Monthly Best Of on 02/28/2025




Intertwining

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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[Please, visit A Virtual Machine for Exploring Space-Time and Beyond, the place where you can find more than 10.000 pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 02/28/2025 and last updated on 02/28/2025 22:11:35 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-422 reference(s)		The 4 first decimals -base 10- of 'pi' on a Bidimensional Hilbert Curve -iteration 1-
2-352 reference(s)		Y2K
3-272 reference(s)		The prime numbers among the 16 first integer numbers on a Bidimensional Hilbert Curve -iteration 2-
4-257 reference(s)
Visualization of the density iso-surfaces (density=0.58)during a tridimensional diffusion process of 114299 particles
5-238 reference(s)		K/LD Matrix -'PNG_A1.02' measures-
6-228 reference(s)		An artistic variation of a monodimensional 'quasi-continuous' cellular automata with random perturbation of the rules
7-199 reference(s)		Distorsion of the Bonan-Jeener-Klein double bottle
8-165 reference(s)
Jean-François COLONNA (on 11/17/1994)with its fractal mountains
9-163 reference(s)		K/LD Matrix -'JPEG2000_Divers.01' measures-
10-155 reference(s)		A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -20.000 digits, -base 10- with 10.000 time steps
11-151 reference(s)		The 'hyperbolic cosine' of a sphere
12-145 reference(s)
From Pluto to the Sun
13-144 reference(s)		The bidimensional field defining the three coordinates of a 'crumpled' sphere
14-134 reference(s)		Segmentation of a picture by means of the local fractal dimension
15-133 reference(s)		K/LD Matrix -'Optimal_CDC_E.01' measures-
16-131 reference(s)
A missed journey from the Earth to Mars starting on 01/01/1950 AD, velocity=10.000 m/s
17-129 reference(s)		A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-
18-127 reference(s)		Fractal 3-foil torus knot
19-127 reference(s)		A succesful journey from the Earth to Mars starting on 01/01/1950 AD, velocity=27.900 m/s, duration=270 days
20-126 reference(s)
K/LD Matrix -'PNG_Z.01' measures-
21-123 reference(s)		The 'J' elementary symbol used to built impossible structures
22-123 reference(s)		The 500 first digits of 'pi/5' displayed as an Impossible Structure
23-121 reference(s)		Autostereogram with an hidden volcano
24-120 reference(s)
Homogeneous random non linear meshing of a cube
25-119 reference(s)		K/LD Matrix -'Optimal_Random.01' measures-
26-118 reference(s)		The construction of the Klein bottle described by means of a Bidimensional Hilbert Curve -iteration 7-
27-118 reference(s)		Tridimensional display of a spiral displaying 'pi' with 4.000 digits -base 10-
28-117 reference(s)
The DNA of Mathematics -the 480 first digits of 'pi' and '2.pi'-
29-113 reference(s)		Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability -display of the Oxygen density-
30-111 reference(s)		Homogeneous/heterogeneous meshing of a square
31-110 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
32-105 reference(s)
The random walk of photons escaping the Sun
33-105 reference(s)		The generalized Ulam spiral
34-104 reference(s)		Circular worm
35-103 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
36-101 reference(s)
A simple geometrical periodical structure
37-100 reference(s)		Heterogeneous -tridimensional gaussian field- random meshing of a cube
38-100 reference(s)		Cauliflowers, seaweeds, shells,...
