Monthly Best Of on 09/28/2020




The Bertrand paradox

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 pas 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 more than 10.000 pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 09/28/2020 and last updated on 10/03/2024 17:04:07 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



A blue Sponge-tree -a Tribute to Yves Klein-
1-71 reference(s)		The random walk of photons escaping the Sun
2-70 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
3-55 reference(s)		64 elementary bidimensional binary cellular automata with 1 white starting central point
4-54 reference(s)
The bidimensional John Conway's life game
5-50 reference(s)		A bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle
6-49 reference(s)		The random walk of photons escaping the Sun
7-47 reference(s)		The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-
8-47 reference(s)
The Ulam spiral
9-47 reference(s)		Monument Valley at sunrise with light cloud dynamics -this sequence being periodical-
10-46 reference(s)		The Bonan-Jeener-Klein triple bottle
11-46 reference(s)		Tridimensional zoom in on the Mandelbrot set
12-45 reference(s)
The first four iterations of the construction of the von Koch snowflake
13-44 reference(s)		Bidimensional zoom in on the Mandelbrot set with display of the arguments
14-44 reference(s)		Quaternionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-
15-44 reference(s)		From Mars to the Sun
16-43 reference(s)
Artistic view of the prime numbers
17-43 reference(s)		Tridimensional display of the Riemann Zeta function inside [-10.0,+20.0]x[-15.0,+15.0] (bird's-eye view)
18-42 reference(s)		Bidimensional geometrical texture animation
19-42 reference(s)		The 'exponential' spreading of a tridimensional epidemic -the COVID-19 coronavirus?- without confinement -1430 particles-, with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-
20-42 reference(s)
The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- with partial confinement -201 particles-, with a zero death rate and a 50% infection, starting with just one infected person -red particle on bottom left picture-
21-42 reference(s)		The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with a zero death rate and with a 50% infection, starting with just one infected person -red particle on bottom left picture-
22-42 reference(s)		The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- with partial confinement -201 particles-, with a zero death rate and a 100% infection, starting with just one infected person -red particle on bottom left picture-
23-42 reference(s)		Tridimensional display of the particle density of a bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle
24-42 reference(s)
Dynamics of the even distribution of 6 points on a sphere -an Octahedron- by means of simulated annealing
25-42 reference(s)		Dynamics of the even distribution of 24 points on a sphere by means of simulated annealing
26-42 reference(s)		The Möbius strip
27-42 reference(s)		Happy new year 2000
28-42 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
29-41 reference(s)		Bidimensional rectangular billiard with a central obstacle and an initial flow of rotating particles
30-40 reference(s)		Tridimensional texture animation by means of the Generalized Product
31-40 reference(s)		Bidimensional texture animation by means of the Generalized Product
32-40 reference(s)
The Ulam spiral with display of the first twin prime numbers ('2-twin' prime numbers)
33-40 reference(s)		The journey of an Earth-like virtuel planet (green)from Pluto (grey) to the Sun (yellow) -point of view of the virtual planet-
34-40 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
35-35 reference(s)		The random walk of photons escaping the Sun
36-33 reference(s)
Autostereogram with an hidden volcano
37-32 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
38-32 reference(s)		The Universe at the heart of a Calabi-Yau manifold
39-28 reference(s)		4 evenly distributed points on a sphere -a Tetrahedron- by means of simulated annealing
40-28 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
41-27 reference(s)		Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 1.083.984 galaxies)obtained by means of a non deterministic fractal process
42-26 reference(s)		Quantum vacuum fluctuations
43-25 reference(s)		A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
44-25 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
45-25 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
46-25 reference(s)		The 20 first digits {141592...} of 'pi' displayed on an helix -orange-
47-24 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
48-24 reference(s)
The Goldbach conjecture -the Goldbach comet- for the even numbers from 6 to 6244
49-23 reference(s)		Autostereogram with an hidden volcano
50-21 reference(s)		Real gravel -256x256 after RLE1+BWT+RLE2-
51-21 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
52-21 reference(s)
Autostereogram of the CMAP
53-20 reference(s)		K/LD Matrix -'CDCM3_I1.01' measures-
54-20 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
55-19 reference(s)		The Jeener-Klein triple bottle
56-19 reference(s)
Pseudo Olympic Rings
