Monthly Best Of on 08/28/2023




Paradoxal structure based on the geometry of the Bonan-Jeener-Klein triple bottle

Jean-François COLONNA
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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 08/28/2023 and last updated on 11/14/2023 17:50:44 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



A close-up of the 'EinStein' aperiodic 'Spectre' tiling
1-126 reference(s)		 Artistic view of the prime numbers
2-117 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the Mandelbrot set border -iteration 5-
3-102 reference(s)		 Jean-François COLONNA (on 11/17/1994)with its fractal mountains
4-101 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
5-99 reference(s)		 The random walk of photons escaping the Sun
6-98 reference(s)		 An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
7-94 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to a periodical impossible structure -iteration 1-
8-92 reference(s)
A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the von Koch Curve -iteration 5-
9-92 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X4(...),Y4(...),Z4(...)} -iteration 4-
10-87 reference(s)		 Along the border of the Mandelbrot set
11-86 reference(s)		 The Piet Mondrian Hypercube -2D, 3D or 4D?-
12-83 reference(s)
The Syracuse conjecture for U(0)={5,10,15,20,...,1310720}
13-82 reference(s)		 The Lorenz attractor
14-82 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
15-81 reference(s)		 Quantum vacuum fluctuations
16-80 reference(s)
A Bidimensional non continous Hilbert-like Curve defined with {X1(...),Y1(...)} related to a periodical 'labyrinthic' structure -iteration 5-
17-79 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the von Koch Curve -iteration 4-
18-78 reference(s)		 A random tiling of a square domain using dominoes (1x2 rectangles)-line after line- with display of clusters of horizontal and vertical rectangles using the 4-connexity
19-78 reference(s)		 A Bidimensional non continous Hilbert-like Curve defined with {X1(...),Y1(...)} related to a periodical 'labyrinthic' structure -iteration 4-
20-77 reference(s)
A Tridimensional Hilbert-like Curve defined with {X2(...),Y2(...),Z2(...)} -iteration 2-
21-77 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the Mandelbrot set border -iteration 3-
22-77 reference(s)		 Fractal synthesis of mountains with vegetation and stormy clouds
23-77 reference(s)		 A random tiling of a square domain using dominoes (1x2 rectangles)-line after line-
24-77 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
25-77 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to a periodical impossible structure -iteration 3-
26-76 reference(s)		 A close-up of the 'EinStein' aperiodic 'Spectre' tiling
27-75 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to a periodical impossible structure -iteration 2-
28-75 reference(s)
A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the Mandelbrot set border -iteration 1-
29-75 reference(s)		 Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
30-75 reference(s)		 The Sierpinski carpet -iteration 1 to 5-
31-74 reference(s)		 Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
32-73 reference(s)
A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to a periodical impossible structure -iteration 4-
33-73 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the von Koch Curve -iteration 3-
34-73 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the von Koch Curve -iteration 1-
35-72 reference(s)		 A torus described by means of a Bidimensional Hilbert Curve -iteration 5-
36-72 reference(s)
A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} -iteration 3-
37-71 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} -iteration 3-
38-71 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the Mandelbrot set border -iteration 4-
39-71 reference(s)		 A regular 3-gon -an equilateral triangle-
40-70 reference(s)
A Bidimensional non continous Hilbert-like Curve defined with {X1(...),Y1(...)} related to a periodical 'labyrinthic' structure -iteration 3-
41-70 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the Mandelbrot set border -iteration 2-
42-70 reference(s)		 Iterations in the complex plane: the computation of the Mandelbrot set
43-70 reference(s)		 Tridimensional Hilbert Curve -iteration 3-
44-70 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
45-69 reference(s)		 Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
46-69 reference(s)		 A Ball described by means of a Tridimensional Hilbert Curve -iteration 4-
47-69 reference(s)		 Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
48-69 reference(s)
Triple impossible staircase and a paradoxal structure
49-69 reference(s)		 Paradoxal structure based on the geometry of the Boy surface
50-68 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X4(...),Y4(...),Z4(...)} -iteration 4-
51-68 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X1(...),Y1(...),Z1(...)} -iteration 1-
52-68 reference(s)
N-body problem integration (N=2)displaying a perfect Keplerian orbit (an ellipse)
53-68 reference(s)		 Cantor's diagonal argument
54-68 reference(s)		 Quantum vacuum fluctuations
55-67 reference(s)		 Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
56-67 reference(s)
A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to a periodical impossible structure -iteration 5-
57-67 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the von Koch Curve -iteration 2-
58-67 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X2(...),Y2(...),Z2(...)} -iteration 2-
59-67 reference(s)		 Mountains and fog
60-67 reference(s)
Quark and gluon structure of a nucleon
61-67 reference(s)		 From Pluto to the Sun
