Monthly Best Of on 10/28/2023




A fractal polyhedron

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 10/28/2023 and last updated on 11/14/2023 17:50:45 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Artistic view of the prime numbers
1-127 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)
2-115 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
3-110 reference(s)		 A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
4-97 reference(s)
The random walk of photons escaping the Sun
5-96 reference(s)		 The Lorenz attractor
6-92 reference(s)		 The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
7-92 reference(s)		 A close-up of the 'EinStein' aperiodic 'Spectre' tiling
8-91 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
9-87 reference(s)		 The generalized Ulam spiral
10-85 reference(s)		 The journey of an Earth-like planet (dark blue)from Pluto (grey) to the Sun (yellow)
11-85 reference(s)		 The 'Mystic' made of two 'EinStein' aperiodic 'Spectre' tiles
12-82 reference(s)
Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
13-81 reference(s)		 Fractal Self-Portrait -a Tribute to René Magritte-
14-79 reference(s)		 Botticelli anomaly on the Moon
15-78 reference(s)		 A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
16-78 reference(s)
Jean-François COLONNA (on 11/17/1994)with its fractal mountains
17-78 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)
18-75 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)
19-74 reference(s)		 Fractal synthesis of mountains with vegetation and stormy clouds
20-74 reference(s)
Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
21-74 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
22-73 reference(s)		 A tridimensional fractal manifold defined by means of three tridimensional fields
23-73 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
24-73 reference(s)
Quantum vacuum fluctuations
25-72 reference(s)		 Along the border of the Mandelbrot set
26-72 reference(s)		 Tridimensional display of the 'EinStein' aperiodic 'Spectre' tiling
27-72 reference(s)		 An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
28-72 reference(s)
Alien
29-71 reference(s)		 Quark and gluon structure of a nucleon
30-71 reference(s)		 Quark and gluon structure of a nucleon
31-70 reference(s)		 Tridimensional representation of a hexadimensional Calabi-Yau manifold
32-70 reference(s)
Empty
33-69 reference(s)		 Mountains and fog
34-68 reference(s)		 The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 7-
35-68 reference(s)		 The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 5-
36-68 reference(s)
The Klein bottle described by means of a Bidimensional Hilbert Curve -iteration 7-
37-67 reference(s)		 The Mystic Island based on the level 3 cluster made of 7 'Spectre' level 2 clusters
38-66 reference(s)		 The Sierpinski carpet -iteration 1 to 5-
39-66 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
40-66 reference(s)
Generation of the 63x63 first Conway's surreal complex numbers
41-65 reference(s)		 True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
42-65 reference(s)		 The Mystic Island based on the level 3 cluster made of 8 'Spectre' level 2 clusters
43-65 reference(s)		 Untitled 0618
44-65 reference(s)
Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
45-65 reference(s)		 Monument Valley at sunrise
46-64 reference(s)		 Untitled 0155 -a Tribute to Yves Tanguy-
47-64 reference(s)		 Triple impossible staircase and a paradoxal structure
48-64 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-
49-64 reference(s)		 Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier-
50-63 reference(s)		 A medium with percolation -top to bottom- using the 8-connexity
51-63 reference(s)		 The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 5-
52-63 reference(s)
The Universe at the heart of a Calabi-Yau manifold
53-62 reference(s)		 Artistic view of the Big Bang
54-62 reference(s)		 The particle trajectories of bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to an attractive central field of gravity
55-62 reference(s)		 The journey of an Earth-like planet (dark blue)from Pluto (grey) to the Sun (yellow)
56-62 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)
57-62 reference(s)		 1-foil torus knot -obvious knot- on its torus and its asociated Möbius strip
58-62 reference(s)		 Quantum vacuum fluctuations
59-61 reference(s)		 Brownian motion of a few heavy slow particles inside a gaz of fast light particles with increasing mass ratio (heavy/light=1,10,100,1000)
60-61 reference(s)
A Tridimensional Hilbert-like Curve defined with {X2(...),Y2(...),Z2(...)} -iteration 2-
61-61 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the Mandelbrot set border -iteration 5-
62-61 reference(s)		 The journey of an Earth-like planet (green)in the Solar System
63-61 reference(s)		 The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
64-61 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
65-61 reference(s)		 Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
66-61 reference(s)		 The Bonan-Jeener-Klein triple bottle
67-61 reference(s)		 Fractal diffusion front in a bidimensional medium obtained by means of identical interacting particles
68-60 reference(s)
A sphere described by means of a Bidimensional Peano Curve -6 digits-
69-60 reference(s)		 Animation of a sunrise on mountains
