Monthly Best Of on 12/28/2023




The 256 first digits -base 10- of 'pi' on a Bidimensional Hilbert Curve -iteration 4-

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 12/28/2023 and last updated on 01/29/2024 10:42:46 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Hypercube
1-189 reference(s)		 The eroded Menger Sponge -iteration 3-
2-109 reference(s)		 Artistic view of the prime numbers
3-100 reference(s)		 The first four iterations of the construction of the von Koch snowflake
4-76 reference(s)
A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
5-74 reference(s)		 The Universe at the heart of a Calabi-Yau manifold
6-69 reference(s)		 A close-up of the 'EinStein' aperiodic 'Spectre' tiling
7-69 reference(s)		 Tridimensional display of a Fractal Square -iteration 1 to 5-
8-61 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
9-60 reference(s)		 The 21 connected components of a Fractal Cube -iteration 1-
10-57 reference(s)		 Tridimensional display of the Mandelbrot Set obtained by means of a bidimensional Fractal Square -iteration 1 to 3-
11-56 reference(s)		 Merry Christmas 2023: A Fractal Cube -iteration 2-
12-55 reference(s)
The random walk of photons escaping the Sun
13-54 reference(s)		 A medium with percolation -top to bottom- using the 8-connexity
14-54 reference(s)		 The Sierpinski Carpet -iteration 1 to 5-
15-51 reference(s)		 The 94 connected components of a Fractal Square -iteration 4-
16-51 reference(s)
Tridimensional display of a Fractal Square -iteration 1 to 5-
17-51 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
18-51 reference(s)		 A Fractal Cube -iteration 2-
19-49 reference(s)		 A Tribute to Maria Callas
20-48 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
21-48 reference(s)		 The Menger Sponge -iteration 5-
22-47 reference(s)		 A 'crumpled' close-up of the 'EinStein' aperiodic 'Spectre' tiling
23-46 reference(s)		 Jean-François COLONNA (on 11/17/1994)with its fractal mountains
24-46 reference(s)
Tridimensional display of a Fractal Square -iteration 1 to 5-
25-46 reference(s)		 The 64 first lines of the Pascal's Triangle
26-45 reference(s)		 Untitled 0622
27-45 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
28-45 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
29-45 reference(s)		 The generalized Ulam spiral
30-44 reference(s)		 Quantum vacuum fluctuation dynamics
31-42 reference(s)		 Mountains and light cloud dynamics -this sequence being periodical-
32-42 reference(s)
Fractal Self-Portrait -a Tribute to René Magritte-
33-42 reference(s)		 Happy new year 2000
34-42 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
35-41 reference(s)		 Generation of the 63x63 first Conway's surreal complex numbers
36-41 reference(s)
The random walk of photons escaping the Sun
37-41 reference(s)		 Tridimensional display of the 'EinStein' aperiodic 'Spectre' tiling
38-41 reference(s)		 The Lorenz attractor
39-41 reference(s)		 Autostereogram with an hidden volcano
40-40 reference(s)
An aperiodic Penrose tiling of the plane
41-39 reference(s)		 24 evenly distributed points on a sphere by means of simulated annealing
42-39 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
43-39 reference(s)		 A periodical tiling of the plane using hexagons
44-39 reference(s)
The level-1 cluster made of 9 'Spectre' tiles with display of all the key-points making quadrilaterals (8 red small and a green big one)
45-38 reference(s)		 A spherical cross-section inside the Menger Sponge -iteration 5-
46-38 reference(s)		 Untitled 0620
47-38 reference(s)		 Untitled 0623
48-38 reference(s)
A Fractal Cube -iteration 2-
49-38 reference(s)		 Untitled 0619
50-37 reference(s)		 An Archimedes spiral displaying 1000 numbers
51-37 reference(s)		 Linear landscape interpolation
52-37 reference(s)
2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
53-37 reference(s)		 A Fractal Cube -iteration 2-
54-37 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
55-37 reference(s)		 Quark and gluon structure of a nucleon
56-36 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
57-36 reference(s)		 A random tiling of a square domain using dominoes (1x2 rectangles)-line after line-
58-36 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
59-36 reference(s)		 Untitled 0621
60-35 reference(s)
Botticelli anomaly on the Moon
61-34 reference(s)		 An extended Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
62-34 reference(s)		 An amazing cross-section inside the Menger Sponge -iteration 5-
63-34 reference(s)		 Happy new year 2000
64-34 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
65-34 reference(s)		 Tridimensional display of a Fractal Square -iteration 1 to 3-
66-34 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
