Monthly Best Of on 07/28/2022




The construction process of the von Koch curve -iteration 1: an equilateral triangle-

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 07/28/2022 and last updated on 11/14/2023 17:50:27 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Quantum vacuum fluctuations
1-146 reference(s)		 The foggy Babel Tower -a Tribute to Brueghel the Elder-
2-134 reference(s)		 A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
3-90 reference(s)		 Artistic view of the prime numbers
4-87 reference(s)
Autostereogram with an hidden volcano
5-84 reference(s)		 Quark and gluon structure of a nucleon
6-81 reference(s)		 Intertwining
7-74 reference(s)		 The generalized Ulam spiral
8-74 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
9-73 reference(s)		 Jean-François COLONNA (on 11/17/1994)with its fractal mountains
10-71 reference(s)		 The 1.000 first digits -base 10- of 'e' displayed on an helix -very bad point of view-
11-65 reference(s)		 Autostereogram with an hidden ring and ghost bows
12-64 reference(s)
Untitled 0599 -a Tribute to Robert & Sonia Delaunay-
13-64 reference(s)		 Bidimensional Sierpinski billiard with 16 random particles, with collisions and display of their gravity center -white particle-
14-63 reference(s)		 The Lorenz attractor
15-63 reference(s)		 Bidimensional clouds or height field
16-62 reference(s)
A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
17-61 reference(s)		 A 'tridimensional epicycloïdal' pseudo-torus
18-61 reference(s)		 Untitled 0267 -a Tribute to Piet Mondrian-
19-61 reference(s)		 Artistic view of the Big Bang
20-60 reference(s)
The random walk of photons escaping the Sun
21-60 reference(s)		 Regular quadrangulation of the volume of a cylinder -8x8x8-
22-60 reference(s)		 The definition of a monodimensional 'quasi-continuous' cellular automata
23-59 reference(s)		 A 'mixing' between a pseudo-quaternionic Mandelbrot set and a pseudo-quaternionic Julia set computed with A=(-0.58...,+0.63...,0,0)-tridimensional cross-section-
24-58 reference(s)
The Menger sponge -iteration 5-
25-57 reference(s)		 The Road to Chaos -06/19/2022-
26-56 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X2(...),Y2(...),Z2(...)} and based on an 'open' 3-foil torus knot -iteration 2-
27-56 reference(s)		 Tridimensional filamentous fractal structure
28-56 reference(s)
A tridimensional fractal manifold defined by means of three tridimensional fields
29-55 reference(s)		 Sixteen interlaced fractal torus
30-54 reference(s)		 Intertwining
31-53 reference(s)		 The 'hyperbolic tangent' of a sphere
32-53 reference(s)
The 'tangent' of a sphere
33-53 reference(s)		 A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-
34-53 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X2(...),Y2(...),Z2(...)} -iteration 2-
35-53 reference(s)		 Circular worm
36-53 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
37-53 reference(s)		 The Road to Chaos -06/19/2022-
38-52 reference(s)		 The same bidimensional scalar field displayed with 4 different color palettes
39-52 reference(s)		 K/LD Matrix -'Optimal_A1.03' measures-
40-52 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
41-52 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
42-52 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
43-51 reference(s)		 Botticelli anomaly on the Moon
44-51 reference(s)
Quark and gluon structure of a nucleon
45-51 reference(s)		 A tridimensional billiard starting with a Menger sponge -iteration 2-
46-51 reference(s)		 Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,...)obtained by means of a non deterministic fractal process
47-51 reference(s)		 Along the border of the Mandelbrot set
48-50 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
49-50 reference(s)		 Tridimensional self-portrait
50-50 reference(s)		 Distorsion of the Möbius strip
51-49 reference(s)		 A thin double spherical cross-section inside the Menger sponge -iteration 5-
52-49 reference(s)
Tridimensional filamentous fractal structure
53-49 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
54-49 reference(s)		 Distorsion of the Bonan-Jeener-Klein double bottle
55-49 reference(s)		 Distorsion of a sphere
56-48 reference(s)
The Sierpinski carpet -iteration 1 to 5-
57-48 reference(s)		 Cloudy Mandelbrot set
58-48 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
59-48 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
60-47 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
61-47 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 7-foil torus knot -iteration 3-
62-47 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} -iteration 3-
63-47 reference(s)		 A Tribute to Piet Mondrian and to David Hilbert
64-47 reference(s)