70-60 reference(s)		 The same bidimensional scalar field displayed with 4 different color palettes
71-60 reference(s)		 An amazing cross-section inside the Menger sponge -iteration 5-
72-60 reference(s)
Close-up on a foggy 'MandelBox' -tridimensional cross-section-
73-60 reference(s)		 Some elementary symbols used to built labyrinths -with a big black ghost structure at pi/4-
74-60 reference(s)		 A 'crumpled' sphere described by means of a Bidimensional Hilbert Curve -iteration 7-
75-60 reference(s)		 Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
76-60 reference(s)
An aperiodic Penrose tiling of the plane -a Tribute to Piet Mondrian and Roger Penrose-
77-59 reference(s)		 The level 2 cluster made of 7 'Spectre' level 1 clusters with display of all the key-points making quadrilaterals (7 small and a big one)
78-59 reference(s)		 The Menger sponge -iteration 5-
79-59 reference(s)		 The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 6-
80-59 reference(s)
A 'fractal plane' with overhangings described by means of a Bidimensional Hilbert Curve -iteration 7-
81-59 reference(s)		 The numerical irreversibility of the bidimensional billiard -1376 particles-
82-58 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the von Koch Curve -iteration 4-
83-58 reference(s)		 The foggy Babel Tower -a Tribute to Brueghel the Elder-
84-58 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one marsian year -Earth point of view and zoom on the four first planets-
85-58 reference(s)		 The Solar System with a dark blue virtual planet -virtual planet point of view-
86-58 reference(s)		 Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
87-58 reference(s)		 A 'fractal plane' with overhangings described by means of a Bidimensional Hilbert-like Curve -iteration 6-
88-58 reference(s)
An aperiodic Penrose tiling of the Golden Decagon -a Tribute to Piet Mondrian and Roger Penrose-
89-57 reference(s)		 A simple geometrical periodical structure
90-57 reference(s)		 Localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
91-57 reference(s)		 A monodimensional 'quasi-continuous' cellular automaton
92-57 reference(s)
The alternative use of two elementary monodimensional binary cellular automata -168,165- with periodical white starting points -on the bottom line-
93-57 reference(s)		 A simple geometrical periodical structure
94-56 reference(s)		 The random walk of photons escaping the Sun
95-56 reference(s)		 From Pluto to the Sun (non linear scales)
96-56 reference(s)
Close-up on a foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
97-56 reference(s)		 The Lorenz attractor
98-56 reference(s)		 A blue sponge-tree -a Tribute to Yves Klein-
99-56 reference(s)		 2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
100-56 reference(s)
The tridimensional Ising Model with 2-state spins, temperature=0.1 and random initial conditions
101-56 reference(s)		 Light clouds at sunset
102-56 reference(s)		 Untitled 0616
103-56 reference(s)		 A bijection
104-56 reference(s)
A monodimensional 'quasi-continuous' cellular automaton
105-56 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-10.0,+20.0]x[-15.0,+15.0] (bird's-eye view)
106-55 reference(s)		 An aperiodic Penrose tiling of the plane -a Tribute to Piet Mondrian and Roger Penrose-
107-55 reference(s)		 Synthesis of tridimensional symmetrical geometrical textures
108-55 reference(s)
Quaternionic butterfly with extended arithmetics -a Tribute to Laurent Schwartz-
109-55 reference(s)		 Polar display of the ten digits -from 0 to 9-
110-55 reference(s)		 Beyond the Gate
111-55 reference(s)		 From Mars to the Sun -extrapolation-
112-55 reference(s)
Close-up on a foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
113-55 reference(s)		 Close-up on a foggy pseudo-quaternionic Mandelbrot set with a (1/O)^2 conformal transformation in the octonionic space -tridimensional cross-section-
114-55 reference(s)		 Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')with a 1/Z conformal transformation in the complex plane -tridimensional cross-section-
115-55 reference(s)		 Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
116-55 reference(s)
Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
117-55 reference(s)		 Happy new year 2000
118-55 reference(s)		 A Ball described by means of a Tridimensional Hilbert Curve -iteration 4-
119-55 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
120-55 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
121-55 reference(s)		 A monodimensional 'quasi-continuous' cellular automaton
122-55 reference(s)		 256 elementary monodimensional binary cellular automata with 1 white starting point (bottom left is the automata number 0 when top right is the number 255)
123-55 reference(s)		 16 complex Julia sets along the border of the Mandelbrot set with display of the iteration numbers
124-54 reference(s)
A torus described by means of a Bidimensional Peano Curve -8 digits-
125-54 reference(s)		 Mountains and light cloud dynamics -this sequence being periodical-
126-54 reference(s)		 The Solar System with a green virtual planet -virtual planet point of view-
127-54 reference(s)		 Tridimensional integration of the anisotropic gaussian Fourier filtering of a random field with a 2.pi rotation of the kernel
128-54 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
1596 reference(s)		 2-Vcatalogue.11
232 reference(s)
3-An2000.01.Fra
214 reference(s)		 4-help.
