Monthly Best Of on 12/29/2021




Tridimensional visualization of the Mandelbrot set

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

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(CMAP28 WWW site: this page was created on 12/29/2021 and last updated on 11/14/2023 17:50:18 -CET-)





Nota:

The number of references of pictures and pages could seem lower than usual. This is due to the set up of a new Web server on 12/15/2021 that causes the loss of the preceding transaction logs.



Contents of this page:


1-The 128 most referenced Pictures (*):

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



Tridimensional representation of a quadridimensional Calabi-Yau manifold
1-39 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
2-34 reference(s)		 Autostereogram with an hidden volcano
3-23 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
4-23 reference(s)
The Universe at the heart of a Calabi-Yau manifold
5-21 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
6-21 reference(s)		 Artistic view of the prime numbers
7-19 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
8-17 reference(s)
Impressionist tridimensional self-Portrait
9-16 reference(s)		 The random walk of photons escaping the Sun
10-14 reference(s)		 Bidimensional zoom in on the Mandelbrot set with display of the arguments
11-13 reference(s)		 Fractal diffusion front in a bidimensional medium obtained by means of a random walk process (zoom in on the first steps)
12-13 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
13-13 reference(s)		 Happy new year 2000
14-12 reference(s)		 The first four iterations of the construction of the von Koch snowflake
15-11 reference(s)		 16 complex Julia sets along the border of the Mandelbrot set with display of the iteration numbers
16-11 reference(s)
Autostereogram with an hidden ring and ghost bows
17-11 reference(s)		 Bidimensional quasi-symmetrical fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
18-11 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
19-11 reference(s)		 Quantum vacuum fluctuations
20-10 reference(s)
A variable Archimedes spiral displaying 1000 numbers
21-10 reference(s)		 An arbitrary surface (Jeener surface 2)in motion
22-10 reference(s)		 Tridimensional Hilbert Curve -iterations 1 to 3-
23-10 reference(s)		 Untitled 0004
24-10 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
25-10 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
26-10 reference(s)		 The Bonan-Jeener-Klein triple bottle
27-10 reference(s)		 The Menger sponge -iteration 5-
28-9 reference(s)
Black dots on a square lattice
29-9 reference(s)		 Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
30-9 reference(s)		 An aperiodic Penrose tiling of the plane
31-8 reference(s)		 An interpolation between an intertwining based on the geometry of the Bonan-Jeener-Klein triple bottle and an intertwining based on the geometry of the sphere
32-8 reference(s)
2000 evenly distributed points on a sphere by means of the Fibonacci spiral
33-8 reference(s)		 Bidimensional quasi-symmetrical fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
34-8 reference(s)		 Tridimensional billiard with 12 -initially- still particles submitted to an attractive central field of gravity
35-8 reference(s)		 How to compute 'pi' with a gun
36-8 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)
37-8 reference(s)		 The velocity vectors -with a common origin- of the 9 planets of the Solar System during one plutonian year
38-8 reference(s)		 Bidimensional zoom in on the Mandelbrot set with display of the arguments
39-8 reference(s)		 A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
40-8 reference(s)
The normal field of a shell (Jeener surface 1)
41-8 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
42-8 reference(s)		 Rotation about X and Y axes of the Jeener-Klein triple bottle
43-8 reference(s)		 The Jeener-Klein triple bottle
44-8 reference(s)
Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
45-7 reference(s)		 Tridimensional self-Portrait -a Tribute to Victor Vasarely-
46-7 reference(s)		 An aperiodic Penrose tiling of the plane
47-7 reference(s)		 An aperiodic Penrose tiling of the plane
48-7 reference(s)
Along the border of the Mandelbrot set
49-7 reference(s)		 An animation of the intertwining based on the geometry of the sphere
50-7 reference(s)		 An interpolation between two intertwinings
51-7 reference(s)		 Autostereogram with an hidden volcano
52-7 reference(s)
The random walk of photons escaping the Sun
53-7 reference(s)		 The numerical irreversibility of the bidimensional billiard -1376 particles-
54-7 reference(s)		 A perfect tridimensional piston with following initial conditions: still piston, high temperature particles at left and low temperature particles at right, in a tridimensional box submitted to a vertical field of gravity
55-7 reference(s)		 Kasner billiard: Time-dependent billiard (from negative curvatures to positive curvature)with one accelerated particle
56-7 reference(s)
Bidimensional rectangular billiard with 50% of small light particles and 50% of big heavy particles submitted to a vertical field of gravity
57-7 reference(s)		 Particles in a bidimensional box submitted to a repulsive central field of gravity
58-7 reference(s)		 Particles in a bidimensional box submitted to an attractive central field of gravity
59-7 reference(s)		 Bidimensional fractal aggregates obtained by means of pasting during collisions with display of the velocity histogram
