Monthly Best Of on 01/16/2002




A perfect bidimensional 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
france telecom, France Telecom R&D

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[The Y2K bug [Le bug de l'an 2000]]
[Do you believe that Real Numbers exist for a computer and that floating point computations are safe?]
[Please, visit A Virtual Space-Time Travel Machine, the place where you can find thousands of pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 01/16/2002 and last updated on 06/30/2018 14:02:31 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures:



No Title 0022
1-346 reference(s)
Welcome aboard A VIRTUAL SPACE-TIME TRAVEL MACHINE
2-318 reference(s)
Artistic view of the prime numbers
3-253 reference(s)
No Title 0023
4-197 reference(s)
Jean-François Colonna
5-181 reference(s)
Quark and gluon structure of a nucleon
6-145 reference(s)
Quark and gluon dynamics of the nucleon
7-142 reference(s)
No Title 0024
8-135 reference(s)
No Title 0031
9-111 reference(s)
No Title 0025
10-107 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
11-104 reference(s)
2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
12-103 reference(s)
Synthesis of bidimensional geometrical textures
13-101 reference(s)
The Birth of the Universe
14-95 reference(s)
No Title 0026
15-91 reference(s)
No Title 0027
16-90 reference(s)
No Title 0028
17-89 reference(s)
The Lorenz attractor
18-86 reference(s)
No Title 0030
19-85 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
20-82 reference(s)
Animation of a sunrise on mountains
21-81 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)
22-80 reference(s)
No Title 0029
23-79 reference(s)
16 earth-like planets initially on the same keplerian trajectory
24-78 reference(s)
The erection of the Babel Tower
25-76 reference(s)
Electron-positron scattering
26-72 reference(s)
Cauliflowers, seaweeds, shells,... with fog
27-68 reference(s)
From Pluto to the Sun (non linear scales)
28-68 reference(s)
Artistic view of the Big Bang
29-63 reference(s)
Mountains at sunrise
30-63 reference(s)
Texture animation by means of the generalized Fourier filtering process
31-63 reference(s)
Zoom in on the von Koch curve
32-62 reference(s)
Three pendulums -the Red one, the Green one and the Blue one- and three magnets -white-
33-60 reference(s)
Double impossible staircase
34-60 reference(s)
Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
35-58 reference(s)
The first true colors autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
36-56 reference(s)
Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
37-54 reference(s)
Rotation about the X axis of the Lorenz attractor (5000 iterations), computed simultaneously on two different computers
38-50 reference(s)
Translation along the fourth axis of a quaternionic Julia set -tridimensional cross-sections-
39-50 reference(s)
Psychedelic hypercube
40-50 reference(s)
From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
41-48 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
42-48 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
43-47 reference(s)
Alien
44-47 reference(s)
Electron-neutrino scattering
45-46 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
46-45 reference(s)
Tridimensional display of 36 eigenstates of the Hydrogen atom (bidimensional computation)
47-45 reference(s)
The three pendulums and three magnets problem computed on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors)
48-44 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)
49-44 reference(s)
The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
50-43 reference(s)
A twisting rope
51-43 reference(s)
16 complex Julia sets along the border of the Mandelbrot set with display of the iteration numbers
52-42 reference(s)
N-body problem integration (N=4)with one yellow star and two planets (the red one being very heavy and the blue one and its white satellite being light)
53-42 reference(s)
Bidimensional zoom in on the Mandelbrot set with display of the arguments
54-42 reference(s)
Electron diffraction
55-42 reference(s)
Zoom in on the von Koch curve
56-41 reference(s)
Animation of a natural form
57-41 reference(s)
Hypercube
58-41 reference(s)
Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold
59-41 reference(s)
N-body problem integration (N=2)displaying a perfect Keplerian orbit
60-40 reference(s)
Very naive view (solar system-like)of the Hydrogen atom
61-40 reference(s)
Zoom in on self-similar light clouds
62-40 reference(s)
Waltzing snowy Rocky Mountains
63-40 reference(s)
LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
64-40 reference(s)
