Monthly Best Of on 11/28/2023




Quaternionic butterfly with extended arithmetics -a Tribute to Laurent Schwartz-

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 11/28/2023 and last updated on 11/28/2023 22:09:04 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Artistic view of the prime numbers
1-149 reference(s)		 A 'crumpled' close-up of the 'EinStein' aperiodic 'Spectre' tiling
2-130 reference(s)		 The random walk of photons escaping the Sun
3-95 reference(s)		 A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
4-88 reference(s)
An arbitrary square trdimensional fractal Dendrite -iteration 3-
5-84 reference(s)		 The Lorenz attractor
6-72 reference(s)		 Along the border of the Mandelbrot set
7-71 reference(s)		 Untitled 0619
8-71 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
9-71 reference(s)		 The Simpson paradox
10-69 reference(s)		 The Universe at the heart of a Calabi-Yau manifold
11-68 reference(s)		 An amazing cross-section inside the Menger sponge -iteration 5-
12-68 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
13-68 reference(s)		 A close-up of the 'EinStein' aperiodic 'Spectre' tiling
14-67 reference(s)		 An Impossible Peace
15-67 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
16-67 reference(s)
A tridimensional fractal manifold defined by means of three tridimensional fields
17-66 reference(s)		 Quark and gluon structure of a nucleon
18-65 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)
19-65 reference(s)		 Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
20-64 reference(s)
An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
21-64 reference(s)		 The generalized Ulam spiral displaying 100 numbers
22-63 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the Mandelbrot set border -iteration 5-
23-63 reference(s)		 An amazing cross-section inside the Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
24-62 reference(s)
The Menger sponge -iteration 5-
25-62 reference(s)		 Jean-François COLONNA (on 11/17/1994)with its fractal mountains
26-62 reference(s)		 The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 6-
27-62 reference(s)		 The first four iterations of the construction of the von Koch snowflake
28-61 reference(s)
The generalized Ulam spiral
29-61 reference(s)		 A medium with percolation -top to bottom- using the 8-connexity
30-61 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
31-61 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
32-60 reference(s)
The Sierpinski carpet -iteration 1 to 5-
33-60 reference(s)		 24 evenly distributed points on a sphere by means of simulated annealing
34-60 reference(s)		 Mountains and fog
35-60 reference(s)		 Botticelli anomaly on the Moon
36-60 reference(s)
An Impossible Peace
37-60 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
38-60 reference(s)		 The Bonan-Jeener-Klein triple bottle
39-60 reference(s)		 The 'Mystic' made of two 'EinStein' aperiodic 'Spectre' tiles
40-59 reference(s)
Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
41-59 reference(s)		 Fractal Self-Portrait -a Tribute to René Magritte-
42-59 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
43-59 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X2(...),Y2(...),Z2(...)} -iteration 2-
44-58 reference(s)
The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 7-
45-58 reference(s)		 A punched paper tape
46-57 reference(s)		 Fractal 'celestial body' based on a torus with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
47-57 reference(s)		 The 126.646 first digits -base 6- of 'pi' displayed as an 'absolute' tridimensional random walk
48-57 reference(s)
Iterations in the complex plane: the computation of the Mandelbrot set
49-57 reference(s)		 The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 5-
50-57 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
51-57 reference(s)		 Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
52-56 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
53-56 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
54-56 reference(s)		 Untitled 0320
55-55 reference(s)		 Tridimensional display of the 'EinStein' aperiodic 'Spectre' tiling
56-55 reference(s)
Untitled 0155 -a Tribute to Yves Tanguy-
57-55 reference(s)		 Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
58-55 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
59-55 reference(s)		 Heterogeneous -tridimensional fractal field- random meshing of a cube
60-55 reference(s)
An aperiodic Penrose tiling of the plane
61-54 reference(s)		 The foggy Babel Tower -a Tribute to Brueghel the Elder-
62-54 reference(s)		 Fractal synthesis of mountains with vegetation and stormy clouds