67-34 reference(s)		 The Bonan-Jeener-Klein triple bottle
68-34 reference(s)
Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability
69-34 reference(s)		 Autostereogram with an hidden volcano
70-33 reference(s)		 The generalized Ulam spiral displaying 100 numbers
71-33 reference(s)		 Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
72-33 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
73-33 reference(s)		 Pseudo Olympic Rings
74-32 reference(s)		 The Ulam spiral with display of the first twin prime numbers ('2-twin' prime numbers)
75-32 reference(s)		 An Archimedes spiral displaying 100000 numbers
76-32 reference(s)
A Fractal Cube: an extended Menger Sponge -iteration 1-
77-32 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
78-32 reference(s)		 The Jeener-Klein triple bottle
79-32 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Pluto point of view-
80-31 reference(s)
The 126.646 first digits -base 6- of 'pi' displayed as an 'absolute' tridimensional random walk
81-31 reference(s)		 Pan on a quaternionic Julia set -tridimensional cross-sections-
82-31 reference(s)		 Iterations in the complex plane: the computation of the Mandelbrot set
83-31 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
84-31 reference(s)
The Goldbach conjecture
85-31 reference(s)		 A Fractal Square -iteration 5-
86-31 reference(s)		 An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
87-31 reference(s)		 A fractal vegetal structure -'the Knowledge Tree'-
88-30 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)
89-30 reference(s)		 The 'Mystic' made of two 'EinStein' aperiodic 'Spectre' tiles
90-30 reference(s)		 Particle collisions without energy loss in a bidimensional space with display of the velocity histogram
91-30 reference(s)		 The distances {Sun-Jupiter,Sun-Saturn,Sun-Uranus,Sun-Neptune} during one neptunian year
92-30 reference(s)
The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
93-30 reference(s)		 Empty
94-30 reference(s)		 Computation of the Lorenz attractor on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors)
95-30 reference(s)		 A Douady rabbit -a complex Julia set computed with A=(-0.13,+0.77)- with display of the arguments
96-30 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
97-30 reference(s)		 A Ball described by means of a Tridimensional Hilbert-like Curve -iteration 4-
98-30 reference(s)		 A Fractal Square -iteration 4-
99-30 reference(s)		 A Fractal Square -iteration 1-
100-30 reference(s)
The Jeener-Klein triple bottle
101-30 reference(s)		 Quantum vacuum fluctuations
102-29 reference(s)		 Generation of the 63 first Conway's surreal numbers
103-29 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
104-29 reference(s)
Untitled 0618
105-29 reference(s)		 An octogonal tiling of the hyperbolic Poincaré disk -iteration 5-
106-29 reference(s)		 Tridimensional zoom in on the Mandelbrot set
107-29 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-
108-29 reference(s)
The Birth of the Universe
109-29 reference(s)		 Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers-
110-29 reference(s)		 La Génèse (1974)
111-29 reference(s)		 A Fractal Cube -iteration 0-
112-29 reference(s)
The iterative process used to generate bidimensional fractal fields (16 iterations)
113-29 reference(s)		 My own quadruple impossible staircase -a Tribute to Maurits Cornelis Escher-
114-29 reference(s)		 Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
115-29 reference(s)		 From the infinitely small to the infinitely big
116-29 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
117-29 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
118-29 reference(s)		 IMAGE ET ORDINATEUR, PHOTO-REVUE, 05/1976, cover
119-29 reference(s)		 Quantum vacuum fluctuations
120-28 reference(s)
Artistic view of the Big Bang
121-28 reference(s)		 Tridimensional display of an aperiodic Penrose tiling of the plane with a fractal noise
122-28 reference(s)		 Along the border of the Mandelbrot set
123-28 reference(s)		 A punched paper tape
124-28 reference(s)
The 16.444 first digits -base 4- of 'pi' displayed as an 'absolute' bidimensional random walk
125-28 reference(s)		 The multiplicative persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-
126-28 reference(s)		 2.pi rotation about the Y axis of a pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
127-28 reference(s)		 A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
128-28 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
1903 reference(s)		 2-Vcatalogue.11
525 reference(s)
3-VAcatalogue.11
394 reference(s)		 4-demo_14
145 reference(s)
5-Pcatalogue.11
143 reference(s)		 6-Galerie_NumberTheory.FV
126 reference(s)
7-ImagesDuVirtuel.01.Fra.FV
122 reference(s)		 8-help.