The irreversibility of the numerical bidimensional billiard
65-39 reference(s)
N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors)
66-39 reference(s)
Artistic view of Ph(Zeta)
67-38 reference(s)
The Eratosthene sieve displaying 10x10 numbers
68-38 reference(s)
Artistic view of a 2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-
69-38 reference(s)
Autostereogram with an hidden volcano and 64 self-portraits
70-38 reference(s)
Rotation about the Y axis of the Boy surface with motion blur
71-37 reference(s)
Botticelli anomaly on the Moon
72-37 reference(s)
Alien spacecrafts on the Moon
73-37 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
74-37 reference(s)
Mountains and light cloud dynamics -this sequence being periodical-
75-36 reference(s)
The Möbius strip
76-36 reference(s)
Rotation about the X axis of the Lorenz attractor
77-36 reference(s)
Tridimensional display of 36 eigenstates of the Hydrogen atom (tridimensional computation)
78-36 reference(s)
Bidimensional visualization of a bidimensional turbulent flow -sensitivity to initial conditions-
79-36 reference(s)
Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
80-35 reference(s)
The Lorenz attractor -sensitivity to initial conditions (displayed as the central point of each frame)-
81-35 reference(s)
The generalized Ulam spiral displaying 100 numbers
82-34 reference(s)
The eye of God -an artistic view of the Solar System-
83-34 reference(s)
Morning sun pool
84-34 reference(s)
Zoom in on mountains (with 3D clipping, bird's-eye view)
85-34 reference(s)
A shell (Jeener surface 1)in motion
86-34 reference(s)
Diffusion between two boxes (initial conditions: the left one is empty, the right one contains 256 particles), with collisions and a time-dependent geometry
87-33 reference(s)
The Eratosthene sieve displaying 100x100 numbers
88-33 reference(s)
The Gate
89-33 reference(s)
Tridimensional zoom in on the Mandelbrot set
90-33 reference(s)
The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
91-33 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
92-32 reference(s)
Texture animation by means of Fourier filtering of a random walk process
93-32 reference(s)
Bidimensional zoom in on the Z=Zeta(Z)iteration with display of the arguments
94-32 reference(s)
Earthquake with multifractal mountains
95-32 reference(s)
Zoom in on a quaternionic Julia set -tridimensional cross-sections-
96-31 reference(s)
Texture animation by means of Fourier interpolation
97-31 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
98-31 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
99-30 reference(s)
Carnival in motion
100-30 reference(s)
The Möbius strip
101-30 reference(s)
The Earth, the Life and the Sun
102-29 reference(s)
Reconstruction of a 3D structure -a cubic lattice-
103-29 reference(s)
Zoom in on the quaternionic Mandelbrot set -tridimensional cross-sections-
104-29 reference(s)
The iterative process used to generate bidimensional fractal fields (16 iterations)
105-29 reference(s)
A higly symmetrical system (a bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle)can lost very fast the memory of its initial symmetry -with display of velocity histograms-
106-28 reference(s)
From Mars to the Sun
107-28 reference(s)
Tridimensional visualization of a bidimensional turbulent flow
108-28 reference(s)
An Archimedes spiral displaying 100 numbers
109-27 reference(s)
Foggy Babel Tower -a tribute to Brueghel the Elder-
110-27 reference(s)
Waltzing Monument Valley
111-27 reference(s)
N-body problem integration (N=10)displaying the actual Solar System with its simultaneous 2.pi rotation
112-27 reference(s)
La Génèse (1974)
113-27 reference(s)
The snake swallows its own tail
114-27 reference(s)
Along the border of the Mandelbrot set
115-26 reference(s)
Peace
116-26 reference(s)
Texture animation by means of the Generalized Product
117-26 reference(s)
An Archimedes spiral displaying 1000 numbers
118-26 reference(s)
Monument Valley at sunrise
119-26 reference(s)
Dynamics of an erosion process (bird's-eye view)
120-26 reference(s)
N-body problem integration (N=10)displaying the actual Solar System with its simultaneous 2.pi rotation, our Earth being at the origin of the coordinates
121-26 reference(s)
An arbitrary surface (Jeener surface 2)in motion
122-26 reference(s)
2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-
123-26 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
124-26 reference(s)
Tridimensional fractal structure
125-26 reference(s)
Archimedes spirals
126-26 reference(s)
The first two iterations of the construction of the von Koch curve
127-25 reference(s)
Bidimensional domino effect
128-25 reference(s)