63-54 reference(s)		 Mountains at sunrise
64-54 reference(s)
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) and with a 0 to pi rotation about the X axis -tridimensional cross-section-
65-54 reference(s)		 Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers-
66-54 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-10.0,+20.0]x[-15.0,+15.0]
67-53 reference(s)		 The random walk of photons escaping the Sun
68-53 reference(s)
Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier-
69-53 reference(s)		 Phase rotation of the wavelet transform of a bidimensional fractal field
70-53 reference(s)		 2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
71-53 reference(s)		 The Birth of the Universe
72-53 reference(s)
Tridimensional Hilbert Curve -iteration 3-
73-53 reference(s)		 An arbitrary square trdimensional fractal Dendrite -iteration 2-
74-53 reference(s)		 Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
75-52 reference(s)		 Artistic view of the Big Bang
76-52 reference(s)
The Mathematics are the key of the Multiverse
77-52 reference(s)		 A simple geometrical periodical structure
78-52 reference(s)		 Mountains and fog
79-52 reference(s)		 A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
80-52 reference(s)
The Klein bottle described by means of a Bidimensional non continous Hilbert-like Curve -iteration 5-
81-52 reference(s)		 The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 5-
82-52 reference(s)		 Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
83-52 reference(s)		 An arbitrary square trdimensional fractal Dendrite -iteration 2-
84-52 reference(s)
The level 2 cluster made of 8 'Spectre' level 1 clusters with display of all the key-points making quadrilaterals (8 small and a big one)
85-51 reference(s)		 Artistic view of gravitational waves
86-51 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} -iteration 1-
87-51 reference(s)		 7-foil torus knot on its torus
88-51 reference(s)
A 'fractal plane' with overhangings described by means of a Bidimensional Hilbert Curve -iteration 7-
89-51 reference(s)		 Hypercube
90-51 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
91-50 reference(s)		 The level 3 cluster made of 8 'Spectre' level 2 clusters with display of all the key-points making quadrilaterals (8 small and a big one)
92-50 reference(s)
Dynamics of the even distribution of 24 points on a sphere by means of simulated annealing
93-50 reference(s)		 Quark and gluon structure of a nucleon
94-50 reference(s)		 An arbitrary square trdimensional fractal Dendrite -iteration 3-
95-50 reference(s)		 Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
96-50 reference(s)
Bidimensional closed pseudo-self-avoiding brownian motion on the Klein bottle
97-50 reference(s)		 The Syracuse conjecture for U(0)={5,10,15,20,...,1310720}
98-49 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
99-49 reference(s)		 Pseudo Olympic Rings
100-49 reference(s)
A regular 8-gon -an octogon-
101-49 reference(s)		 Quaternionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-
102-49 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
103-49 reference(s)		 The Klein bottle
104-49 reference(s)
An aperiodic Penrose tiling of the plane -a Tribute to Piet Mondrian and Roger Penrose-
105-48 reference(s)		 The level-1 cluster made of 9 'Spectre' tiles with display of all the key-points making quadrilaterals (8 small and a big one)
106-48 reference(s)		 A 'fractal plane' with overhangings described by means of a Bidimensional Hilbert-like Curve -iteration 6-
107-48 reference(s)		 A 'crumpled' sphere described by means of a Bidimensional Hilbert Curve -iteration 7-
108-48 reference(s)
The golden binary tree
109-48 reference(s)		 About the fractal dimension with the first two iterations -red and magenta respectively- of the construction of the von Koch curve
110-47 reference(s)		 Quantum vacuum fluctuations
111-47 reference(s)		 Artistic view of an aperiodic Penrose tiling of the Golden Decagon
112-47 reference(s)
The Sierpinski carpet -iteration 3-
113-47 reference(s)		 A regular 5-gon -a pentagon-
114-47 reference(s)		 Mountains and light cloud dynamics -this sequence being periodical-
115-47 reference(s)		 Close-up on a foggy 'MandelBox' -tridimensional cross-section-
116-47 reference(s)
Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
117-47 reference(s)		 Maurits Cornelis Escher meets Piet Mondrian
118-47 reference(s)		 A Ball described by means of an 'open' 3-foil torus knot -iteration 4-
119-47 reference(s)		 The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 5-
120-47 reference(s)
The Jeener hypocycloidal snail
121-47 reference(s)		 Universe or Multiverse -The fractal Universe-?
