Monthly Best Of on 01/28/2025




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 01/28/2025 and last updated on 01/28/2025 22:08:17 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-334 reference(s)		Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
2-304 reference(s)		Y2K
3-263 reference(s)		Visualization of the density iso-surfaces (density=0.58)during a tridimensional diffusion process of 114299 particles
4-253 reference(s)
K/LD Matrix -'CDCM1_B4.01' measures-
5-251 reference(s)		Monument Valley
6-235 reference(s)		Erosion of a bidimensional random (with small and large scale correlations)island
7-228 reference(s)		K/LD Matrix -'PNG_A1.02' measures-
8-215 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-
9-215 reference(s)		K/LD Matrix -'CDCM2_CDC_1.01' measures-
10-203 reference(s)		Tridimensional visualization of the Verhulst dynamics
11-196 reference(s)		An artistic variation of a monodimensional 'quasi-continuous' cellular automata with random perturbation of the rules
12-195 reference(s)
K/LD Matrix -'CDCM4_CDC_D__CDC_E.01' measures-
13-193 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-
14-188 reference(s)		K/LD Matrix -'CDCM2_Y.01' measures-
15-185 reference(s)		Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
16-182 reference(s)
Anaglyph of a close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
17-182 reference(s)		The random walk of photons escaping the Sun
18-180 reference(s)		N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors)
19-178 reference(s)		The 2 connected components of a Fractal Cube -iteration 0-
20-177 reference(s)
K/LD Matrix -'CDCM4_Y.01' measures-
21-164 reference(s)		K/LD Matrix -'CDCM3_CDC_E.01' measures-
22-162 reference(s)		Distorsion of the Bonan-Jeener-Klein double bottle
23-161 reference(s)		The 16 most referenced pictures on 10/14/1997
24-159 reference(s)
A Fractal Cube -iteration 0-
25-155 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-
26-150 reference(s)		K/LD Matrix -'CDCM1_CDC_4.01' measures-
27-146 reference(s)		K/LD Matrix -'CDCM2_R.01' measures-
28-145 reference(s)
A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -20.000 digits, -base 10- with 10.000 time steps
29-144 reference(s)		K/LD Matrix -'bzip2_CDC_4.01' measures-
30-141 reference(s)		K/LD Matrix -'JPEG2000_Divers.01' measures-
31-141 reference(s)		The bidimensional field defining the three coordinates of a 'crumpled' sphere
32-140 reference(s)
Erosion of a bidimensional random (with large scale correlations)island
33-140 reference(s)		Tridimensional display of the particle density of a bidimensional crenellated billiard
34-139 reference(s)		A Fractal Square -iteration 2-
35-136 reference(s)		From Pluto to the Sun
36-135 reference(s)
The 500 first digits of 'pi/5' displayed as an Impossible Structure
37-134 reference(s)		K/LD Matrix -'CDCM2_CDC_F.01' measures-
38-130 reference(s)		Bidimensional zoom in on the Mandelbrot set with display of the arguments
39-130 reference(s)		A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
40-129 reference(s)
K/LD Matrix -'Optimal_CDC_E.01' measures-
41-127 reference(s)		Erosion of a bidimensional random island
42-126 reference(s)		Chaotic trajectory: multiple reflexions between two parallel planes -static view-
43-125 reference(s)		K/LD Matrix -'CDCM1_A1.01' measures-
44-124 reference(s)
A Fractal Square -iteration 4-
45-124 reference(s)		The self-similarity of the von Koch curve displayed by means of a zoom in with a ratio that is equal to 3
46-123 reference(s)		Empty
47-123 reference(s)		Segmentation of a picture by means of the local fractal dimension
48-122 reference(s)
Jean-François COLONNA (on 11/17/1994)with its fractal mountains
49-122 reference(s)		Three hexagons defining 28 different points (13 vertices plus 15 'middle' points)
50-121 reference(s)		Fractal 3-foil torus knot
51-121 reference(s)		K/LD Matrix -'CDCM1_Z.01' measures-
52-119 reference(s)
Along the border of the Mandelbrot set in the complex plane
53-118 reference(s)		Homogeneous random non linear meshing of a cube
54-118 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-
55-116 reference(s)		A fractal polyhedron
56-116 reference(s)
K/LD Matrix -'PNG_Z.01' measures-
57-114 reference(s)		The Eratosthene sieve displaying 100x100 numbers
58-112 reference(s)		Circular worm
59-112 reference(s)		Light cloud dynamics -this sequence being periodical-
60-112 reference(s)