Happy new year 2000
65-47 reference(s)		 Distorsion of the Bonan-Jeener-Klein triple bottle
66-47 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
67-46 reference(s)		 Monument Valley at sunrise
68-46 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
69-46 reference(s)		 Distorsion of the Möbius strip
70-46 reference(s)		 Untitled 0597
71-46 reference(s)		 Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
72-46 reference(s)
Autostereogram with an hidden volcano and 64 self-portraits
73-46 reference(s)		 Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
74-46 reference(s)		 Tridimensional Hilbert Curve -iteration 4-
75-46 reference(s)		 The 'hyperbolic tangent' of a sphere
76-45 reference(s)
A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 5-foil torus knot -iteration 3-
77-45 reference(s)		 Foggy Monument Valley
78-45 reference(s)		 Table mountain
79-45 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-
80-45 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
81-45 reference(s)		 Anaglyph -blue=right, red=left- of a close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
82-45 reference(s)		 Tridimensional filamentous fractal structure
83-45 reference(s)		 The 'Earth' of a diffusion process obtained by means of a random walk process
84-45 reference(s)
Distorsion of the Bonan-Jeener-Klein double bottle
85-45 reference(s)		 The Universe at the heart of a Calabi-Yau manifold
86-44 reference(s)		 Autostereogram with an hidden volcano
87-44 reference(s)		 Distorsion of a sphere
88-44 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)
89-44 reference(s)		 The Menger sponge -iteration 4-
90-44 reference(s)		 Untitled 0258
91-44 reference(s)		 Electron-positron scattering
92-44 reference(s)
A distorded -for the sake of display- 5-cube -an hyperhypercube-
93-44 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
94-44 reference(s)		 A parallelepipedic extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
95-43 reference(s)		 Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
96-43 reference(s)
The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
97-43 reference(s)		 Anaglyph -blue=right, red=left- of a fractal polyhedron
98-43 reference(s)		 Tridimensional fractal structure
99-43 reference(s)		 A periodical tiling of the plane using squares
100-43 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
101-42 reference(s)		 A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-
102-42 reference(s)		 Untitled 0596
103-42 reference(s)		 Iterations in the complex plane
104-42 reference(s)
Tridimensional Hilbert Curve -iteration 3-
105-42 reference(s)		 Hypercube
106-42 reference(s)		 From the infinitely small to the infinitely big
107-42 reference(s)		 Untitled 0598 -a Tribute to Robert & Sonia Delaunay-
108-42 reference(s)
The Radical of the integer numbers from 2 to 257
109-42 reference(s)		 The 'tangent' of a sphere
110-41 reference(s)		 Bidimensional rectangular billiard with 4 random particles, with collisions and display of their gravity center -white particle-
111-41 reference(s)		 Distorsion of the Menger sponge -iteration 3-
112-41 reference(s)
The intersection of the Menger sponge -iteration 5- and of a quadridimensional Calabi-Yau manifold -tridimensional representation-
113-41 reference(s)		 An amazing cross-section inside the Menger sponge -iteration 5-
114-41 reference(s)		 Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
115-41 reference(s)		 Close-up on a foggy 'MandelBox' -tridimensional cross-section-
116-41 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
117-41 reference(s)		 Fractal diffusion front in a bidimensional medium obtained by means of a random walk process
118-41 reference(s)		 An aperiodic Penrose tiling of the plane
119-40 reference(s)		 Self-transformation of an arbitrary geometrical texture
120-40 reference(s)
The additive persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-
121-40 reference(s)		 A Bidimensional Hilbert-like Curve defined with {X5(...),Y5(...)} -iteration 5-
122-40 reference(s)		 Color palette 'pmc.53'
123-40 reference(s)		 A quaternionic Julia set -tridimensional cross-section-
124-40 reference(s)
The bidimensional Ising Model with 2-state spins, temperature=0.2 and random initial conditions -display of tilting sites only-
125-40 reference(s)		 Tridimensional fractal structure
126-40 reference(s)		 Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
127-40 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
128-40 reference(s)




2-The 128 most referenced Pages (*):

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



1-An2000.01.Fra
806 reference(s)		 2-AVirtualSpaceTimeTravelMachine.Ang
719 reference(s)
3-copyright.01.