122-46 reference(s)		 An aperiodic Penrose tiling of the plane
123-46 reference(s)		 The Ulam spiral with display of the first twin prime numbers ('2-twin' prime numbers)
124-46 reference(s)
A half-random extended Menger sponge -iteration 5-
125-46 reference(s)		 The Goldbach conjecture
126-46 reference(s)		 An arbitrary square trdimensional fractal Dendrite -iteration 2-
127-46 reference(s)		 A random tiling of a square domain using dominoes (1x2 rectangles)-line after line- with display of clusters of vertical rectangles using the 4-connexity
128-46 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
1482 reference(s)		 2-Vcatalogue.11
276 reference(s)
3-VAcatalogue.11
167 reference(s)		 4-Stereogrammes_AutoStereogrammes.01
151 reference(s)
5-help.
148 reference(s)		 6-demo_14
144 reference(s)
7-ChatGPT.01.Fra
138 reference(s)		 8-An2000.01.Fra
122 reference(s)
9-Galerie_DeterministicFractalGeometry.FV
120 reference(s)		 10-mail.01.vv
116 reference(s)
11-copyright.01.
113 reference(s)		 12-catalogue.11
105 reference(s)
13-Web_Mail.01.vv
104 reference(s)		 14-ImagesDuVirtuel.01.Fra.FV
102 reference(s)
15-Galerie_NumberTheory.FV
101 reference(s)		 16-AProposSite.01.Fra
94 reference(s)
17-LesCourbesRemplissantes.02.Fra
91 reference(s)		 18-Galerie_GeneralitiesVisualization.FV
89 reference(s)
19-AVirtualSpaceTimeTravelMachine.Fra
89 reference(s)		 20-LOG_xiMc.11
86 reference(s)
21-Galerie_ArtisticCreation.FV
86 reference(s)		 22-Fractal.11
83 reference(s)
23-Informations_GoodNewsAndBadNews.01.Fra
80 reference(s)		 24-Informations_AboutPicturesAnimationsAndFiles.01.Ang
79 reference(s)
25-Polynomials_RationalNumbers.01.Fra
78 reference(s)		 26-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
77 reference(s)
27-Galerie_ParticleSystems.FV
75 reference(s)		 28-FloatingPointNumbers.01.Fra
74 reference(s)
29-GenieLogiciel_VisualisationScientifique.01.vv
72 reference(s)		 30-EntrelacsIntertwinings.01.Fra
72 reference(s)
31-Pcatalogue.11
71 reference(s)		 32-xiirv_____.nota.t.
70 reference(s)
33-Galerie_ArtAndScience.FV
70 reference(s)		 34-UlamSpiral.01.Fra
68 reference(s)
35-GoldenTriangle.01.Ang
68 reference(s)		 36-Galerie_ImagesDesMathematiques.FV
68 reference(s)
37-Fractal.21
68 reference(s)		 38-Fractal.01
68 reference(s)
39-MonodimensionalCellularAutomata.01.Fra
67 reference(s)		 40-MathematiquesPhysiqueFractales.12
67 reference(s)
41-Galerie_CelestialMechanics.FV
65 reference(s)		 42-Exposition_EcolePolytechnique_FeteDeLaScience_201910
65 reference(s)
43-Bard.01.Ang
65 reference(s)		 44-Galerie_BestOf.FV
64 reference(s)
45-DecimalesDePi.01.Fra
64 reference(s)		 46-NDimensionalDeterministicFractalSets.01.Fra
62 reference(s)
47-FloatingPointNumbers.01.Ang
62 reference(s)		 48-create.03.
61 reference(s)
49-MathematiquesPhysiqueFractales.22
61 reference(s)		 50-GoldenTriangle.01.Fra
61 reference(s)
51-Galerie_DeterministicChaos.FV
61 reference(s)		 52-RealNumbers.01.Fra
60 reference(s)
53-IllusionConnaissance.02
60 reference(s)		 54-Galerie_QuantumMechanics.FV
60 reference(s)
55-DieuScience.01.Ang
60 reference(s)		 56-Galerie_NewPictures.FV
59 reference(s)
57-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
59 reference(s)		 58-present.01.
58 reference(s)
59-LesCourbesRemplissantes.01.Fra
58 reference(s)		 60-GenieLogiciel.01.Fra
58 reference(s)
61-Galerie_TextureSynthesis.FV
58 reference(s)		 62-ExpV_VirE.11
58 reference(s)
63-UlamSpiral.01.Ang
57 reference(s)		 64-PerteDeLAssociativite.01
57 reference(s)
65-Kepler.02.