62-67 reference(s)		 3-foil torus knot on its torus
63-67 reference(s)		 Fractal Self-Portrait -a Tribute to René Magritte-
64-67 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
65-67 reference(s)		 The journey of an Earth-like planet (dark blue)from Pluto (grey) to the Sun (yellow)
66-66 reference(s)		 Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
67-66 reference(s)		 2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
68-66 reference(s)
Triple impossible staircase painting a paradoxal structure
69-66 reference(s)		 About the fractal dimension with the first two iterations -red and green respectively- of the construction of the von Koch curve
70-65 reference(s)		 Artistic view of the Big Bang
71-65 reference(s)		 The Ulam spiral with display of the first twin prime numbers ('2-twin' prime numbers)
72-65 reference(s)
A Bidimensional non continous Hilbert-like Curve defined with {X1(...),Y1(...)} related to a periodical 'labyrinthic' structure -iteration 2-
73-65 reference(s)		 Empty
74-65 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
75-65 reference(s)		 A 'square' spiral on the Bonan-Jeener-Klein triple bottle
76-65 reference(s)
One of the two subdivisions of the 'flat' Golden Triangle
77-64 reference(s)		 The 'green' reflection of a red tetrahedron obtained by a 'blue' symmetry of each red vertex about the opposite red face
78-64 reference(s)		 The Ulam spiral
79-64 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X1(...),Y1(...),Z1(...)} -iteration 1-
80-64 reference(s)
Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
81-64 reference(s)		 The Piet Mondrian quadridimensional Calabi-Yau manifold -2D, 3D or 4D?-
82-64 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
83-64 reference(s)		 Untitled 0267 -a Tribute to Piet Mondrian-
84-64 reference(s)
A 'square' spiral on the Klein bottle
85-64 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
86-63 reference(s)		 The first two iterations of the construction of the von Koch curve
87-63 reference(s)		 The Bonan-Jeener double bottle described by means of a Bidimensional Hilbert-like Curve -iteration 5-
88-63 reference(s)
A Tridimensional Hilbert-like Curve defined with {X2(...),Y2(...),Z2(...)} and based on an 'open' 3-foil torus knot -iteration 2-
89-63 reference(s)		 Botticelli anomaly on the Moon
90-63 reference(s)		 From Pluto to the Sun (linear scales)
91-63 reference(s)		 The complement of the Menger sponge -iteration 2-
92-63 reference(s)
The Continuum Hypothesis (CH)
93-63 reference(s)		 My own quadruple impossible staircase -a Tribute to Maurits Cornelis Escher-
94-63 reference(s)		 The Klein bottle
95-63 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
96-62 reference(s)
Isotropic random walk of 64 particles on a bidimensional square lattice
97-62 reference(s)		 The generalized Ulam spiral
98-62 reference(s)		 Untitled 0155 -a Tribute to Yves Tanguy-
99-62 reference(s)		 A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
100-62 reference(s)
Triple impossible staircase
101-62 reference(s)		 The Ptolemaic system -without equant- with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend- centered on the Earth -blue sphere-
102-62 reference(s)		 Bidimensional closed pseudo-self-avoiding brownian motion on the Bonan-Jeener-Klein triple bottle
103-62 reference(s)		 An aperiodic Penrose tiling of the plane -a Tribute to Piet Mondrian and Roger Penrose-
104-61 reference(s)
A 'square' spiral
105-61 reference(s)		 Bidimensional brownian motion
106-61 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X2(...),Y2(...)} -iteration 2-
107-61 reference(s)		 Untitled 0137 -'Jour de Lenteur', a Tribute to Yves Tanguy-
108-61 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)
109-61 reference(s)		 Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
110-61 reference(s)		 Close-up on a foggy 'MandelBox' -tridimensional cross-section-
111-61 reference(s)		 Tridimensional visualization of the Mandelbrot set with mapping of the arguments
112-61 reference(s)
The Klein bottle described by means of a Bidimensional non continous Hilbert-like Curve -iteration 5-
113-61 reference(s)		 The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 5-
114-61 reference(s)		 A Ball described by means of a Tridimensional Hilbert-like Curve -iteration 4-
115-61 reference(s)		 Tridimensional Hilbert Curve -iteration 4-
116-61 reference(s)
The Goldbach conjecture
117-61 reference(s)		 Bidimensional brownian motion -the colors used (magenta,red,yellow,green,cyan)are an increasing function of the time- and its 'external border' -white-
118-61 reference(s)		 An aperiodic Penrose tiling of the plane
119-60 reference(s)		 Bidimensional brownian motion on a torus
120-60 reference(s)
Bidimensional closed pseudo-self-avoiding brownian motion on the Boy surface
121-60 reference(s)		 Bidimensional domino effect
122-60 reference(s)		 A regular 5-gon -a pentagon-
123-60 reference(s)		 The same bidimensional scalar field displayed with 4 different color palettes
124-60 reference(s)
Bidimensional closed self-avoiding brownian motion on the Möbius strip
125-60 reference(s)		 The Menger sponge -iteration 5-
126-60 reference(s)		 Journey on the Complex Plane by means of a Bidimensional Hilbert Curve -iteration 4- with display of Julia sets
127-60 reference(s)		 A Douady rabbit -a complex Julia set computed with A=(-0.13,+0.77)- with display of the arguments
128-60 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
1428 reference(s)		 2-An2000.01.Fra
251 reference(s)
3-demo_14
159 reference(s)		 4-ChatGPT.01.Fra
132 reference(s)
5-Galerie_NumberTheory.FV
124 reference(s)		 6-Vcatalogue.11
114 reference(s)
7-an2000.01.fra
107 reference(s)		 8-help.