60-7 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-
61-7 reference(s)		 A porous membrane with following initial conditions: high temperature particles at left and low temperature particles at right
62-7 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
63-7 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-
64-7 reference(s)
Isotropic random walk of 64 particles on a tridimensional square lattice
65-7 reference(s)		 Non isotropic random walk of 64 particles on a bidimensional square lattice in a 'ring' potential
66-7 reference(s)		 The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
67-7 reference(s)		 N-body problem integration (N=3)displaying two planets with symmetrical initial conditions on circular trajectories
68-7 reference(s)
N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed on two 'compatible' computers (the Yellow one and the Cyan one: sensitivity to rounding-off errors)
69-7 reference(s)		 The journey of an Earth-like planet (green)from Pluto (grey) to the Sun (yellow)
70-7 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
71-7 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System, our Earth being at the origin of the coordinates
72-7 reference(s)
Bidimensional zoom in on the Mandelbrot set with display of the arguments
73-7 reference(s)		 Rotation about the X axis of the Lorenz attractor (5000 iterations), computed simultaneously on two different computers
74-7 reference(s)		 The Lorenz attractor
75-7 reference(s)		 Zoom in on a quaternionic Julia set -tridimensional cross-sections-
76-7 reference(s)
2.pi rotation about Y and Z axes of a quaternionic Julia set (64 views)-tridimensional cross-section-
77-7 reference(s)		 2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-
78-7 reference(s)		 Artistic view of a 2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-
79-7 reference(s)		 Fractal self-portrait
80-7 reference(s)
The bidimensional Ising Model with 2-state spins, a centred gaussian temperature field (minimum=0.035,maximum=0.6)and random initial conditions
81-7 reference(s)		 The tridimensional Ising Model with 2-state spins, temperature=0.4 and random initial conditions
82-7 reference(s)		 The tridimensional Ising Model with 2-state spins, temperature=0.2 and random initial conditions
83-7 reference(s)		 Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation and bird's-eye view)
84-7 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
85-7 reference(s)		 From a sphere to the Boy surface
86-7 reference(s)		 Cross-sections inside the density during a tridimensional diffusion process of 114299 particles
87-7 reference(s)		 Erosion of a bidimensional random (with small and large scale correlations)island
88-7 reference(s)
The erosion process of a mysterious foggy island
89-7 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
90-7 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
91-7 reference(s)		 Rotation about the X axis of a tridimensional brownian motion
92-7 reference(s)
Untitled 0382
93-6 reference(s)		 An aperiodic Penrose tiling of the Golden Decagon
94-6 reference(s)		 An aperiodic Penrose tiling of the plane
95-6 reference(s)		 An aperiodic Penrose tiling of the plane
96-6 reference(s)
Two multiplexed autostereograms by means of a pi/2 rotation
97-6 reference(s)		 Autostereogram of the CMAP
98-6 reference(s)		 The generalized Ulam spiral displaying 1024 numbers
99-6 reference(s)		 The generalized Ulam spiral
100-6 reference(s)
Sixteen portraits (Lena)with an increasing size of the pixels -from 1 to 16-
101-6 reference(s)		 The Birth of the Universe
102-6 reference(s)		 Tridimensional fractal structure
103-6 reference(s)		 Isle of the Dead -a Tribute to Arnold Böcklin-
104-6 reference(s)
The Jeener flower
105-6 reference(s)		 Fractal diffusion front in a bidimensional medium obtained by means of a random walk process
106-6 reference(s)		 Rotation about the Y (vertical)axis of the CMAP logo that can also be viewed as a set of 4x3 stereograms
107-6 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
108-6 reference(s)
The evolution of the Klein bottle using the Lorenz attractor
109-6 reference(s)		 64 elementary bidimensional binary cellular automata with 1 white starting central point
110-6 reference(s)		 Self-Portrait
111-5 reference(s)		 An aperiodic Penrose tiling of the plane
112-5 reference(s)
An aperiodic Penrose tiling of the plane
113-5 reference(s)		 The 'sharp' Golden Triangle
114-5 reference(s)		 A perfect bidimensional fractal tree and the self-similarity
115-5 reference(s)		 Intertwining
116-5 reference(s)
Autostereogram of 8 color-multiplexed quaternionic Julia sets -tridimensional cross-sections-
117-5 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
118-5 reference(s)		 Autostereogram with an hidden volcano
119-5 reference(s)		 The construction process of the Sierpinski carpet
120-5 reference(s)
The Sierpinski carpet -iteration 1 to 5-
121-5 reference(s)		 The numerical irreversibility of the bidimensional billiard -768 particles-
122-5 reference(s)		 A tridimensional fractal manifold defined by means of three tridimensional fields
123-5 reference(s)		 Sunny Monument Valley
124-5 reference(s)
Botticelli anomaly on the Moon
125-5 reference(s)		 True colors autostereogram of a fractal landscape
126-5 reference(s)		 Quark and gluon structure of a nucleon
127-5 reference(s)		 Quark and gluon structure of a nucleon
128-5 reference(s)