199 reference(s)
5-demo_14
186 reference(s)		 6-Informations_AboutPicturesAnimationsAndFiles.01.Ang
176 reference(s)
7-mail.01.vv
153 reference(s)		 8-copyright.01.
148 reference(s)
9-ChatGPT.01.Fra
126 reference(s)		 10-Web_Mail.01.vv
122 reference(s)
11-Galerie_NumberTheory.FV
116 reference(s)		 12-catalogue.11
115 reference(s)
13-AProposSite.01.Fra
111 reference(s)		 14-Galerie_ArtisticCreation.FV
97 reference(s)
15-LesCourbesRemplissantes.02.Fra
95 reference(s)		 16-Stereogrammes_AutoStereogrammes.01
90 reference(s)
17-xiirv_____.nota.t.
89 reference(s)		 18-Galerie_GeneralitiesVisualization.FV
89 reference(s)
19-Fractal.01
86 reference(s)		 20-MathematiquesPhysiqueFractales.02
85 reference(s)
21-AVirtualSpaceTimeTravelMachine.Fra
83 reference(s)		 22-Informations_GoodNewsAndBadNews.01.Fra
82 reference(s)
23-MathematiquesPhysiqueFractales.12
81 reference(s)		 24-ImagesDuVirtuel.01.Fra.FV
79 reference(s)
25-Galerie_ImagesDesMathematiques.FV
78 reference(s)		 26-Galerie_ArtAndScience.FV
78 reference(s)
27-MonodimensionalCellularAutomata.01.Fra
77 reference(s)		 28-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
77 reference(s)
29-GoldenTriangle.01.Ang
76 reference(s)		 30-GenieLogiciel_VisualisationScientifique.01.vv
76 reference(s)
31-FloatingPointNumbers.01.Fra
74 reference(s)		 32-SurfaceProjector.01.Ang
73 reference(s)
33-MathematiquesPhysiqueFractales.22
73 reference(s)		 34-Fractal.21
73 reference(s)
35-LOG_xiMc.11
72 reference(s)		 36-ImagesDuVirtuel.01.Fra
72 reference(s)
37-Galerie_DeterministicFractalGeometry.FV
71 reference(s)		 38-DecimalesDePi.01.Fra
71 reference(s)
39-Polynomials_RationalNumbers.01.Fra
70 reference(s)		 40-SurfaceProjector.01.Fra
69 reference(s)
41-NDimensionalDeterministicFractalSets.01.Fra
69 reference(s)		 42-Fractal.11
69 reference(s)
43-Galerie_ParticleSystems.FV
67 reference(s)		 44-EntrelacsIntertwinings.01.Fra
67 reference(s)
45-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
67 reference(s)		 46-PerteDeLAssociativite.01
65 reference(s)
47-NatureDesMathematiques.01.vv.Fra
65 reference(s)		 48-LeParadoxeDeFermi.01.Fra
65 reference(s)
49-Exposition_EcolePolytechnique_FeteDeLaScience_201910
65 reference(s)		 50-DieuScience.01.Fra
65 reference(s)
51-Galerie_Tributes.FV
64 reference(s)		 52-MathematiquesPhysiqueFractales.02.1
63 reference(s)
53-FloatingPointNumbers.01.Ang
63 reference(s)		 54-UlamSpiral.01.Fra
62 reference(s)
55-RealNumbers.01.Fra
62 reference(s)		 56-Galerie_CelestialMechanics.FV
62 reference(s)
57-Multivers.01.Fra
61 reference(s)		 58-MathematiquesPhysiqueFractales.02.15
61 reference(s)
59-GenieLogiciel.01.Fra
61 reference(s)		 60-Galerie_NewPictures.FV
61 reference(s)
61-DecimalesPi_1_100.vv
61 reference(s)		 62-infinity.02.vv
60 reference(s)
63-MathematiquesPhysiqueFractales.02.22
60 reference(s)		 64-Informations_AboutPicturesAnimationsAndFiles.01.Fra
60 reference(s)
65-GoldenTriangle.01.Fra
60 reference(s)		 66-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
59 reference(s)
67-Galerie_QuantumMechanics.FV
59 reference(s)		 68-ExpV_VirE.11
59 reference(s)
69-DecimalesPi_100000.vv
59 reference(s)		 70-AnimFractal.01.