39-98 reference(s)		K/LD Matrix -'CDCM2_CDC_1.01' measures-
40-97 reference(s)
The Sierpinski Carpet -iteration 1 to 5-
41-96 reference(s)		K/LD Matrix -'JPEG2000_ZB_ZC.01' measures-
42-96 reference(s)		The construction of a tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
43-95 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
44-95 reference(s)
Along the border of the Mandelbrot set
45-94 reference(s)		The bidimensional field defining the 'Z' coordinate of a 'fractal plane' with overhangings
46-94 reference(s)		The 16 most referenced pictures on 10/14/1997
47-94 reference(s)		The 500 first digits of 'pi/3' displayed as an Impossible Structure
48-93 reference(s)
K/LD Matrix -'PNG_CDC_D__CDC_E.01' measures-
49-93 reference(s)		Anaglyph of a close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
50-92 reference(s)		A fractal polyhedron
51-92 reference(s)		The construction of a tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
52-90 reference(s)
K/LD Matrix -'CDCM4_Y.01' measures-
53-90 reference(s)		Visualization of the density iso-surfaces (density=0.07)during a tridimensional diffusion process of 114299 particles
54-90 reference(s)		Fractal Self-Portrait -a Tribute to René Magritte-
55-89 reference(s)		Visualization of the density iso-surfaces (density=0.22)during a tridimensional diffusion process of 114299 particles
56-89 reference(s)
Distorsion of the Bonan-Jeener-Klein double bottle
57-89 reference(s)		The first four iterations of the construction of the von Koch snowflake
58-88 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
59-88 reference(s)		Fractal 3-foil torus knot
60-88 reference(s)
Recursive intertwining
61-87 reference(s)		Autostereogram of the CMAP
62-87 reference(s)		Along the border of the Mandelbrot set
63-84 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
64-84 reference(s)
Bidimensional Mandelbrot billiard with 64 isotropic particles and without collisions
65-84 reference(s)		The prime numbers among the 256 first integer numbers on a Bidimensional Hilbert Curve -iteration 4-
66-84 reference(s)		Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
67-84 reference(s)		The bidimensional field defining the three coordinates of a 'crumpled' torus
68-83 reference(s)
Artistic view of the prime numbers
69-83 reference(s)		Tridimensional fractal Self-Portrait
70-82 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-
71-82 reference(s)		The 16 most referenced pictures on 01/30/1996
72-82 reference(s)
The Ptolemaic system with a moving equant -grey circle above the Earth- with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend-
73-81 reference(s)		K/LD Matrix -'bzip2_E2.01' measures-
74-80 reference(s)		A quaternionic Julia set -tridimensional cross-section-
75-80 reference(s)		The construction of the bidimensional Hilbert Curve -iteration 3-
76-80 reference(s)
Distorsion of the Möbius strip
77-79 reference(s)		K/LD Matrix -'CDCM2_Y.01' measures-
78-79 reference(s)		Fractal diffusion front in a bidimensional medium obtained by means of a random walk process
79-79 reference(s)		A distorded -for the sake of display- 5-cube -an hyperhypercube-
80-79 reference(s)
The Bonan-Jeener-Klein triple bottle
81-79 reference(s)		The Sierpinski Carpet -iteration 3-
82-78 reference(s)		Visualization by means of a set of 4x3 stereograms of the density iso-surfaces (density=0.58)during a tridimensional diffusion process of 128312 particles
83-77 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
84-76 reference(s)
The Klein bottle
85-76 reference(s)		Binary self-portrait
86-75 reference(s)		Tridimensional visualization of the Verhulst dynamics with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
87-74 reference(s)		Rotation about the X axis of the Lorenz attractor (1000 iterations), computed simultaneously on two different computers
88-74 reference(s)
The Ptolemaic system with equant -grey circle above the Earth- with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend-
89-74 reference(s)		Foggy island
90-74 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
91-74 reference(s)		Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability
92-72 reference(s)
Double random triangulation of the volume of a sphere -8x8x8-
93-71 reference(s)		The bidimensional field defining the 'Z' coordinate of a Fourier interpolation between a 'double sphere' and the Bonan-Jeener-Klein triple bottle
94-70 reference(s)		The Menger Sponge -iteration 5-
95-70 reference(s)		Regular quadrangulation of the surface of a cylinder -18x18-
96-70 reference(s)
France covered with digits
97-70 reference(s)		The random walk of photons escaping the Sun
98-69 reference(s)		Quark and gluon structure of a nucleon
99-69 reference(s)		The Legendre Conjecture with 0 < n < 201
100-69 reference(s)
The Ptolemaic system with equant -grey circle above the Earth- with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend-
101-69 reference(s)		The 'Islands' of a diffusion process obtained by means of a random walk process
102-69 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)
103-68 reference(s)		Autostereogram of 8 color-multiplexed quaternionic Julia sets -tridimensional cross-sections-
104-67 reference(s)
Visualization by means of a set of 4x3 stereograms of the density iso-surfaces (density=0.73)during a tridimensional diffusion process of 128312 particles
105-67 reference(s)		The set of bidimensional fields defining the 'Y' coordinate of an interpolation between a rectangle and a cylinder
106-66 reference(s)		The 500 first digits of 'pi/7' displayed as an Impossible Structure
107-66 reference(s)		Quark and gluon structure of a nucleon
108-66 reference(s)
The Legendre Conjecture with 0 < n < 51 and display of Prime Number alignments
109-66 reference(s)		The construction of the bidimensional Hilbert Curve -iteration 4-
110-66 reference(s)		The dynamics of the diffusion process in a bidimensional medium obtained by means of a random walk process
111-66 reference(s)		Untitled 0637
112-66 reference(s)
Visualization by means of a set of 4x3 stereograms of the density iso-surfaces (density=0.03)during a tridimensional diffusion process of 128312 particles
113-65 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
114-64 reference(s)		A one sheet hyperboloid of revolution -negative curvature-
115-64 reference(s)		The construction of the tridimensional Hilbert Curve -iteration 3-
116-64 reference(s)
Tridimensional fractal structure
117-64 reference(s)		The Ulam spiral
118-63 reference(s)		Color palette 'cercle.35'
119-63 reference(s)		The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
120-63 reference(s)
An half-random extended Menger Sponge -iteration 3-
121-63 reference(s)		Bidimensional zoom in on the Mandelbrot set
122-63 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-
123-62 reference(s)		K/LD Matrix -'PNG_CDC_1.01' measures-
124-62 reference(s)
Random quadrangulation of the surface of a torus -18x18-
125-62 reference(s)		Tridimensional visualization of an aperiodic Penrose tiling of the Golden Decagon
126-61 reference(s)		Autostereogram with an hidden volcano
127-61 reference(s)		The Eratosthene sieve displaying 10x10 numbers
128-61 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
2018 reference(s)		2-help.