The 256 first digits -base 10- of 'pi' on a Bidimensional Hilbert Curve -iteration 4- mapped on a sphere
61-109 reference(s)		Visualization of the density iso-surfaces (density=0.80)during a tridimensional diffusion process of 128312 particles
62-109 reference(s)		Visualization of the density iso-surfaces (density=0.73)during a tridimensional diffusion process of 128312 particles
63-109 reference(s)		A surface between a cylinder and a torus
64-108 reference(s)
Visualization of the density iso-surfaces (density=0.87)during a tridimensional diffusion process of 128312 particles
65-108 reference(s)		K/LD Matrix -'CDCM4_CDC_1.01' measures-
66-107 reference(s)		The 9 connected components of a Fractal Square -iteration 3-
67-107 reference(s)		The Klein bottle in motion
68-107 reference(s)
The bidimensional field defining the 'X' coordinate of a 'crumpled' Klein bottle
69-106 reference(s)		K/LD Matrix -'bzip2_E2.01' measures-
70-106 reference(s)		The Bonan-Jeener-Klein triple bottle
71-106 reference(s)		Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability -display of the Oxygen density-
72-106 reference(s)
Visualization of the density iso-surfaces (density=0.65)during a tridimensional diffusion process of 114299 particles
73-105 reference(s)		Erosion of a bidimensional random (with small and large scale correlations)island -last step-
74-105 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
75-105 reference(s)		An extended Menger Sponge -iteration 1-
76-104 reference(s)
K/LD Matrix -'Optimal_Random.01' measures-
77-104 reference(s)		Computation of the roots of Z^3=1 using Newton's method
78-103 reference(s)		An 128x128 empty lattice
79-103 reference(s)		K/LD Matrix -'CDCM1_CDC_9.01' measures-
80-103 reference(s)
K/LD Matrix -'CDCM1_ZL.01' measures-
81-102 reference(s)		A Fractal Square -iteration 5-
82-102 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-
83-101 reference(s)		K/LD Matrix -'CDCM2_CDC_B.01' measures-
84-101 reference(s)
The 'J' elementary symbol used to built impossible structures
85-101 reference(s)		N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed with 2 slightly different sets of initial conditions (sensitivity to initial conditions)
86-100 reference(s)		Homogeneous/heterogeneous meshing of a square
87-99 reference(s)		Bidimensional texture animation by means of the Generalized Product
88-98 reference(s)
The 81 first digits of 'pi' displayed as sets of concentric various curves (bird's-eye view)
89-98 reference(s)		N-body problem integration (N=10)displaying the actual Solar System with its simultaneous 2.pi rotation
90-98 reference(s)		K/LD Matrix -'CDCM4_CDC_F.01' measures-
91-98 reference(s)		K/LD Matrix -'CDCM3_CDC_D.01' measures-
92-98 reference(s)
K/LD Matrix -'CDCM2_CDC_2.01' measures-
93-98 reference(s)		Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus
94-98 reference(s)		Segmentation of a picture by means of the local fractal dimension
95-97 reference(s)		Monument Valley at sunrise with light cloud dynamics -this sequence being periodical-
96-96 reference(s)
K/LD Matrix -'CDCM3_CDC_8.01' measures-
97-96 reference(s)		The construction of the tridimensional Hilbert Curve -iteration 3-
98-96 reference(s)		A Fractal Square -iteration 4-
99-96 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
100-96 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-
101-95 reference(s)		Fractal 7-foil torus knot
102-95 reference(s)		The bidimensional field defining the 'Z' coordinate of a 'fractal plane' with overhangings
103-94 reference(s)		A 'crumpled' Klein bottle defined by means of three bidimensional fields
104-94 reference(s)
The 500 first digits of 'pi/3' displayed as an Impossible Structure
105-94 reference(s)		K/LD Matrix -'Optimal_CDC_9.01' measures-
106-94 reference(s)		The construction of the bidimensional Hilbert Curve -iteration 3-
107-94 reference(s)		Distorsion of the Bonan-Jeener-Klein double bottle
108-94 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
109-93 reference(s)		Autostereogram -using periodical light clouds as desguise texture- with a hidden gaussian mountain
110-93 reference(s)		An impossible bijection
111-93 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
112-92 reference(s)
A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
113-92 reference(s)		The 16 most referenced pictures on 07/26/1996
114-92 reference(s)		Flore on the Moon (waiting for Cyrano de Bergerac?)