57-18 reference(s)		Quark and gluon structure of a nucleon
58-18 reference(s)		A spherical cross-section inside the Menger Sponge -iteration 5-
59-18 reference(s)		Tridimensional visualization of the Verhulst dynamics
60-18 reference(s)
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) and with a 0 to pi rotation about the X axis -tridimensional cross-section-
61-18 reference(s)		Tridimensional representation of a hexadimensional Calabi-Yau manifold
62-18 reference(s)		The Jeener-Klein triple bottle
63-18 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
64-17 reference(s)
The generalized Ulam spiral
65-17 reference(s)		The 1.000 first digits -base 10- of 'pi' displayed on an helix -good point of view-
66-17 reference(s)		Real blackboard with formulas
67-17 reference(s)		Tridimensional Hilbert Curve -iteration 3-
68-17 reference(s)
Rotation about the Y (vertical)axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms
69-17 reference(s)		Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
70-16 reference(s)		Metropolis -a Tribute to Fritz Lang-
71-16 reference(s)		The 50 first digits {4,1,4,2,1,3,5,6,2,3,...} of the square root of 2 displayed on an helix -orange-
72-16 reference(s)
IMAGE_INEXISTANTE=DOSSIER__ART_ET_SCIENCE__1971_1991__COUVERTURE
73-16 reference(s)		A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
74-15 reference(s)		Autostereogram with an hidden volcano
75-14 reference(s)		2000 evenly distributed points on a sphere by means of the Fibonacci spiral
76-14 reference(s)
The Sierpinski Carpet -iteration 3-
77-14 reference(s)		Fractal natural form
78-14 reference(s)		The generalized Ulam spiral displaying 2025 numbers
79-14 reference(s)		The 20 first digits {141592...} of 'pi' displayed on an helix -orange-
80-14 reference(s)
An arbitrary surface (Jeener surface 2)in motion
81-14 reference(s)		An arbitrary surface (Jeener surface 2)in motion
82-14 reference(s)		Tridimensional filamentous fractal structure
83-14 reference(s)		Isle of the Dead -a Tribute to Arnold Böcklin-
84-14 reference(s)
Electron diffraction
85-14 reference(s)		A 4-cube -an hypercube-
86-14 reference(s)		The normal field of a tridimensional representation of a quadridimensional Calabi-Yau manifold
87-14 reference(s)		LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
88-14 reference(s)
Quantum vacuum fluctuation dynamics
89-13 reference(s)		Two multiplexed autostereograms by means of a pi/2 rotation
90-13 reference(s)		Autostereogram with an hidden volcano
91-13 reference(s)		The 2-17 first digits -base 10- of 'pi' displayed on a circle
92-13 reference(s)
The same bidimensional scalar field displayed with 4 different color palettes
93-13 reference(s)		Color palette 'cyan.21'
94-13 reference(s)		From Pluto to the Sun (non linear scales)
95-13 reference(s)		The Lorenz attractor
96-13 reference(s)
The Goldbach conjecture -the Goldbach comet or the Goldbach rainbow- for the even numbers from 6 to 41518
97-13 reference(s)		The dynamics of the diffusion process in a bidimensional medium obtained by means of a random walk process
98-13 reference(s)		Tridimensional representation of a hexadimensional Calabi-Yau manifold
99-13 reference(s)		The evolution of the Klein bottle using the Lorenz attractor
100-13 reference(s)
Quantum vacuum fluctuations
101-12 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
102-12 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
103-12 reference(s)		Artistic variation on the generalized Ulam spiral displaying 81 numbers
104-12 reference(s)
The generalized Ulam spiral displaying 100 numbers
105-12 reference(s)		Rotation about the X axis of the Lorenz attractor
106-12 reference(s)		Sixteen interlaced fractal torus
107-12 reference(s)		A shell (Jeener surface 1)in motion
108-12 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
109-12 reference(s)		The Klein bottle
110-12 reference(s)		Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
111-11 reference(s)		An aperiodic Penrose tiling of the plane
112-11 reference(s)
An aperiodic Penrose tiling of the plane
113-11 reference(s)		16 complex Julia sets along the border of the Mandelbrot set with display of the iteration numbers
114-11 reference(s)		A tridimensional intertwining inside the Bonan-Jeener-Klein triple bottle
115-11 reference(s)		Autostereogram with an hidden ring and ghost bows
116-11 reference(s)
The Sierpinski Carpet -iteration 5-
117-11 reference(s)		Reconstruction of a 3D structure -a cubic lattice-
118-11 reference(s)		The generalized Ulam spiral displaying 1024 numbers
119-11 reference(s)		Monument Valley à la David Hockney
120-11 reference(s)
Autostereogram of Monument Valley
121-11 reference(s)		True colors autostereogram of a fractal landscape
122-11 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)
123-11 reference(s)		The intersection of the Menger Sponge -iteration 5- and of a quadridimensional Calabi-Yau manifold -tridimensional representation-
124-11 reference(s)
Hypercube
125-11 reference(s)		A shell (Jeener surface 1)
126-11 reference(s)		Erosion of a bidimensional random (with small and large scale correlations)medium
127-11 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
128-11 reference(s)