105 reference(s)
9-mail.01.vv
95 reference(s)		 10-Galerie_GeneralitiesVisualization.FV
92 reference(s)
11-Web_Mail.01.vv
84 reference(s)		 12-LesCourbesRemplissantes.02.Fra
83 reference(s)
13-Informations_AboutPicturesAnimationsAndFiles.01.Ang
82 reference(s)		 14-Galerie_ArtisticCreation.FV
82 reference(s)
15-Stereogrammes_AutoStereogrammes.01
81 reference(s)		 16-copyright.01.
77 reference(s)
17-Fractal.01
76 reference(s)		 18-present.01.
75 reference(s)
19-NombresPremiers_10000.vv
74 reference(s)		 20-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
74 reference(s)
21-UlamSpiral.01.Fra
73 reference(s)		 22-LeNoeudInfini.01.Fra
71 reference(s)
23-Galerie_ImagesDesMathematiques.FV
68 reference(s)		 24-MonodimensionalCellularAutomata.01.Fra
67 reference(s)
25-EntrelacsIntertwinings.01.Fra
67 reference(s)		 26-DieuScience.01.Fra
67 reference(s)
27-Galerie_ParticleSystems.FV
66 reference(s)		 28-Fractal.21
66 reference(s)
29-Fractal.11
66 reference(s)		 30-MathematiquesPhysiqueFractales.12
65 reference(s)
31-Galerie_DeterministicFractalGeometry.FV
65 reference(s)		 32-Galerie_ArtAndScience.FV
65 reference(s)
33-FloatingPointNumbers.01.Fra
63 reference(s)		 34-Commentaires_VarieteHexaDecaDimensionnelleCalabiYau.01
63 reference(s)
35-Bard.01.Ang
63 reference(s)		 36-RemarquesCerveau.01
62 reference(s)
37-NDimensionalDeterministicFractalSets.01.Fra
62 reference(s)		 38-ChatGPT.01.Ang
62 reference(s)
39-GenieLogiciel.01.Fra
61 reference(s)		 40-Galerie_ImagesDidactiques.FV
61 reference(s)
41-DecimalesDePi.01.Fra
61 reference(s)		 42-PerteDeLAssociativite.01
60 reference(s)
43-Galerie_SensitivityToRoundingOffErrors.FV
60 reference(s)		 44-Labyrinthes.01.Ang
59 reference(s)
45-Informations_GoodNewsAndBadNews.01.Fra
59 reference(s)		 46-Polynomials_RationalNumbers.01.Fra
58 reference(s)
47-NatureDesMathematiques.01.vv.Fra
58 reference(s)		 48-Galerie_TextureSynthesis.FV
58 reference(s)
49-Galerie_CelestialMechanics.FV
58 reference(s)		 50-Exposition_EcolePolytechnique_FeteDeLaScience_201910
58 reference(s)
51-RealNumbers.01.Fra
57 reference(s)		 52-FaireDesMathematiques.01.Fra
57 reference(s)
53-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
56 reference(s)		 54-LeParadoxeDeFermi.01.Fra
56 reference(s)
55-LeParadoxeDeFermi.01.Ang
56 reference(s)		 56-GoldenTriangle.01.Fra
56 reference(s)
57-Commentaires_DefinitionComplexes.01
56 reference(s)		 58-MathematiquesPhysiqueFractales.02.23
55 reference(s)
59-Commentaires_ProblemeDesNCorps.01
55 reference(s)		 60-Multivers.01.Fra
54 reference(s)
61-MathematiquesPhysiqueFractales.02.13
54 reference(s)		 62-LesCourbesRemplissantes.01.Ang
54 reference(s)
63-xiirv_____.nota.t.