115-91 reference(s)		K/LD Matrix -'JPEG2000_ZB_ZC.01' measures-
116-91 reference(s)
The journey of an Earth-like virtuel planet (green)from Pluto (grey) to the Sun (yellow) -point of view of the virtual planet-
117-90 reference(s)		Tridimensional display of a Fractal Square -iteration 1 to 3-
118-90 reference(s)		A Fractal Square -iteration 3-
119-90 reference(s)		A fractal polyhedron
120-90 reference(s)
A simple geometrical periodical structure
121-89 reference(s)		The bidimensional field defining the three coordinates of a 'crumpled' torus
122-89 reference(s)		Visualization of the density iso-surfaces (density=0.50)during a tridimensional diffusion process of 114299 particles
123-89 reference(s)		Visualization of the density iso-surfaces (density=0.22)during a tridimensional diffusion process of 114299 particles
124-89 reference(s)
Along the border of the Mandelbrot set
125-88 reference(s)		Synthesis of tridimensional textures
126-88 reference(s)		Anaglyph of a close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
127-88 reference(s)		Tridimensional visualization of the Verhulst dynamics
128-88 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
1671 reference(s)		2-Galerie_DeterministicFractalGeometry.FV
428 reference(s)
3-Definitions_4_connexite.01
330 reference(s)		4-CompressionDeCompression_ComplexiteStructurelle.PNG_ZP.01
238 reference(s)
5-CompressionDeCompression_ComplexiteStructurelle.PNG_A1.02
203 reference(s)		6-Web_Mail.01.vv
176 reference(s)
7-Galerie_NumberTheory.FV
158 reference(s)		8-mail.01.vv
110 reference(s)
9-An2000.01.Fra
105 reference(s)		10-Stereogrammes_AutoStereogrammes.01
95 reference(s)
11-xiav_____.nota.t.
89 reference(s)		12-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
89 reference(s)
13-copyright.01.
88 reference(s)		14-FloatingPointNumbers.01.Ang
87 reference(s)
15-demo_14
79 reference(s)		16-Galerie_Animations.FV
79 reference(s)
17-CompressionDeCompression_ComplexiteStructurelle.PNG_B4.01
79 reference(s)		18-xtp_____AXmB.01.python.
78 reference(s)
19-CompressionDeCompression_ComplexiteStructurelle.PNG_A1.03
77 reference(s)		20-PerteDeLAssociativite.01.MUL3
75 reference(s)
21-Definitions_8_connexite.01
74 reference(s)		22-help.
73 reference(s)
23-SourceExemple_____xtc_____stereogra.01.c.
72 reference(s)		24-An2000.03.Fra
72 reference(s)
25-Fractal.21
68 reference(s)		26-ChatGPT.01.Fra
68 reference(s)
27-Vcatalogue.11
65 reference(s)		28-CompressionDeCompression_ComplexiteStructurelle.PNG_C2.01
63 reference(s)
29-xiirv_____.nota.t.
62 reference(s)		30-MathematiquesPhysiqueFractales.12
62 reference(s)
31-ChatGPT.11.Fra
61 reference(s)		32-LOG_xiMc.11
60 reference(s)
33-Galerie_NewPictures.FV
58 reference(s)		34-CompressionDeCompression_ComplexiteStructurelle.PNG_I1.01
58 reference(s)
35-AProposSite.01.Fra
56 reference(s)		36-CompressionDeCompression_ComplexiteStructurelle.PNG_E2.01
55 reference(s)
37-Fractal.01
53 reference(s)		38-IAGenerativesImages.01.Fra
52 reference(s)
39-CompressionDeCompression_ComplexiteStructurelle.PNG_ZK.01
51 reference(s)		40-MathematiquesPhysiqueFractales.02.27
50 reference(s)
41-LesCourbesRemplissantes.01.Fra
50 reference(s)		42-Informations_GoodNewsAndBadNews.01.Fra
49 reference(s)
43-UlamSpiral.01.Fra
48 reference(s)		44-Galerie_ParticleSystems.FV
47 reference(s)
45-avirtualspacetimetravelmachine.ang
44 reference(s)		46-Informations_GoodNewsAndBadNews.01.Ang
44 reference(s)
47-Informations_AboutPicturesAnimationsAndFiles.01.Ang
44 reference(s)		48-xiirc_____.nota.t.
43 reference(s)
49-fractal.01
43 reference(s)		50-LesNombresTranscendants.01.Fra
43 reference(s)
51-LesNombresTranscendants.01.Ang
43 reference(s)		52-FloatingPointNumbers.01.Fra
43 reference(s)
53-DecimalesPi_100000.vv
43 reference(s)		54-SurfaceProjector.01.Ang
42 reference(s)
55-GoldenTriangle.01.Fra
41 reference(s)		56-CompressionDeCompression_ComplexiteStructurelle.PNG_ZL.01
41 reference(s)
57-xiirf_____.nota.t.
40 reference(s)		58-NombresEtLumiere.02.vv.Ang
40 reference(s)
59-Galerie_CollaborativeWorks.