57 reference(s)		 66-Galerie_SelfPortraits.FV
57 reference(s)
67-DecimalesPi_1_100.vv
57 reference(s)		 68-SurfaceProjector.01.Fra
56 reference(s)
69-OrdinateursEtCalculs.01.Fra
56 reference(s)		 70-MathematiquesPhysiqueFractales.02
56 reference(s)
71-LesApprentisDieux.01
56 reference(s)		 72-ImagesDuVirtuel.01.Fra
56 reference(s)
73-Galerie_Tributes.FV
56 reference(s)		 74-Galerie_Astrophysics.FV
56 reference(s)
75-LeParadoxeDeFermi.01.Ang
55 reference(s)		 76-Bard.01.Fra
55 reference(s)
77-subject.01.
54 reference(s)		 78-MorePages.Ang.
54 reference(s)
79-AnimFractal.01.
54 reference(s)		 80-infinity.02.vv
53 reference(s)
81-RemarquesCerveau.01
53 reference(s)		 82-Galerie_ImagesDidactiques.FV
53 reference(s)
83-DieuScience.01.Fra
53 reference(s)		 84-OrdinateurMathematiquesArt.01.Fra
52 reference(s)
85-LeParadoxeDeFermi.01.Fra
52 reference(s)		 86-ImpossibleStructures.01.Fra
52 reference(s)
87-Fractal.03
52 reference(s)		 88-infinity.01.vv
51 reference(s)
89-Spheres.01
51 reference(s)		 90-MonodimensionalCellularAutomata.01.Ang
51 reference(s)
91-ImagesEncadreesDisponibles.01
51 reference(s)		 92-Exposition_OperaDeMassy_201912_202001
51 reference(s)
93-DecimalesPi_100000.vv
51 reference(s)		 94-NombresPremiers_10000.vv
50 reference(s)
95-Multivers.01.Fra
50 reference(s)		 96-MartiensEtMathematiques.01.Fra
50 reference(s)
97-LesCourbesRemplissantes.01.Ang
50 reference(s)		 98-Informations_GoodNewsAndBadNews.01.Ang
50 reference(s)
99-Galerie_SignalProcessing.FV
50 reference(s)		 100-SurfaceProjector.01.Ang
49 reference(s)
101-NombresEtLumiere.01.vv.Fra
49 reference(s)		 102-Commentaires_HyperSphere.01
49 reference(s)
103-NatureDesMathematiques.01.vv.Fra
48 reference(s)		 104-NDimensionalDeterministicFractalSets.01.Ang
48 reference(s)
105-Galerie_FluidMechanics.FV
48 reference(s)		 106-FaireDeLaRecherche.01.vv
48 reference(s)
107-Commentaires_SpiraleJeenerBottle.01
48 reference(s)		 108-Autostereograms.01.
48 reference(s)
109-xiirs_____.nota.t.
47 reference(s)		 110-VirtualChaos.01.Fra
47 reference(s)
111-Exposition_MairieCinquiemeArrondissementParis_202001_202002
47 reference(s)		 112-EntrelacsIntertwinings.01.Ang
47 reference(s)
113-DuModeleALImage.02.Fra
47 reference(s)		 114-ConjectureDeSyracuse_0256.vv
47 reference(s)
115-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
46 reference(s)		 116-Exposition_EcolePolytechnique_FeteDeLaScience_201810
46 reference(s)
117-Commentaires_EnsembleMandelbrotOctonion.01
46 reference(s)		 118-PatrimoineHumanite.02.Fra
45 reference(s)
119-MathematiquesModeleOutilArtiste.02.Ang
45 reference(s)		 120-ManyChaos.01.Ang
45 reference(s)
121-LeNoeudInfini.01.Ang
45 reference(s)		 122-ArtScience.11.Ang
45 reference(s)
123-VCcatalogue.11
44 reference(s)		 124-ManyChaos.01.Fra
44 reference(s)
125-LeNoeudInfini.01.Fra
44 reference(s)		 126-Fractal.02
44 reference(s)
127-Exposition_EcolePolytechnique_FeteDeLaScience_201510
44 reference(s)		 128-Downloading.01.vv
44 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.