2-The 128 most referenced Pages:



1-demo_14
1627 reference(s)
2-An2000.01.Fra
677 reference(s)
3-AVirtualSpaceTimeTravelMachine.Ang
430 reference(s)
4-BEST.20000323
162 reference(s)
5-help.
139 reference(s)
6-demo_14.FV
125 reference(s)
7-AVirtualSpaceTimeTravelMachine.Fra
120 reference(s)
8-Galerie_ArtisticCreation.FV
118 reference(s)
9-Fractal.01
118 reference(s)
10-MonumentValley.01.Ang
97 reference(s)
11-BEST.20010925
96 reference(s)
12-present.01.
94 reference(s)
13-copyright.01.
81 reference(s)
14-BEST.20010125
79 reference(s)
15-BEST.20010424
75 reference(s)
16-Commentaires_DefinitionComplexes.01
73 reference(s)
17-Commentaires_EnsembleMandelbrotComplexe.01
70 reference(s)
18-BEST.20010529
70 reference(s)
19-ExpV_VirE.Fra
68 reference(s)
20-ImagesDuVirtuel.01.Fra
62 reference(s)
21-GenieLogiciel.01.Fra
62 reference(s)
22-BEST.20000403
55 reference(s)
23-AVirtualSpaceTimeTravelMachine.Fra.FV
54 reference(s)
24-hydrogene.61.K.
52 reference(s)
25-Galerie_DeterministicChaos.FV
51 reference(s)
26-Galerie_CelestialMechanics.FV
46 reference(s)
27-AvantPropos.01.Ang
46 reference(s)
28-Galerie_GeneralitiesVisualization.FV
45 reference(s)
29-Galerie_FromTheInfinitelySmallToTheInfinitelyBig.FV
45 reference(s)
30-Commentaires_DefinitionTransformeeDeFourier.01
45 reference(s)
31-An2000.01.Ang
45 reference(s)
32-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
44 reference(s)
33-Galerie_CelestialMechanics
44 reference(s)
34-Commentaires_ProblemeDesNCorps.01
44 reference(s)
35-An2000.02.Fra
44 reference(s)
36-Commentaires_SystemeSolaire.01
41 reference(s)
37-mail.01.vv
38 reference(s)
38-Commentaires_VarieteQuadriDimensionnelleCalabiYau.01
38 reference(s)
39-Galerie_QuantumMechanics
36 reference(s)
40-Galerie_DeterministicChaos
36 reference(s)
41-An2000.05.Fra
36 reference(s)
42-Galeries.01.vv
35 reference(s)
43-An2000.06.Fra
35 reference(s)
44-AVirtualSpaceTimeTravelMachine.Ang.FV
35 reference(s)
45-AProposSite.01.Fra
35 reference(s)
46-Informations_AboutAnimationAndFiles.01.Ang
34 reference(s)
47-AQuoiServentLesMathematiques.01
34 reference(s)
48-RemarquesCerveau.01
33 reference(s)
49-Informations_GoodNewsAndBadNews.01.Ang
33 reference(s)
50-BEST.20000905
33 reference(s)
51-VisSci_SciVis.01
32 reference(s)
52-ManyChaos.01.Fra
32 reference(s)
53-BEST.20000517
32 reference(s)
54-An2000.03.Fra
31 reference(s)
55-subject.01.
30 reference(s)
56-ImagesDuVirtuel.01.Fra.FV
30 reference(s)
57-Galerie_TextureSynthesis.FV
30 reference(s)
58-RealNumbers.01.Fra
29 reference(s)
59-Galerie_QuantumMechanics.FV
29 reference(s)
60-Galerie_DeterministicFractalGeometry.FV
29 reference(s)
61-Commentaires_EnsembleJuliaComplexe.01
29 reference(s)
62-Commentaires_DefinitionQuaternions.01
29 reference(s)
63-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis
28 reference(s)
64-Galerie_NewPictures
28 reference(s)
65-ArtScience.01
28 reference(s)
66-AnimFractal.01.
28 reference(s)
67-create.03.
27 reference(s)