2-The 128 most referenced Pages (*):

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



1-Galerie_NumberTheory.FV
572 reference(s)		2-demo_14
556 reference(s)
3-AVirtualSpaceTimeTravelMachine.Ang
449 reference(s)		4-An2000.01.Fra
396 reference(s)
5-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
389 reference(s)		6-Vcatalogue.11
374 reference(s)
7-Galerie_ArtisticCreation.FV
333 reference(s)		8-Galerie_GeneralitiesVisualization.FV
330 reference(s)
9-Galerie_ParticleSystems.FV
302 reference(s)		10-MorePages.
271 reference(s)
11-Galerie_DeterministicFractalGeometry.FV
244 reference(s)		12-Galerie_CelestialMechanics.FV
236 reference(s)
13-help.
235 reference(s)		14-Fractal.01
231 reference(s)
15-Galerie_ArtAndScience.FV
223 reference(s)		16-FloatingPointNumbers.01.Fra
216 reference(s)
17-RealNumbers.01.Fra
204 reference(s)		18-UlamSpiral.01.Fra
195 reference(s)
19-Galerie_TextureSynthesis.FV
195 reference(s)		20-Galerie_QuantumMechanics.FV
190 reference(s)
21-Galerie_SensitivityToRoundingOffErrors.FV
184 reference(s)		22-AProposSite.01.Fra
184 reference(s)
23-mail.01.vv
174 reference(s)		24-Galerie_ImagesDidactiques.FV
174 reference(s)
25-Galerie_DeterministicChaos.FV
170 reference(s)		26-GoldenTriangle.01.Fra
168 reference(s)
27-AVirtualSpaceTimeTravelMachine.Fra
167 reference(s)		28-Commentaires_NKleinBottle.01
166 reference(s)
29-Galerie_Tributes.FV
162 reference(s)		30-demo
161 reference(s)
31-Stereogrammes_AutoStereogrammes.01
160 reference(s)		32-realnumbers
159 reference(s)
33-logiciel
159 reference(s)		34-demo14
159 reference(s)
35-demo.14
159 reference(s)		36-an2000
159 reference(s)
37-copyright.01.
158 reference(s)		38-Galerie_SignalProcessing.FV
158 reference(s)
39-Galerie_Astrophysics.FV
158 reference(s)		40-nombresreels
157 reference(s)
41-genielogiciel
157 reference(s)		42-LOG_xiMc.11
156 reference(s)
43-Galerie_NewPictures.FV
156 reference(s)		44-SurfaceProjector.01.Ang
149 reference(s)
45-Fractal.11
149 reference(s)		46-DecimalesDePi.01.Fra
149 reference(s)
47-Galerie_FluidMechanics.FV
147 reference(s)		48-ExpV_VirE.11
146 reference(s)
49-FloatingPointNumbers.01.Ang
144 reference(s)		50-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
142 reference(s)
51-Galerie_BestOf.FV
142 reference(s)		52-subject.01.
141 reference(s)
53-NDimensionalDeterministicFractalSets.01.Ang
141 reference(s)		54-GenieLogiciel.01.Fra
141 reference(s)
55-NatureDesMathematiques.01.vv.Fra
140 reference(s)		56-MonodimensionalCellularAutomata.01.Fra
139 reference(s)
57-Kepler.02.
139 reference(s)		58-PerteDeLAssociativite.01
137 reference(s)
59-GenieLogiciel_VisualisationScientifique.01.vv
137 reference(s)		60-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
137 reference(s)
61-Galerie_NumbersAndLight.FV
136 reference(s)		62-Galerie_ImagesDesMathematiques.FV
136 reference(s)
63-Exposition_EcolePolytechnique_FeteDeLaScience_201910
134 reference(s)		64-DieuScience.01.Fra
134 reference(s)
65-NDimensionalDeterministicFractalSets.01.Fra
132 reference(s)		66-MathematiquesPhysiqueFractales.12
132 reference(s)
67-MathematiquesPhysiqueFractales.02
132 reference(s)		68-SurfaceProjector.01.Fra
