
4-327 reference(s)
The Lorenz attractor
5-227 reference(s)
Hypercube
6-212 reference(s)
Quark and gluon structure of a nucleon
7-195 reference(s)
Foggy Babel Tower -a tribute to Brueghel the Elder-
8-194 reference(s)
Quark and gluon structure of a nucleon
9-191 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
10-188 reference(s)
Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
11-170 reference(s)
Happy new year 2000
12-156 reference(s)
Paradoxal Monument Valley at sunset
13-152 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
14-151 reference(s)
A 'cloudy' pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
15-150 reference(s)
Rotation about the X axis of the Lorenz attractor (5000 iterations), computed simultaneously on two different computers
16-150 reference(s)
Jean-François Colonna
17-147 reference(s)
Fractal synthesis of mountains with vegetation and stormy clouds
18-146 reference(s)
Artistic view of the Big Bang
19-145 reference(s)
Autostereogram with an hidden ring and ghost bows
20-145 reference(s)
The random walk of photons escaping the Sun
21-139 reference(s)
A pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
22-139 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-
23-138 reference(s)
The Birth of the Universe
24-137 reference(s)
Artistic view of the prime numbers
25-129 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
26-122 reference(s)
Along the border of the Mandelbrot set
27-121 reference(s)
24 evenly distributed points on a sphere by means of simulated annealing
28-120 reference(s)
From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
29-116 reference(s)
Recursive intertwining
30-115 reference(s)
From Pluto to the Sun (non linear scales)
31-115 reference(s)
Autostereogram with an hidden volcano and 64 self-portraits
32-114 reference(s)
16 complex Julia sets along the border of the Mandelbrot set with display of the iteration numbers
33-113 reference(s)
Rotation about the X axis of the Lorenz attractor
34-111 reference(s)
From the infinitely small to the infinitely big
35-110 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
36-103 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
37-103 reference(s)
Translation along the fourth axis of a pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
38-102 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
39-98 reference(s)
A tridimensional fractal manifold defined by means of three tridimensional fields
40-97 reference(s)
Bidimensional zoom in on the Mandelbrot set with display of the arguments
41-97 reference(s)
2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
42-93 reference(s)
Self-Portrait with intertwining
43-92 reference(s)
Light cloud dynamics
44-90 reference(s)
A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
45-90 reference(s)
Quark and gluon dynamics of the nucleon
46-89 reference(s)
Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
47-85 reference(s)
Botticelli anomaly on the Moon
48-85 reference(s)
Animation of a sunrise on mountains
49-84 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
50-82 reference(s)
The Scream -a Tribute to Edvard Munch-
51-81 reference(s)
A pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-'the children round' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
52-79 reference(s)
The generalized Ulam spiral displaying 100 numbers
53-78 reference(s)
From the infinitely small to the infinitely big
54-78 reference(s)
Zoom in on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
55-76 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)
56-75 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
57-75 reference(s)
A shell (Jeener surface 1)in motion
58-75 reference(s)
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
59-73 reference(s)
Alien
60-72 reference(s)
32 points on a trigonometric circle
61-72 reference(s)
Double impossible staircase
62-72 reference(s)
A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
63-71 reference(s)
Mountains at sunrise
64-69 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
65-69 reference(s)
Along the border of the Mandelbrot set
66-68 reference(s)
A 'mixing' between a pseudo-quaternionic Mandelbrot set (a 'MandelBulb')and a tridimensional fractal structure -tridimensional cross-section-
67-67 reference(s)
The erection of the Babel Tower
68-66 reference(s)
2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')-tridimensional cross-section-
69-66 reference(s)
The same bidimensional scalar field displayed with 4 different color palettes
70-65 reference(s)
Artistic view of a bidimensional texture obtained by means of the self-transformation of a fractal process
71-63 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)
72-63 reference(s)