59 reference(s)
71-present.01.
58 reference(s)		 72-VAcatalogue.11
58 reference(s)
73-MathematiquesPhysiqueFractales.02.23
58 reference(s)		 74-LesCourbesRemplissantes.01.Fra
58 reference(s)
75-FaireDesMathematiques.01.Fra
58 reference(s)		 76-OrdinateursEtCalculs.01.Fra
57 reference(s)
77-LesCourbesRemplissantes.01.Ang
57 reference(s)		 78-infinity.01.vv
56 reference(s)
79-IllusionConnaissance.02
56 reference(s)		 80-Notations_AppartientA.01
55 reference(s)
81-NombresPremiers_10000.vv
55 reference(s)		 82-MathematiquesPhysiqueFractales.02.27
55 reference(s)
83-MathematiquesPhysiqueFractales.02.21
54 reference(s)		 84-LeNoeudInfini.01.Fra
54 reference(s)
85-Labyrinthes.01.Fra
54 reference(s)		 86-Galerie_ImagesDidactiques.FV
54 reference(s)
87-Commentaires_DefinitionPseudoOctonions.01
54 reference(s)		 88-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_2
53 reference(s)
89-RemarquesCerveau.01
53 reference(s)		 90-MathematiquesPhysiqueFractales.02.28
53 reference(s)
91-MathematiquesPhysiqueFractales.02.24
53 reference(s)		 92-LesCourbesRemplissantes.02.Ang
53 reference(s)
93-Informations_GoodNewsAndBadNews.01.Ang
53 reference(s)		 94-Galerie_AnthropomorphicPatterns.FV
53 reference(s)
95-FaireDeLaRecherche.01.vv
53 reference(s)		 96-Galerie_TextureSynthesis.FV
52 reference(s)
97-Commentaires_VarieteHexaDecaDimensionnelleCalabiYau.01
52 reference(s)		 98-Commentaires_DefinitionPseudoQuaternions.01
52 reference(s)
99-RasoirDOccamEtMathematiques.01.vv.Fra
51 reference(s)		 100-PerteDeLAssociativite.01.MUL3
51 reference(s)
101-Notations_Intersection.01
51 reference(s)		 102-MathematiquesPhysiqueFractales.02.14
51 reference(s)
103-Galerie_BestOf.FV
51 reference(s)		 104-Galerie_SignalProcessing.FV
50 reference(s)
105-Commentaires_DefinitionQuaternions.01
50 reference(s)		 106-ArtScience.01
50 reference(s)
107-PerteDeLAssociativite.01.ADD3
49 reference(s)		 108-Pcatalogue.11
49 reference(s)
109-Exposition_EcolePolytechnique_FeteDeLaScience_201810
49 reference(s)		 110-Exposition_EcolePolytechnique_AnneeMondialeDeLaPhysique_2005
49 reference(s)
111-DieuScience.01.Ang
49 reference(s)		 112-Commentaires_VarieteQuadriDimensionnelleCalabiYau.01
49 reference(s)
113-Galerie_SelfPortraits.FV
48 reference(s)		 114-Galerie_DeterministicChaos.FV
48 reference(s)
115-Galerie_Astrophysics.FV
48 reference(s)		 116-Exposition_EcolePolytechnique_FeteDeLaScience_201510
48 reference(s)
117-Commentaires_EspaceLyapunovComplexe.01
48 reference(s)		 118-Commentaires_EnsembleMandelbrotOctonion.01
48 reference(s)
119-VisualisationRelief.01.vv.Fra
47 reference(s)		 120-MathematiquesPhysiqueFractales.02.3
47 reference(s)
121-JFC
47 reference(s)		 122-IllusionConnaissance.01
47 reference(s)
123-Fractal.02
47 reference(s)		 124-Exposition_MairieCinquiemeArrondissementParis_202001_202002
47 reference(s)
125-DuModeleALImage.02.Fra
47 reference(s)		 126-LeParadoxeDeFermi.01.Ang
46 reference(s)
127-ImpossibleStructures.01.Fra
46 reference(s)		 128-Commentaires_DefinitionOctonions.01
46 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.