92 reference(s)
9-Web_Mail.01.vv
88 reference(s)		 10-Galerie_GeneralitiesVisualization.FV
88 reference(s)
11-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
83 reference(s)		 12-Galerie_DeterministicFractalGeometry.FV
83 reference(s)
13-MorePages.Ang.
82 reference(s)		 14-Stereogrammes_AutoStereogrammes.01
78 reference(s)
15-Galerie_ArtisticCreation.FV
77 reference(s)		 16-GenieLogiciel_VisualisationScientifique.01.vv
76 reference(s)
17-MathematiquesPhysiqueFractales.22
74 reference(s)		 18-LOG_xiMc.11
69 reference(s)
19-xiirs_____.nota.t.
68 reference(s)		 20-Galerie_ImagesDesMathematiques.FV
66 reference(s)
21-AProposSite.01.Fra
65 reference(s)		 22-An2000.01.Fra
64 reference(s)
23-AVirtualSpaceTimeTravelMachine.Fra
64 reference(s)		 24-ChatGPT.01.Fra
62 reference(s)
25-xiirv_____.nota.t.
61 reference(s)		 26-MathematiquesPhysiqueFractales.12
61 reference(s)
27-Galerie_ArtAndScience.FV
61 reference(s)		 28-Galerie_ParticleSystems.FV
60 reference(s)
29-LeParadoxeDeFermi.01.Fra
59 reference(s)		 30-Informations_GoodNewsAndBadNews.01.Fra
58 reference(s)
31-Galerie_SelfPortraits.FV
56 reference(s)		 32-Polynomials_RationalNumbers.01.Fra
52 reference(s)
33-mail.01.vv
49 reference(s)		 34-catalogue.11
49 reference(s)
35-compressiondecompression_complexitestructurelle.cdcm4_a1.03
48 reference(s)		 36-ExpV_VirE.Ang
48 reference(s)
37-Fractal.01
47 reference(s)		 38-VCcatalogue.11
46 reference(s)
39-UlamSpiral.01.Fra
46 reference(s)		 40-UlamSpiral.01.Ang
46 reference(s)
41-Informations_GoodNewsAndBadNews.01.Ang
46 reference(s)		 42-copyright.01.
45 reference(s)
43-Informations_AboutPicturesAnimationsAndFiles.01.Ang
45 reference(s)		 44-FloatingPointNumbers.01.Fra
45 reference(s)
45-create.03.
43 reference(s)		 46-GoldenTriangle.01.Fra
43 reference(s)
47-Galerie_CelestialMechanics.FV
43 reference(s)		 48-Fractal.21
43 reference(s)
49-GenieLogiciel.01.Fra
42 reference(s)		 50-DuModeleALImage.02.Fra
42 reference(s)
51-MathematiquesPhysiqueFractales.02
41 reference(s)		 52-LesApprentisDieux.01
41 reference(s)
53-Bard.01.Fra
41 reference(s)		 54-present.01.
40 reference(s)
55-OrdinateurMathematiquesArt.01.Fra
40 reference(s)		 56-Galerie_NewPictures.FV
40 reference(s)
57-Fractal.11
40 reference(s)		 58-EntrelacsIntertwinings.01.Fra
39 reference(s)
59-AVirtualSpaceTimeTravelMachine.Ang.FV
39 reference(s)		 60-RealNumbers.01.Ang
38 reference(s)
61-relai_universel.01.vv
37 reference(s)		 62-LesCourbesRemplissantes.01.Fra
36 reference(s)
63-Fractal.03
36 reference(s)		 64-DecimalesPi_1_100.vv
36 reference(s)
65-DecimalesDePi.01.Fra
36 reference(s)		 66-NombresEtLumiere.01.vv.Fra
35 reference(s)
67-Galerie_ArtisticCreation.DIAPO.0203
35 reference(s)		 68-FloatingPointNumbers.01.Ang
35 reference(s)
69-ChatGPT.01.Ang
35 reference(s)		 70-Galerie_QuantumMechanics.FV
34 reference(s)
71-FaireDeLaRecherche.01.vv
34 reference(s)		 72-FaireConnaitre_FaireAimer_les_Mathematiques_en_2022.01.vv.Fra
34 reference(s)
73-ExpV_VirE.11
34 reference(s)		 74-RemarquesCerveau.01
33 reference(s)
75-MorePages.Fra.