Tridimensional display of the Riemann Zeta function inside (-10.0,+60.0)x(-35.0,+35.0) (bird's-eye view)
73-61 reference(s)
Tridimensional fractal structure
74-61 reference(s)
The normal field of a fractal surface defined by means of three bidimensional fields
75-60 reference(s)
Pi rotation about the Y axis of a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
76-58 reference(s)
Zoom in on the quaternionic Mandelbrot set -tridimensional cross-sections-
77-58 reference(s)
From Pluto to the Sun -extrapolation 2- (non linear scales)
78-57 reference(s)
An elementary monodimensional binary cellular automaton -86- with 1 white starting point -bottom middle-
79-57 reference(s)
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
80-56 reference(s)
Intertwining based on the geometry of the sphere
81-56 reference(s)
Autostereogram with an hidden volcano
82-53 reference(s)
'There is a war' -a Tribute to Leonard Cohen-
83-53 reference(s)
The Möbius strip
84-53 reference(s)
A pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
85-53 reference(s)
Electron-positron scattering
86-53 reference(s)
Fractal texture dynamics
87-52 reference(s)
A foggy pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-
88-52 reference(s)
Tridimensional fractal structure
89-52 reference(s)
The Lorenz attractor in motion
90-51 reference(s)
A bidimensional fern computed by means of an 'Iterated Function System' -IFS-
91-51 reference(s)
The pseudo-quaternionic fractal set obtained when computing the roots of Q^3=1 using Newton's method with translation along the third axis of the pseudo-quaternionic space (a 'NewtonBulb')-tridimensional cross-section-
92-50 reference(s)
The special Liouville function displayed as a bidimensional random walk for the integer numbers from 2 to 400001 (Red), 2 to 800001 (Green) and 2 to 1600001 (Blue)
93-50 reference(s)
Intertwining
94-49 reference(s)
Mountains and light cloud dynamics -this sequence being periodical-
95-49 reference(s)
A quaternionic Julia set -tridimensional cross-section-
96-49 reference(s)
A monodimensional 'quasi-continuous' cellular automaton with random perturbation of the rules
97-49 reference(s)
Artistic view of the trajectories of bidimensional fractal aggregates obtained by means of pasting during collisions of particles submitted to an attractive central field of gravity
98-48 reference(s)
Artistic view of the trajectories of tridimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity
99-47 reference(s)
Autostereogram of Monument Valley
100-47 reference(s)
Zoom in on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
101-47 reference(s)
Tridimensional display of 36 eigenstates of the Hydrogen atom (bidimensional computation)
102-47 reference(s)
The Lorenz attractor
103-46 reference(s)
Autostereogram with an hidden volcano
104-45 reference(s)
Artistic view of a quadridimensional Calabi-Yau manifold
105-45 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
106-44 reference(s)
An arbitrary geometrical texture
107-44 reference(s)
Quaternionic shell
108-44 reference(s)
6 evenly distributed points on a sphere -an Octahedron- by means of simulated annealing
109-44 reference(s)
An Archimedes spiral displaying 1000 numbers
110-44 reference(s)
Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
111-44 reference(s)
No Title 0031
112-43 reference(s)
A 'spiraling plane' defined by means of three bidimensional fields
113-43 reference(s)
The special Liouville function displayed as a bidimensional random walk for the integer numbers from 2 to 200001 (Red), 2 to 400001 (Green) and 2 to 800001 (Blue)
114-43 reference(s)
The quaternionic Mandelbrot set -tridimensional cross-section-
115-43 reference(s)
3-foil torus knots
116-43 reference(s)
Psychedelic hypercube
117-43 reference(s)
Intertwining based on the geometry of a Möbius strip
118-43 reference(s)
Tridimensional visualization of a bidimensional turbulent flow
119-42 reference(s)
LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
120-42 reference(s)
Synthesis of bidimensional geometrical textures
121-41 reference(s)
The 8 vertices of a 3-cube
122-41 reference(s)
A quaternionic Julia set -tridimensional cross-section-
123-41 reference(s)
Tridimensional visualization of a bidimensional turbulent flow -sensitivity to initial conditions (the Red one, the Green one and the Blue one)-
124-41 reference(s)
Foggy steep island
125-41 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
126-41 reference(s)
The Klein bottle
127-41 reference(s)
Autostereogram with an hidden volcano
128-40 reference(s)




2-The 128 most referenced Pages:



1-demo_14
1211 reference(s)
2-AVirtualSpaceTimeTravelMachine.Ang
753 reference(s)
3-NDimensionalDeterministicFractalSets.01.Fra
535 reference(s)
4-An2000.01.Fra
519 reference(s)
5-help.