68-PourLaScience.01.Fra
27 reference(s)
69-stereogra.01.c.
26 reference(s)
70-Commentaires_ProblemeDesNAimants.01
26 reference(s)
71-ArtOrdinateur.01
26 reference(s)
72-An2000.04.Fra
26 reference(s)
73-MonumentValley.01.Fra
25 reference(s)
74-Galerie_SensitivityToRoundingOffErrors.FV
25 reference(s)
75-ExpV_VirE.Ang
25 reference(s)
76-BEST.20001024
25 reference(s)
77-BEST.20000717
25 reference(s)
78-Autostereograms.01.
25 reference(s)
79-Galerie_ParticleSystems
24 reference(s)
80-Galerie_NumberTheory.FV
24 reference(s)
81-PresidentRepublique.01.Fra
23 reference(s)
82-PatrimoineHumanite.02.Fra
23 reference(s)
83-GenieLogiciel.01.Ang
23 reference(s)
84-ExpV_VirE.01.Fra
23 reference(s)
85-Commentaires_StructuresVivantesRecursives.01
23 reference(s)
86-Commentaires_NKleinBottle.01
23 reference(s)
87-Commentaires_ModeleIsingBiDimensionnel.01
23 reference(s)
88-ManyChaos.01.Ang
22 reference(s)
89-Commentaires_SurfaceDeBoy.01
22 reference(s)
90-Spheres.01
21 reference(s)
91-JFC
21 reference(s)
92-Informations_AboutAnimationAndFiles.01.Fra
21 reference(s)
93-Galerie_SalonDAutomne
21 reference(s)
94-Galerie_GeneralitiesVisualization
21 reference(s)
95-Galerie_ArtisticCreation
21 reference(s)
96-Galerie_ArtAndScience
21 reference(s)
97-Commentaires_RacinesTroisiemesUniteComplexes.01
21 reference(s)
98-Vcatalogue.11
20 reference(s)
99-RealNumbers.01.Ang
20 reference(s)
100-Galerie_SignalProcessing.FV
20 reference(s)
101-Galerie_NumberTheory
20 reference(s)
102-Galerie_NewPictures.FV
20 reference(s)
103-Commentaires_EnsembleJuliaQuaternion.01
20 reference(s)
104-An2000.11.Fra
20 reference(s)
105-nCube.21.I.
19 reference(s)
106-infinity.01.vv
19 reference(s)
107-LumiereVirtuelleParadoxale.01
19 reference(s)
108-Galerie_BestOf
19 reference(s)
109-BEST.20001205
19 reference(s)
110-Ariane501.01.Fra
19 reference(s)
111-relativity.01.
18 reference(s)
112-catalogue.11
18 reference(s)
113-T_DuReelAuVirtuel_ExpReelle.01.Fra.0002
18 reference(s)
114-Kepler.02.
18 reference(s)
115-Informations_GoodNewsAndBadNews.01.Fra
18 reference(s)
116-Galerie_FromTheInfinitelySmallToTheInfinitelyBig
18 reference(s)
117-Galerie_DeterministicFractalGeometry
18 reference(s)
118-Commentaires_VarieteHexaDimensionnelleCalabiYau.01
18 reference(s)
119-Commentaires_RacinesNIemesUniteComplexes.01
18 reference(s)
120-cerveau.01.vv.
17 reference(s)
121-T_DuReelAuVirtuel_MetaOrdinateur.01.Fra.0000
17 reference(s)
122-LOG_xiMc.11
17 reference(s)
123-Galerie_SensitivityToRoundingOffErrors
17 reference(s)
124-Galerie_ArtAndScience.FV
17 reference(s)
125-Commentaires_ModeleIsingTriDimensionnel.01
17 reference(s)
126-Commentaires_EnsembleMandelbrotQuaternion.01
17 reference(s)
127-ImpossibleStructures.01.Ang
16 reference(s)
128-Galerie_SignalProcessing
16 reference(s)

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




Copyright (c) Jean-François Colonna, 2002-2018.
Copyright (c) France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2002-2018.