39 reference(s)		60-DecimalesDePi.01.Fra
39 reference(s)
61-ConjectureDeSyracuse_0128.Parity.vv
39 reference(s)		62-CompressionDeCompression_ComplexiteStructurelle.PNG_A1.01
39 reference(s)
63-AVirtualSpaceTimeTravelMachine.Fra
39 reference(s)		64-UlamSpiral.01.Ang
38 reference(s)
65-NDimensionalDeterministicFractalSets.01.Ang
38 reference(s)		66-LesCourbesRemplissantes.02.Fra
38 reference(s)
67-Galerie_NumbersAndLight.FV
38 reference(s)		68-Fractal.11
38 reference(s)
69-Galerie_ArtAndScience.FV
37 reference(s)		70-AnimFractal.01.
37 reference(s)
71-xiirs_____.nota.t.
36 reference(s)		72-NombresEtLumiere.01.vv.Fra
36 reference(s)
73-Galerie_GeneralitiesVisualization.FV
36 reference(s)		74-Exposition_EcolePolytechnique_CentenaireNaissanceBenoitMandelbrot_202410_202411_202412
36 reference(s)
75-SIlVousPlaitDessineMoiLInfini.01.Fra
35 reference(s)		76-PerteDeLAssociativite.01
35 reference(s)
77-GenieLogiciel.01.Fra
35 reference(s)		78-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis
35 reference(s)
79-xiac_____.nota.t.
34 reference(s)		80-MathematiquesPhysiqueFractales.22
34 reference(s)
81-ImagesDuVirtuel.01.Fra.FV
34 reference(s)		82-DecimalesPi_1_100.vv
34 reference(s)
83-ChatGPT.11.Ang
34 reference(s)		84-present.01.
33 reference(s)
85-catalogue.11
33 reference(s)		86-RealNumbers.01.Fra
33 reference(s)
87-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
33 reference(s)		88-MathematiquesPhysiqueFractales.02
33 reference(s)
89-LesCourbesRemplissantes.01.Ang
33 reference(s)		90-LesApprentisDieux.01
33 reference(s)
91-LeCinquantenaireDuCMAP.01.vv.Fra
33 reference(s)		92-Galerie_ImagesDesMathematiques.DIAPO.0006
33 reference(s)
93-Galerie_ArtisticCreation.FV
33 reference(s)		94-DieuScience.01.Ang
33 reference(s)
95-ChatGPT.01.Ang
33 reference(s)		96-xiia_____.nota.t.
32 reference(s)
97-xias_____.nota.t.
32 reference(s)		98-SourceExemple_____xrq_____hydrogene.61.K.
32 reference(s)
99-RemarquesCerveau.01
32 reference(s)		100-NatureDesMathematiques.01.vv.Fra
32 reference(s)
101-MonodimensionalCellularAutomata.01.Fra
32 reference(s)		102-Informations_AboutPicturesAnimationsAndFiles.01.Fra
32 reference(s)
103-IAGenerativesImages.01.Ang
32 reference(s)		104-Exposition_OperaDeMassy_201912_202001
32 reference(s)
105-Exposition_EcolePolytechnique_FeteDeLaScience_201910
32 reference(s)		106-Commentaires_DefinitionOctonions.01
32 reference(s)
107-Bard.01.Fra
32 reference(s)		108-Autostereograms.01.
32 reference(s)
109-An2000.06.Fra
32 reference(s)		110-xiaf_____.nota.t.
31 reference(s)
111-infinity.01.vv
31 reference(s)		112-VoyagesInfinimentPetitInfinimentGrand.01.Fra
31 reference(s)
113-Multivers.01.Ang
31 reference(s)		114-LesCourbesRemplissantes.02.Ang
31 reference(s)
115-Le_Chat.01.Fra
31 reference(s)		116-GoldenTriangle.01.Ang
31 reference(s)
117-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
31 reference(s)		118-xiirk_____.nota.t.
30 reference(s)
119-stereogrammes_autostereogrammes.01
30 reference(s)		120-PatrimoineHumanite.02.Fra
30 reference(s)
121-NombresPremiers_10000.vv
30 reference(s)		122-MonodimensionalCellularAutomata.01.Ang
30 reference(s)
123-MathematiquesPhysiqueFractales.02.23
30 reference(s)		124-Galerie_CelestialMechanics.DIAPO.0001
30 reference(s)
125-xiak_____.nota.t.
29 reference(s)		126-VCcatalogue.11
29 reference(s)
127-OrdinateursEtCalculs.01.Ang
29 reference(s)		128-NDimensionalDeterministicFractalSets.01.Fra
29 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.