400 reference(s)
6-AVirtualSpaceTimeTravelMachine.Fra
394 reference(s)
7-Fractal.01
393 reference(s)
8-FloatingPointNumbers.01.Fra
373 reference(s)
9-Galerie_GeneralitiesVisualization.FV
340 reference(s)
10-FloatingPointNumbers.01.Ang
340 reference(s)
11-NDimensionalDeterministicFractalSets.01.Ang
328 reference(s)
12-AQuoiServentLesMathematiques.01
312 reference(s)
13-Galerie_ArtisticCreation.FV
310 reference(s)
14-GenieLogiciel_VisualisationScientifique.01.vv
307 reference(s)
15-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
304 reference(s)
16-Informations_AboutPicturesAnimationsAndFiles.01.Ang
303 reference(s)
17-SurfaceProjector.01.Ang
296 reference(s)
18-Galerie_DeterministicFractalGeometry.FV
294 reference(s)
19-AProposSite.01.Fra
287 reference(s)
20-Galerie_NewPictures.FV
279 reference(s)
21-copyright.01.
278 reference(s)
22-SurfaceProjector.01.Fra
278 reference(s)
23-EnsembleDesGaleries.DIAPO.0001
277 reference(s)
24-mail.01.vv
276 reference(s)
25-Galerie_ParticleSystems.FV
270 reference(s)
26-Galerie_CelestialMechanics.FV
269 reference(s)
27-Stereogrammes_AutoStereogrammes.01
263 reference(s)
28-GenieLogiciel.01.Fra
261 reference(s)
29-catalogue.11
259 reference(s)
30-Galerie_DeterministicChaos.FV
259 reference(s)
31-AnimFractal.01.
259 reference(s)
32-Galerie_NumberTheory.FV
256 reference(s)
33-EnsembleDesGaleries.DIAPO.0002
253 reference(s)
34-RealNumbers.01.Fra
251 reference(s)
35-ImagesDuVirtuel.01.Fra.FV
251 reference(s)
36-Galerie_ArtisticCreation.DIAPO.0024
250 reference(s)
37-EnsembleDesGaleries.DIAPO.0003
250 reference(s)
38-Galerie_QuantumMechanics.FV
249 reference(s)
39-EntrelacsIntertwinings.01.Fra
248 reference(s)
40-Galerie_ArtisticCreation.DIAPO.0020
245 reference(s)
41-Galerie_ArtAndScience.FV
245 reference(s)
42-Galerie_ArtisticCreation.DIAPO.0022
244 reference(s)
43-Galerie_ArtisticCreation.DIAPO.0027
243 reference(s)
44-present.01.
242 reference(s)
45-Galerie_NewPictures.DIAPO.0030
241 reference(s)
46-Galerie_NewPictures.DIAPO.0027
241 reference(s)
47-Galerie_BestOf.FV
241 reference(s)
48-Galerie_ArtisticCreation.DIAPO.0021
241 reference(s)
49-Galerie_NewPictures.DIAPO.0026
240 reference(s)
50-Galerie_TextureSynthesis.FV
239 reference(s)
51-Galerie_ArtisticCreation.DIAPO.0023
239 reference(s)
52-EnsembleDesGaleries.DIAPO.0004
239 reference(s)
53-Kepler.02.
238 reference(s)
54-Galerie_ArtisticCreation.DIAPO.0029
238 reference(s)
55-ImagesDuVirtuel.01.Fra
237 reference(s)
56-Galerie_NewPictures.DIAPO.0031
236 reference(s)
57-Galerie_NewPictures.DIAPO.0028
236 reference(s)
58-Galerie_NewPictures.DIAPO.0029
235 reference(s)
59-Galerie_ArtisticCreation.DIAPO.0030
235 reference(s)
60-Galerie_NewPictures.DIAPO.0032
234 reference(s)
61-ExpV_VirE.Fra
234 reference(s)
62-Galerie_ArtisticCreation.DIAPO.0025
233 reference(s)
63-Galerie_ArtisticCreation.DIAPO.0019
231 reference(s)
64-Galerie_ArtisticCreation.DIAPO.0018
231 reference(s)
65-Galerie_NewPictures.DIAPO.0025
230 reference(s)
66-Galerie_NewPictures.DIAPO.0024
230 reference(s)
67-Galerie_NewPictures.DIAPO.0023
230 reference(s)
68-Galerie_NewPictures.DIAPO.0022
230 reference(s)
69-Galerie_ArtisticCreation.DIAPO.0028
230 reference(s)
70-EnsembleDesGaleries.DIAPO.0019
230 reference(s)