597 reference(s)		 4-mail.01.vv
487 reference(s)
5-Informations_AboutPicturesAnimationsAndFiles.01.Ang
361 reference(s)		 6-Informations_AboutPicturesAnimationsAndFiles.01.Fra
344 reference(s)
7-Vcatalogue.11
318 reference(s)		 8-demo_14
121 reference(s)
9-help.
120 reference(s)		 10-Informations_GoodNewsAndBadNews.01.Fra
88 reference(s)
11-Galerie_GeneralitiesVisualization.FV
88 reference(s)		 12-VirtualChaos.01.Fra
87 reference(s)
13-Galerie_ArtisticCreation.FV
83 reference(s)		 14-MonodimensionalCellularAutomata.01.Ang
77 reference(s)
15-Galerie_TextureSynthesis.FV
73 reference(s)		 16-Galerie_ParticleSystems.FV
73 reference(s)
17-BEST.20170128
72 reference(s)		 18-NDimensionalDeterministicFractalSets.01.Fra
71 reference(s)
19-Fractal.11
71 reference(s)		 20-EntrelacsIntertwinings.01.Ang.DIAPO.0572
71 reference(s)
21-Galerie_FluidMechanics.FV
67 reference(s)		 22-Galerie_AnthropomorphicPatterns.FV
67 reference(s)
23-MonodimensionalCellularAutomata.01.Fra
65 reference(s)		 24-EntrelacsIntertwinings.01.Ang.DIAPO.0461
64 reference(s)
25-UlamSpiral.01.Fra
63 reference(s)		 26-SurfaceProjector.01.Fra
62 reference(s)
27-PerteDeLAssociativite.01
62 reference(s)		 28-Galerie_NumberTheory.FV
62 reference(s)
29-Fractal.01
62 reference(s)		 30-EntrelacsIntertwinings.01.Ang
62 reference(s)
31-Galerie_NewPictures.FV
61 reference(s)		 32-Galerie_CelestialMechanics.FV
61 reference(s)
33-AProposSite.01.Fra
61 reference(s)		 34-MathematiquesPhysiqueFractales.02.1
60 reference(s)
35-Galerie_ImagesDesMathematiques.FV
60 reference(s)		 36-EntrelacsIntertwinings.01.Ang.DIAPO.0257
60 reference(s)
37-ArtScience.11.Ang.DIAPO.0024
60 reference(s)		 38-SurfaceProjector.01.Ang
57 reference(s)
39-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
57 reference(s)		 40-Stereogrammes_AutoStereogrammes.01
56 reference(s)
41-EntrelacsIntertwinings.01.Fra
56 reference(s)		 42-NDimensionalDeterministicFractalSets.01.Ang
55 reference(s)
43-LOG_xiMc.11
55 reference(s)		 44-EntrelacsIntertwinings.01.Ang.DIAPO.0226
55 reference(s)
45-AVirtualSpaceTimeTravelMachine.Fra
55 reference(s)		 46-MathematiquesPhysiqueFractales.12
54 reference(s)
47-Galerie_ImagesDidactiques.FV
54 reference(s)		 48-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
53 reference(s)
49-GoldenTriangle.01.Fra
53 reference(s)		 50-EntrelacsIntertwinings.01.Ang.DIAPO.0366
53 reference(s)
51-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
53 reference(s)		 52-Galerie_DeterministicFractalGeometry.FV
52 reference(s)
53-EntrelacsIntertwinings.01.Ang.DIAPO.0215
52 reference(s)		 54-DecimalesPi_1_100.vv
52 reference(s)
55-ImpossibleStructures.01.Fra
51 reference(s)		 56-ImpossibleStructures.01.Ang
51 reference(s)
57-Galerie_FluidMechanics.DIAPO.0004
51 reference(s)		 58-Commentaires_DefinitionPseudoQuaternions.01
51 reference(s)
59-Exposition_EcolePolytechnique_FeteDeLaScience_201910
50 reference(s)		 60-GenieLogiciel_VisualisationScientifique.01.vv
49 reference(s)
61-Galerie_QuantumMechanics.FV
49 reference(s)		 62-EntrelacsIntertwinings.01.Ang.DIAPO.0566
49 reference(s)
63-EntrelacsIntertwinings.01.Ang.DIAPO.0517
49 reference(s)		 64-EntrelacsIntertwinings.01.Ang.DIAPO.0105