2-The 128 most referenced Pages (*):

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



1-Vcatalogue.11
130 reference(s)		 2-AVirtualSpaceTimeTravelMachine.Ang
130 reference(s)
3-An2000.01.Fra
104 reference(s)		 4-demo_14
97 reference(s)
5-Galerie_NumberTheory.FV
75 reference(s)		 6-help.
63 reference(s)
7-mail.01.vv
60 reference(s)		 8-SurfaceProjector.01.Ang
58 reference(s)
9-ExpV_VirE.11
58 reference(s)		 10-Galerie_ArtisticCreation.FV
56 reference(s)
11-LOG_xiMc.11
55 reference(s)		 12-An2000.01.Ang
55 reference(s)
13-Stereogrammes_AutoStereogrammes.01
54 reference(s)		 14-Kepler.02.
54 reference(s)
15-copyright.01.
51 reference(s)		 16-SurfaceProjector.01.Fra
51 reference(s)
17-Galerie_GeneralitiesVisualization.FV
51 reference(s)		 18-AVirtualSpaceTimeTravelMachine.Fra
51 reference(s)
19-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
49 reference(s)		 20-Autostereograms.01.
47 reference(s)
21-Galerie_ParticleSystems.FV
45 reference(s)		 22-AProposSite.01.Fra
45 reference(s)
23-Galerie_DeterministicFractalGeometry.FV
43 reference(s)		 24-OrdinateursEtCalculs.01.Ang
42 reference(s)
25-present.01.
41 reference(s)		 26-Galerie_QuantumMechanics.FV
41 reference(s)
27-Galerie_ImagesDesMathematiques.FV
41 reference(s)		 28-Fractal.21
41 reference(s)
29-DieuScience.01.Fra
41 reference(s)		 30-Commentaires_NKleinBottle.01
41 reference(s)
31-Informations_GoodNewsAndBadNews.01.Fra
40 reference(s)		 32-Galerie_ArtAndScience.FV
40 reference(s)
33-VirtualChaos.01.Fra
39 reference(s)		 34-MorePages.Ang.
39 reference(s)
35-GoldenTriangle.01.Fra
39 reference(s)		 36-Galerie_ImagesDidactiques.FV
39 reference(s)
37-Galerie_TextureSynthesis.FV
38 reference(s)		 38-Galerie_SignalProcessing.FV
38 reference(s)
39-Galerie_SensitivityToRoundingOffErrors.FV
38 reference(s)		 40-Galerie_NewPictures.FV
38 reference(s)
41-Galerie_CelestialMechanics.FV
38 reference(s)		 42-FloatingPointNumbers.01.Fra
38 reference(s)
43-infinity.01.vv
37 reference(s)		 44-NatureDesMathematiques.01.vv.Fra
37 reference(s)
45-NDimensionalDeterministicFractalSets.01.Fra
37 reference(s)		 46-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
37 reference(s)
47-MonodimensionalCellularAutomata.01.Fra
37 reference(s)		 48-MonodimensionalCellularAutomata.01.Ang
36 reference(s)
49-GenieLogiciel_VisualisationScientifique.01.vv
36 reference(s)		 50-Fractal.11
36 reference(s)
51-Fractal.03
36 reference(s)		 52-DecimalesPi_1_100.vv
36 reference(s)
53-DecimalesDePi.01.Fra
36 reference(s)		 54-Web_Mail.01.vv
35 reference(s)
55-MathematiquesPhysiqueFractales.12
35 reference(s)		 56-Galerie_GeneralitiesVisualization
35 reference(s)
57-Galerie_FluidMechanics.FV
35 reference(s)		 58-Galerie_DeterministicChaos.FV
35 reference(s)
59-Fractal.01
35 reference(s)		 60-EntrelacsIntertwinings.01.Ang
35 reference(s)
61-AnimFractal.01.
35 reference(s)		 62-Informations_AboutPicturesAnimationsAndFiles.01.Ang
34 reference(s)
63-Galerie_Tributes.FV
34 reference(s)		 64-Galerie_BestOf.FV
34 reference(s)
65-Galerie_Astrophysics.FV
34 reference(s)		 66-Exposition_EcolePolytechnique_FeteDeLaScience_201910
34 reference(s)
67-catalogue.11
33 reference(s)		 68-Spheres.01