71-Galerie_NewPictures.DIAPO.0040
229 reference(s)
72-Galerie_NewPictures.DIAPO.0021
228 reference(s)
73-Galerie_ArtisticCreation.DIAPO.0032
228 reference(s)
74-Galerie_ArtisticCreation.DIAPO.0026
228 reference(s)
75-EnsembleDesGaleries.DIAPO.0016
228 reference(s)
76-EnsembleDesGaleries.DIAPO.0006
228 reference(s)
77-Galerie_ArtisticCreation.DIAPO.0031
227 reference(s)
78-EnsembleDesGaleries.DIAPO.0021
227 reference(s)
79-EnsembleDesGaleries.DIAPO.0015
227 reference(s)
80-Galerie_ArtisticCreation.DIAPO.0060
226 reference(s)
81-ExpV_VirE.11
226 reference(s)
82-EnsembleDesGaleries.DIAPO.0018
226 reference(s)
83-Galerie_NewPictures.DIAPO.0044
225 reference(s)
84-EnsembleDesGaleries.DIAPO.0468
225 reference(s)
85-EnsembleDesGaleries.DIAPO.0188
225 reference(s)
86-EnsembleDesGaleries.DIAPO.0184
225 reference(s)
87-EnsembleDesGaleries.DIAPO.0017
225 reference(s)
88-EnsembleDesGaleries.DIAPO.0005
225 reference(s)
89-Galerie_ArtisticCreation.DIAPO.0106
224 reference(s)
90-Galerie_ArtisticCreation.DIAPO.0039
224 reference(s)
91-Galerie_ArtisticCreation.DIAPO.0038
224 reference(s)
92-EnsembleDesGaleries.DIAPO.0020
224 reference(s)
93-Galerie_NewPictures.DIAPO.0038
223 reference(s)
94-Galerie_NewPictures.DIAPO.0037
223 reference(s)
95-Galerie_ArtisticCreation.DIAPO.0048
223 reference(s)
96-EnsembleDesGaleries.DIAPO.0187
223 reference(s)
97-EnsembleDesGaleries.DIAPO.0186
223 reference(s)
98-EnsembleDesGaleries.DIAPO.0057
223 reference(s)
99-EnsembleDesGaleries.DIAPO.0052
223 reference(s)
100-EnsembleDesGaleries.DIAPO.0051
223 reference(s)
101-Galerie_NewPictures.DIAPO.0036
222 reference(s)
102-Galerie_NewPictures.DIAPO.0035
222 reference(s)
103-Galerie_NewPictures.DIAPO.0019
222 reference(s)
104-Galerie_Astrophysics.FV
222 reference(s)
105-Galerie_ArtisticCreation.DIAPO.0110
222 reference(s)
106-EnsembleDesGaleries.DIAPO.0185
222 reference(s)
107-Galerie_NewPictures.DIAPO.0043
221 reference(s)
108-Galerie_ArtisticCreation.DIAPO.0037
221 reference(s)
109-Galerie_ArtisticCreation.DIAPO.0033
221 reference(s)
110-EnsembleDesGaleries.DIAPO.0476
221 reference(s)
111-EnsembleDesGaleries.DIAPO.0467
221 reference(s)
112-EnsembleDesGaleries.DIAPO.0189
221 reference(s)
113-EnsembleDesGaleries.DIAPO.0172
221 reference(s)
114-EnsembleDesGaleries.DIAPO.0014
221 reference(s)
115-EnsembleDesGaleries.DIAPO.0012
221 reference(s)
116-EnsembleDesGaleries.DIAPO.0007
221 reference(s)
117-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
220 reference(s)
118-Galerie_NewPictures.DIAPO.0042
220 reference(s)
119-Galerie_NewPictures.DIAPO.0020
220 reference(s)
120-Galerie_ArtisticCreation.DIAPO.0118
220 reference(s)
121-Galerie_ArtisticCreation.DIAPO.0062
220 reference(s)
122-Galerie_ArtisticCreation.DIAPO.0055
220 reference(s)
123-Galerie_ArtisticCreation.DIAPO.0050
220 reference(s)
124-Galerie_ArtisticCreation.DIAPO.0041
220 reference(s)
125-Galerie_ArtisticCreation.DIAPO.0017
220 reference(s)
126-EnsembleDesGaleries.DIAPO.0465
220 reference(s)
127-EnsembleDesGaleries.DIAPO.0464
220 reference(s)
128-EnsembleDesGaleries.DIAPO.0050
220 reference(s)

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




Copyright (c) Jean-François Colonna, 2010-2018.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2010-2018.