728 reference(s)
3-Exposition_EcolePolytechnique_CentenaireNaissanceBenoitMandelbrot_202410_202411_202412
610 reference(s)		4-Galerie_DeterministicFractalGeometry.FV
447 reference(s)
5-Definitions_4_connexite.01
343 reference(s)		6-CompressionDeCompression_ComplexiteStructurelle.PNG_B4.01
332 reference(s)
7-CompressionDeCompression_ComplexiteStructurelle.PNG_ZP.01
279 reference(s)		8-Web_Mail.01.vv
242 reference(s)
9-CompressionDeCompression_ComplexiteStructurelle.PNG_A1.02
216 reference(s)		10-Galerie_ParticleSystems.FV
197 reference(s)
11-mail.01.vv
187 reference(s)		12-Galerie_NumberTheory.FV
183 reference(s)
13-Commentaires_ModeleIsingTriDimensionnel.01
162 reference(s)		14-Vcatalogue.11
156 reference(s)
15-copyright.01.
135 reference(s)		16-An2000.01.Fra
126 reference(s)
17-Stereogrammes_AutoStereogrammes.01
120 reference(s)		18-demo_14
113 reference(s)
19-Informations_GoodNewsAndBadNews.01.Fra
106 reference(s)		20-FloatingPointNumbers.01.Ang
103 reference(s)
21-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
101 reference(s)		22-Informations_AboutPicturesAnimationsAndFiles.01.Ang
99 reference(s)
23-AVirtualSpaceTimeTravelMachine.Fra
99 reference(s)		24-Informations_GoodNewsAndBadNews.01.Ang
97 reference(s)
25-CompressionDeCompression_ComplexiteStructurelle.PNG_A1.03
94 reference(s)		26-ChatGPT.01.Fra
93 reference(s)
27-Galerie_Animations.FV
92 reference(s)		28-Definitions_8_connexite.01
90 reference(s)
29-LOG_xiMc.11
89 reference(s)		30-Informations_AboutPicturesAnimationsAndFiles.01.Fra
88 reference(s)
31-avirtualspacetimetravelmachine.ang
87 reference(s)		32-IAGenerativesImages.01.Fra
86 reference(s)
33-DeepSeek.01.Fra
84 reference(s)		34-ChatGPT.11.Fra
81 reference(s)
35-xiirC_____.nota.t.
78 reference(s)		36-PerteDeLAssociativite.01.MUL3
78 reference(s)
37-CompressionDeCompression_ComplexiteStructurelle.PNG_C2.01
78 reference(s)		38-UlamSpiral.01.Fra
77 reference(s)
39-ImagesDuVirtuel.01.Fra.FV
75 reference(s)		40-LesNombresTranscendants.01.Fra
74 reference(s)
41-xtp_____AXmB.01.python.
73 reference(s)		42-MathematiquesPhysiqueFractales.02
73 reference(s)
43-IAGenerativesImages.01.Ang
73 reference(s)		44-xiirv_____.nota.t.
71 reference(s)
45-SIlVousPlaitDessineMoiLInfini.01.Fra
70 reference(s)		46-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
70 reference(s)
47-LesNombresTranscendants.01.Ang
69 reference(s)		48-FloatingPointNumbers.01.Fra
69 reference(s)
49-Fractal.01
68 reference(s)		50-CompressionDeCompression_ComplexiteStructurelle.PNG_E2.01
68 reference(s)
51-Galerie_IdMCNRS.FV
67 reference(s)		52-NDimensionalDeterministicFractalSets.01.Ang
66 reference(s)
53-CompressionDeCompression_ComplexiteStructurelle.PNG_I1.01
66 reference(s)		54-An2000.03.Fra
66 reference(s)
55-Galerie_ImagesEssentiellesDesMathematiques.FV
64 reference(s)		56-CompressionDeCompression_ComplexiteStructurelle.PNG_ZK.01
64 reference(s)
57-xiav_____.nota.t.