130 reference(s)
69-infinity.01.vv
129 reference(s)		70-Informations_GoodNewsAndBadNews.01.Fra
129 reference(s)
71-Fractal.21
129 reference(s)		72-present.01.
128 reference(s)
73-create.03.
128 reference(s)		74-Informations_AboutPicturesAnimationsAndFiles.01.Ang
128 reference(s)
75-EntrelacsIntertwinings.01.Ang
128 reference(s)		76-AnimFractal.01.
128 reference(s)
77-UlamSpiral.01.Ang
127 reference(s)		78-NombresEtLumiere.01.vv.Fra
127 reference(s)
79-DuModeleALImage.02.Fra
127 reference(s)		80-LesApprentisDieux.01
126 reference(s)
81-Informations_GoodNewsAndBadNews.01.Ang
126 reference(s)		82-IllusionConnaissance.02
126 reference(s)
83-GoldenTriangle.01.Ang
126 reference(s)		84-OrdinateursEtCalculs.01.Fra
125 reference(s)
85-Autostereograms.01.
125 reference(s)		86-ImpossibleStructures.01.Ang
124 reference(s)
87-FaireDeLaRecherche.01.vv
124 reference(s)		88-ExpV_VirE.Ang
124 reference(s)
89-VirtualChaos.01.Ang
123 reference(s)		90-OrdinateursEtCalculs.01.Ang
123 reference(s)
91-Multivers.01.Fra
123 reference(s)		92-MathematiquesPhysiqueFractales.22
123 reference(s)
93-ImagesDuVirtuel.01.Fra.FV
123 reference(s)		94-MonodimensionalCellularAutomata.01.Ang
122 reference(s)
95-ImpossibleStructures.01.Fra
122 reference(s)		96-ConjectureDeSyracuse_0256.vv
122 reference(s)
97-ArtScience.01
122 reference(s)		98-PatrimoineHumanite.02.Fra
121 reference(s)
99-ConjectureDeSyracuse_0128.Parity.vv
121 reference(s)		100-VisualisationRelief.01.vv.Fra
120 reference(s)
101-RemarquesCerveau.01
120 reference(s)		102-MathematiquesModeleOutilArtiste.02.Ang
120 reference(s)
103-ManyChaos.01.Fra
120 reference(s)		104-FaireDesMathematiques.01.Fra
120 reference(s)
105-VirtualChaos.01.Fra
119 reference(s)		106-OrdinateurMathematiquesArt.01.Fra
119 reference(s)
107-ImagesDuVirtuel.01.Fra
119 reference(s)		108-Exposition_EcolePolytechnique_FeteDeLaScience_201810
119 reference(s)
109-Exposition_EcolePolytechnique_AnneeMondialeDeLaPhysique_2005
119 reference(s)		110-EntrelacsIntertwinings.01.Fra
119 reference(s)
111-EnsembleDesGaleries.DIAPO.0001
119 reference(s)		112-RasoirDOccamEtMathematiques.01.vv.Fra
118 reference(s)
113-Polynomials_RationalNumbers.01.Fra
118 reference(s)		114-infinity.02.vv
117 reference(s)
115-Pcatalogue.11
117 reference(s)		116-Exposition_EcolePolytechnique_FeteDeLaScience_201510
117 reference(s)
117-Commentaires_JumelleJeenerBottle.01
117 reference(s)		118-VisitesGaleriesEnfouies.01.Fra
116 reference(s)
119-Fractal.02
116 reference(s)		120-Exposition_OperaDeMassy_201912_202001
116 reference(s)
121-ManyChaos.01.Ang
115 reference(s)		122-ImagesEncadreesDisponibles.01
115 reference(s)
123-Galerie_ArtAndScience.DIAPO.0099
115 reference(s)		124-Exposition_MairieCinquiemeArrondissementParis_202001_202002
115 reference(s)
125-AvantPropos.01.Fra
115 reference(s)		126-galerie_numbertheory.fv
114 reference(s)
127-catalogue.11
114 reference(s)		128-MiseEnSceneDesNombres.01.vv.Fra
114 reference(s)

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




Copyright © Jean-François COLONNA, 2020-2024.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2020-2024.