53 reference(s)		 64-Notations_AppartientA.01
53 reference(s)
65-MathematiquesPhysiqueFractales.22
53 reference(s)		 66-HommageBenoitMandelbrot.21
53 reference(s)
67-GenieLogiciel_VisualisationScientifique.01.vv
53 reference(s)		 68-Galerie_SelfPortraits.FV
53 reference(s)
69-Galerie_QuantumMechanics.FV
53 reference(s)		 70-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
53 reference(s)
71-VirtualChaos.01.Ang
52 reference(s)		 72-MathematiquesPhysiqueFractales.02
52 reference(s)
73-IllusionConnaissance.02
52 reference(s)		 74-GoldenTriangle.01.Ang
52 reference(s)
75-Exposition_EcolePolytechnique_FeteDeLaScience_201810
52 reference(s)		 76-DieuScience.01.Ang
52 reference(s)
77-Commentaires_HyperCubeDimensionN.01
52 reference(s)		 78-Commentaires_EnsembleMandelbrotComplexe.01
52 reference(s)
79-Commentaires_DefinitionQuaternions.01
52 reference(s)		 80-AVirtualSpaceTimeTravelMachine.Fra
52 reference(s)
81-LesCourbesRemplissantes.02.Ang
51 reference(s)		 82-LesCourbesRemplissantes.01.Fra
51 reference(s)
83-LOG_xiMc.11
51 reference(s)		 84-ImpossibleStructures.01.Fra
51 reference(s)
85-Commentaires_HyperSphere.01
51 reference(s)		 86-VirtualChaos.01.Fra
50 reference(s)
87-PerteDeLaDistributivite.01.DIS2
50 reference(s)		 88-Notations_Logarithme.01
50 reference(s)
89-Galerie_Astrophysics.FV
50 reference(s)		 90-FloatingPointNumbers.01.Ang
50 reference(s)
91-Commentaires_VarieteQuadriDimensionnelleCalabiYau.01
50 reference(s)		 92-Commentaires_EnsembleMandelbrotQuaternion.01
50 reference(s)
93-Commentaires_EnsembleMandelbrotOctonion.01
50 reference(s)		 94-SourceExemple_____xrq_____hydrogene.61.K.
49 reference(s)
95-Notations_QuelQueSoit.01
49 reference(s)		 96-MathematiquesPhysiqueFractales.02.24
49 reference(s)
97-ManyChaos.01.Ang
49 reference(s)		 98-FaireDeLaRecherche.01.vv
49 reference(s)
99-ConjectureDeSyracuse_0256.vv
49 reference(s)		 100-Bard.01.Fra
49 reference(s)
101-AProposSite.01.Fra
49 reference(s)		 102-MathematiquesPhysiqueFractales.02.25
48 reference(s)
103-Labyrinthes.01.Fra
48 reference(s)		 104-GenieLogiciel.01.Ang
48 reference(s)
105-Galerie_Tributes.FV
48 reference(s)		 106-Exposition_MairieCinquiemeArrondissementParis_202001_202002
48 reference(s)
107-EntrelacsIntertwinings.01.Ang
48 reference(s)		 108-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_14
47 reference(s)
109-NombresEtLumiere.01.vv.Fra
47 reference(s)		 110-MathematiquesPhysiqueFractales.02.22
47 reference(s)
111-MathematiquesPhysiqueFractales.02.15
47 reference(s)		 112-MathematiquesPhysiqueFractales.02.14
47 reference(s)
113-Galerie_DeterministicChaos.FV
47 reference(s)		 114-ExpV_VirE.11
47 reference(s)
115-DecimalesPi_100000.vv
47 reference(s)		 116-BEST.20170828
47 reference(s)
117-An2000.01.Ang
47 reference(s)		 118-T_MathematiquesPhysiqueFractales.02.1_NumerotationDesRationnels.01.vv.Fra.0001
46 reference(s)
119-T_Cryptographie_Alphabet.01.vv.Fra.0002
46 reference(s)		 120-Notations_Union.01
46 reference(s)
121-MathematiquesPhysiqueFractales.02.12
46 reference(s)		 122-ManyChaos.01.Fra
46 reference(s)
123-IllusionConnaissance.01
46 reference(s)		 124-Commentaires_SystemeSolaire.01
46 reference(s)
125-Commentaires_DefinitionPseudoQuaternions.01
46 reference(s)		 126-catalogue.11
45 reference(s)
127-VisualisationRelief.01.vv.Fra
45 reference(s)		 128-RealNumbers.01.Ang
45 reference(s)

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




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