33 reference(s)		 76-Galerie_ImagesDidactiques.FV
33 reference(s)
77-Galerie_ArtisticCreation.DIAPO.0205
33 reference(s)		 78-Galerie_ArtisticCreation.DIAPO.0204
33 reference(s)
79-DieuScience.01.Fra
33 reference(s)		 80-Commentaires_HyperSphere.01
33 reference(s)
81-MorePages.
32 reference(s)		 82-FaireDesMathematiques.01.Fra
32 reference(s)
83-PerteDeLAssociativite.01
31 reference(s)		 84-LeParadoxeDeFermi.01.Ang
31 reference(s)
85-Galerie_TextureSynthesis.FV
31 reference(s)		 86-GoldenTriangle.01.Ang
30 reference(s)
87-Galerie_Tributes.FV
30 reference(s)		 88-Galerie_ArtisticCreation.DIAPO.0202
30 reference(s)
89-Exposition_EcolePolytechnique_FeteDeLaScience_201910
30 reference(s)		 90-DieuScience.01.Ang
30 reference(s)
91-DecimalesPi_100000.vv
30 reference(s)		 92-Autostereograms.01.
30 reference(s)
93-OrdinateursEtCalculs.01.Fra
29 reference(s)		 94-NDimensionalDeterministicFractalSets.01.Ang.DIAPO.0381
29 reference(s)
95-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
29 reference(s)		 96-MonodimensionalCellularAutomata.01.Fra
29 reference(s)
97-Galerie_ArtisticCreation.DIAPO.0201
29 reference(s)		 98-Exposition_OperaDeMassy_201912_202001
29 reference(s)
99-RealNumbers.01.Fra
28 reference(s)		 100-Polynomials_RationalNumbers.01.Ang
28 reference(s)
101-NatureDesMathematiques.01.vv.Fra
28 reference(s)		 102-MonodimensionalCellularAutomata.01.Ang
28 reference(s)
103-MathematiquesModeleOutilArtiste.02.Ang
28 reference(s)		 104-Kepler.02.
28 reference(s)
105-ImagesDuVirtuel.01.Fra
28 reference(s)		 106-Galerie_CelestialMechanics.DIAPO.0021
28 reference(s)
107-Galerie_Astrophysics.FV
28 reference(s)		 108-AnimFractal.01.
28 reference(s)
109-demo_14.FV
27 reference(s)		 110-NDimensionalDeterministicFractalSets.01.Ang.DIAPO.0383
27 reference(s)
111-Galerie_ArtisticCreation.DIAPO.0196
27 reference(s)		 112-EntrelacsIntertwinings.01.Ang.DIAPO.0472
27 reference(s)
113-ArtScience.01
27 reference(s)		 114-xiac_____.nota.t.
26 reference(s)
115-NDimensionalDeterministicFractalSets.01.Ang.DIAPO.0379
26 reference(s)		 116-Galerie_SensitivityToRoundingOffErrors.FV
26 reference(s)
117-Galerie_ArtisticCreation.DIAPO.0197
26 reference(s)		 118-xDarchivesG__SMC__sources__procedures_____DEF_ITEM
25 reference(s)
119-NDimensionalDeterministicFractalSets.01.Ang.DIAPO.0375
25 reference(s)		 120-MathematiquesPhysiqueFractales.02.1
25 reference(s)
121-LesCourbesRemplissantes.02.Fra
25 reference(s)		 122-Galerie_DeterministicChaos.FV
25 reference(s)
123-EntrelacsIntertwinings.01.Ang.DIAPO.0515
25 reference(s)		 124-EntrelacsIntertwinings.01.Ang.DIAPO.0514
25 reference(s)
125-EntrelacsIntertwinings.01.Ang.DIAPO.0513
25 reference(s)		 126-EntrelacsIntertwinings.01.Ang.DIAPO.0473
25 reference(s)
127-AVirtualSpaceTimeTravelMachine.Fra.FV
25 reference(s)		 128-infinity.01.vv
24 reference(s)

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




Copyright © Jean-François COLONNA, 2023-2024.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2023-2024.