49 reference(s)
65-Galerie_SelfPortraits.FV
48 reference(s)		 66-Galerie_DeterministicFractalGeometry.DIAPO.0043
48 reference(s)
67-Galerie_DeterministicChaos.FV
48 reference(s)		 68-FloatingPointNumbers.01.Ang
48 reference(s)
69-Commentaires_Hyperboloide.01
48 reference(s)		 70-Galerie_SignalProcessing.FV
47 reference(s)
71-Galerie_DeterministicFractalGeometry
47 reference(s)		 72-FloatingPointNumbers.01.Fra
47 reference(s)
73-GoldenTriangle.01.Ang
46 reference(s)		 74-Informations_GoodNewsAndBadNews.01.Ang
45 reference(s)
75-BEST.20180428
45 reference(s)		 76-Galerie_NewPictures
44 reference(s)
77-Galerie_AnthropomorphicPatterns
44 reference(s)		 78-BEST.20151228
44 reference(s)
79-VisitesGaleriesEnfouies.01.Fra
43 reference(s)		 80-NatureDesMathematiques.01.vv.Fra
43 reference(s)
81-Galerie_ArtAndScience.FV
43 reference(s)		 82-EnsembleDesGaleries.DIAPO.0638
43 reference(s)
83-EnsembleDesGaleries.DIAPO.0559
43 reference(s)		 84-Commentaires_NautileDeJeener.01
43 reference(s)
85-Commentaires_DefinitionTransformeeDeFourier.01
43 reference(s)		 86-AnimFractal.01.
42 reference(s)
87-xiirv_____.nota.t.
41 reference(s)		 88-Galerie_Tributes.FV
41 reference(s)
89-Autostereograms.01.
41 reference(s)		 90-EntrelacsIntertwinings.01.Ang.DIAPO.0158
40 reference(s)
91-BEST.20141128
40 reference(s)		 92-present.01.
39 reference(s)
93-Kepler.02.
39 reference(s)		 94-ImagesEncadreesDisponibles.01
39 reference(s)
95-Galerie_NumbersAndLight.FV
39 reference(s)		 96-Fractal.21
39 reference(s)
97-EnsembleDesGaleries.DIAPO.0139
39 reference(s)		 98-OrdinateurMathematiquesArt.01.Fra
38 reference(s)
99-MathematiquesPhysiqueFractales.02
38 reference(s)		 100-ImagesDuVirtuel.01.Fra.FV
38 reference(s)
101-Fractal.03
38 reference(s)		 102-subject.01.
37 reference(s)
103-infinity.02.vv
37 reference(s)		 104-Web_Mail.01.vv
37 reference(s)
105-OrdinateursEtCalculs.01.Fra
37 reference(s)		 106-Galerie_DeterministicFractalGeometry.DIAPO.0028
37 reference(s)
107-Galerie_BestOf.FV
37 reference(s)		 108-ExpV_VirE.11
37 reference(s)
109-DieuScience.01.Fra
37 reference(s)		 110-BEST.20190128
37 reference(s)
111-catalogue.11
36 reference(s)		 112-LeParadoxeDeFermi.01.Ang
36 reference(s)
113-EntrelacsIntertwinings.01.Ang.DIAPO.0549
36 reference(s)		 114-EntrelacsIntertwinings.01.Ang.DIAPO.0503
36 reference(s)
115-EntrelacsIntertwinings.01.Ang.DIAPO.0413
36 reference(s)		 116-EntrelacsIntertwinings.01.Ang.DIAPO.0308
36 reference(s)
117-EnsembleDesGaleries.DIAPO.0496
36 reference(s)		 118-EnsembleDesGaleries.DIAPO.0189
36 reference(s)
119-DuModeleALImage.02.Fra
36 reference(s)		 120-DecimalesPi_100000.vv
36 reference(s)
121-FaireDeLaRecherche.01.vv
35 reference(s)		 122-EntrelacsIntertwinings.01.Ang.DIAPO.0066
35 reference(s)
123-BEST.20171228
35 reference(s)		 124-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_4
34 reference(s)
125-NombresPremiers_10000.vv
34 reference(s)		 126-LeParadoxeDeFermi.01.Fra
34 reference(s)
127-HommageBenoitMandelbrot.21
34 reference(s)		 128-ExpV_VirE.01.Fra
34 reference(s)

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Copyright © Jean-François COLONNA, 2022-2023.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2022-2023.