63 reference(s)		58-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis
63 reference(s)
59-AProposSite.01.Fra
63 reference(s)		60-VCcatalogue.11
62 reference(s)
61-SourceExemple_____xtc_____stereogra.01.c.
62 reference(s)		62-LesCourbesRemplissantes.01.Fra
62 reference(s)
63-ChatGPT.11.Ang
62 reference(s)		64-LesCourbesRemplissantes.02.Fra
61 reference(s)
65-fractal.01
60 reference(s)		66-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
60 reference(s)
67-SurfaceProjector.01.Ang
58 reference(s)		68-MorePages.Ang.
57 reference(s)
69-MathematiquesPhysiqueFractales.12
57 reference(s)		70-ComplexiteStructurelleClassements.11
57 reference(s)
71-Autostereograms.01.
57 reference(s)		72-UlamSpiral.01.Ang
56 reference(s)
73-MathematiquesPhysiqueFractales.22
56 reference(s)		74-Galerie_ImagesDesMathematiques.FV
56 reference(s)
75-Galerie_CelestialMechanics.FV
56 reference(s)		76-MesExpositionsPassees.01
55 reference(s)
77-Fractal.21
55 reference(s)		78-Exposition_EcolePolytechnique_FeteDeLaScience_201910
55 reference(s)
79-CompressionDeCompression_ComplexiteStructurelle.PNG_ZL.01
55 reference(s)		80-LesApprentisDieux.01
54 reference(s)
81-Galerie_GeneralitiesVisualization.FV
54 reference(s)		82-Fractal.11
54 reference(s)
83-Commentaires_DefinitionOctonions.01
54 reference(s)		84-xDarchivesG__SMC__sources__SMC_____SI_HELP
53 reference(s)
85-DecimalesPi_100000.vv
53 reference(s)		86-subject.01.
52 reference(s)
87-Le_Chat.01.Fra
52 reference(s)		88-DecimalesPi_1_100.vv
52 reference(s)
89-CompressionDeCompression_ComplexiteStructurelle.PNG_A1.01
52 reference(s)		90-AQuoiServentLesMathematiques.01
52 reference(s)
91-xDarchivesG__SMC__sources__SMC_____SI_TN
51 reference(s)		92-PerteDeLAssociativite.01
51 reference(s)
93-LeCinquantenaireDuCMAP.01.vv.Fra
51 reference(s)		94-GoldenTriangle.01.Fra
51 reference(s)
95-Galerie_CollaborativeWorks..FV
51 reference(s)		96-EntrelacsIntertwinings.01.Ang
51 reference(s)
97-Downloading.01.vv
51 reference(s)		98-NombresPremiers_10000.vv
50 reference(s)
99-LeParadoxeDeFermi.01.Fra
50 reference(s)		100-GoldenTriangle.01.Ang
50 reference(s)
101-DuModeleALImage.02.Fra
50 reference(s)		102-catalogue.11
49 reference(s)
103-VoyagesInfinimentPetitInfinimentGrand.01.Fra
49 reference(s)		104-RealNumbers.01.Fra
49 reference(s)
105-NatureDesMathematiques.01.vv.Fra
49 reference(s)		106-NDimensionalDeterministicFractalSets.01.Fra
49 reference(s)
107-GenieLogiciel.01.Fra
49 reference(s)		108-Galerie_SignalProcessing.FV
49 reference(s)
109-Galerie_NewPictures.FV
49 reference(s)		110-DecimalesDePi.01.Fra
49 reference(s)
111-AnimFractal.01.
49 reference(s)		112-stereogrammes_autostereogrammes.01
48 reference(s)
113-MathematiquesPhysiqueFractales.32
48 reference(s)		114-Galerie_SensitivityToRoundingOffErrors.FV
48 reference(s)
115-Galerie_QuantumMechanics.FV
48 reference(s)		116-Galerie_Pi.FV
48 reference(s)
117-ExpV_VirE.Ang
48 reference(s)		118-BEST.20000905
48 reference(s)
119-Multivers.01.Fra
47 reference(s)		120-MonodimensionalCellularAutomata.01.Fra
47 reference(s)
121-MonodimensionalCellularAutomata.01.Ang
47 reference(s)		122-ManyChaos.01.Ang
47 reference(s)
123-LesCourbesRemplissantes.01.Ang
47 reference(s)		124-Exposition_EcolePolytechnique_FeteDeLaScience_201810
47 reference(s)
125-Exposition_EcolePolytechnique_FeteDeLaScience_201510
47 reference(s)		126-Commentaires_DefinitionPseudoQuaternions.01
47 reference(s)
127-SurfaceProjector.01.Fra
46 reference(s)		128-NombresEtLumiere.01.vv.Fra
46 reference(s)

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




Copyright © Jean-François COLONNA, -2025.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, -2025.