33 reference(s)
69-MathematiquesPhysiqueFractales.22
33 reference(s)		 70-ImpossibleStructures.01.Ang
33 reference(s)
71-ImagesDuVirtuel.01.Fra.FV
33 reference(s)		 72-UlamSpiral.01.Fra
32 reference(s)
73-NombresEtLumiere.01.vv.Fra
32 reference(s)		 74-NDimensionalDeterministicFractalSets.01.Ang
32 reference(s)
75-GoldenTriangle.01.Ang
32 reference(s)		 76-Commentaires_EnsembleJuliaOctonion.01
32 reference(s)
77-Commentaires_DefinitionPseudoOctonions.01
32 reference(s)		 78-VisitesGaleriesEnfouies.01.Fra
31 reference(s)
79-OrdinateurMathematiquesArt.01.Fra
31 reference(s)		 80-ManyChaos.01.Ang
31 reference(s)
81-LeParadoxeDeFermi.01.Fra
31 reference(s)		 82-ImpossibleStructures.01.Fra
31 reference(s)
83-ImagesDuVirtuel.01.Fra
31 reference(s)		 84-FloatingPointNumbers.01.Ang
31 reference(s)
85-FaireDesMathematiques.01.Fra
31 reference(s)		 86-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
31 reference(s)
87-BEST.20141228
31 reference(s)		 88-ArtScience.01
31 reference(s)
89-ArtEtMathematiques.01
31 reference(s)		 90-xDarchivesG__SMC__sources__SMC_____SI_G2
30 reference(s)
91-subject.01.
30 reference(s)		 92-infinity.02.vv
30 reference(s)
93-create.03.
30 reference(s)		 94-SourceExemple_____xrq_____hydrogene.61.K.
30 reference(s)
95-Polynomials_RationalNumbers.01.Fra
30 reference(s)		 96-MorePages.Fra.
30 reference(s)
97-MathematiquesPhysiqueFractales.02
30 reference(s)		 98-ManyChaos.01.Fra
30 reference(s)
99-IllusionConnaissance.02
30 reference(s)		 100-EntrelacsIntertwinings.01.Fra
30 reference(s)
101-EnsembleDesGaleries.DIAPO.0001
30 reference(s)		 102-DieuScience.01.Ang
30 reference(s)
103-Commentaires_NKleinBottle.02
30 reference(s)		 104-BEST.20170228
30 reference(s)
105-ImagesEncadreesDisponibles.01
29 reference(s)		 106-FaireDeLaRecherche.01.vv
29 reference(s)
107-Exposition_MairieCinquiemeArrondissementParis_202001_202002
29 reference(s)		 108-BEST.20140828
29 reference(s)
109-Pcatalogue.11
28 reference(s)		 110-MathematiquesPhysiqueFractales.01
28 reference(s)
111-MathematiquesModeleOutilArtiste.02.Ang
28 reference(s)		 112-LeParadoxeDeFermi.01.Ang
28 reference(s)
113-Informations_AboutPicturesAnimationsAndFiles.01.Fra
28 reference(s)		 114-Galerie_SalonDAutomne.FV
28 reference(s)
115-Galerie_ArtisticCreation.DIAPO.0010
28 reference(s)		 116-Galerie_AnthropomorphicPatterns.FV
28 reference(s)
117-Fractal.02
28 reference(s)		 118-Exposition_EcolePolytechnique_AnneeMondialeDeLaPhysique_2005
28 reference(s)
119-Commentaires_KleinBottle.01
28 reference(s)		 120-Commentaires_Hyperboloide.02
28 reference(s)
121-Commentaires_Epicycloide.02
28 reference(s)		 122-AQuoiServentLesMathematiques.01
28 reference(s)
123-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_12
27 reference(s)		 124-Tcatalogue.11
27 reference(s)
125-RemarquesCerveau.01
27 reference(s)		 126-RasoirDOccamEtMathematiques.01.vv.Fra
27 reference(s)
127-QuelquesQuestionsSurLaRecherche.01.Fra
27 reference(s)		 128-PerteDeLAssociativite.01
27 reference(s)

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




Copyright © Jean-François COLONNA, 2021-2023.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2021-2023.