Monthly Best Of on 04/28/2025




A surface between a rectangle and the Möbius strip

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 04/28/2025 and last updated on 04/28/2025 22:10:13 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-437 reference(s)		Kasner billiard: Time-dependent billiard (from negative curvatures to positive curvature)with one accelerated particle
2-150 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
3-134 reference(s)		The bidimensional brownian motion of 891 particles
4-111 reference(s)
A distorded -for the sake of display- 5-cube -an hyperhypercube-
5-110 reference(s)		Autostereogram with an hidden volcano
6-109 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
7-105 reference(s)		The tridimensional brownian motion of 1815 particles
8-102 reference(s)
A regular 7-gon -an heptagon-
9-100 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
10-99 reference(s)		Autostereogram of the CMAP
11-92 reference(s)		The random walk of photons escaping the Sun
12-91 reference(s)
The first four iterations of the construction of the von Koch snowflake
13-88 reference(s)		Simulation of 'from Pluto to the Sun' with pure uniform circular motions (linear scales)
14-87 reference(s)		Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier and Carl Friedrich Gauss-
15-84 reference(s)		The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
16-82 reference(s)
The Klein bottle
17-81 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
18-81 reference(s)		The Universe at the heart of a Calabi-Yau manifold
19-80 reference(s)		The Sierpinski Carpet -iteration 3-
20-80 reference(s)
Autostereogram of 8 color-multiplexed quaternionic Julia sets -tridimensional cross-sections-
21-79 reference(s)		The Sierpinski Carpet -iteration 3-
22-78 reference(s)		The generalized Ulam spiral
23-77 reference(s)		Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
24-76 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
25-75 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
26-74 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-
27-73 reference(s)		Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier and Carl Friedrich Gauss-
28-72 reference(s)
Black dots on a square lattice
29-72 reference(s)		Artistic view of the prime numbers
30-72 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
31-71 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
32-70 reference(s)
The Simpson paradox
33-69 reference(s)		Untitled 0535 (1972-1976)-as it was displayed on a Tektronix T4010/T4014 screen-
34-69 reference(s)		The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
35-69 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
36-69 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
37-69 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
38-69 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
39-68 reference(s)		The Bonan-Jeener-Klein triple bottle
40-68 reference(s)
The execution of a very simple program on a Turing Machine
41-67 reference(s)		A regular 3-gon -an equilateral triangle-
42-67 reference(s)		An arbitrary surface (Jeener surface 2)
43-67 reference(s)		64 elementary bidimensional binary cellular automata with 1 white starting central point
44-67 reference(s)
The Sierpinski Carpet -iteration 5-
45-66 reference(s)		The numerical reversibility of the bidimensional billiard -192 particles-
46-66 reference(s)		The Menger Sponge -iteration 5-
47-66 reference(s)		The Lorenz attractor
48-66 reference(s)
A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 5-foil torus knot -iteration 3-
49-65 reference(s)		The relief -modulus- of the function sin(z)defined by means of three bidimensional fields
50-65 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
51-65 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
52-65 reference(s)
Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
53-64 reference(s)		Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
54-64 reference(s)		The tridimensional brownian motion of 1738 light and small particles + 77 heavier and bigger ones
55-64 reference(s)		The Klein bottle
56-64 reference(s)
A Tridimensional Hilbert-like Curve defined with {X4(...),Y4(...),Z4(...)} -iteration 4-
57-64 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
58-64 reference(s)		The generalized Ulam spiral displaying 100 numbers
59-63 reference(s)		A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
60-63 reference(s)
A double spherical cross-section inside the Menger Sponge -iteration 5-
61-63 reference(s)		A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
62-63 reference(s)		Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
63-62 reference(s)		The numerical irreversibility of the bidimensional billiard -1376 particles-
64-62 reference(s)
Gravitation and space-time curvature
65-62 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)
66-62 reference(s)		From 'geocentrism' to 'heliocentrism'
67-62 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
68-62 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
69-62 reference(s)		Untitled 0601 -a Tribute to Jean-Michel Atlan-
70-62 reference(s)		The 64 first lines of the Pascal's Triangle -modulo 5-
71-61 reference(s)		A tridimensional structure made of six Golden Decagons with aperiodic Penrose tilings
72-61 reference(s)
An aperiodic Penrose tiling of the plane
73-61 reference(s)		A fractal vegetal structure
74-61 reference(s)		A regular 4-gon -a square-
75-61 reference(s)		The Node, Rama Revealed -a Tribute to Arthur C. Clarke and Gentry Lee-
76-61 reference(s)
The journey of an Earth-like planet (dark blue)from Pluto (grey) to the Sun (yellow)
77-61 reference(s)		A 'conic' cross-section inside the Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
78-61 reference(s)		Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
79-61 reference(s)		Fractal Self-Portrait -a Tribute to René Magritte-
80-61 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
81-61 reference(s)		Rotation about the Y (vertical)axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms
82-61 reference(s)		A tridimensional field
83-60 reference(s)		Intertwining
84-60 reference(s)
The generalized Ulam spiral displaying 1024 numbers
85-60 reference(s)		A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
86-60 reference(s)		A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
87-60 reference(s)		N-body problem integration (N=4)with one yellow star and two planets (the red one being very heavy and the blue one and its white satellite being light)
88-60 reference(s)
The intersection of the Menger Sponge -iteration 5- and of a quadridimensional Calabi-Yau manifold -tridimensional representation- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
89-60 reference(s)		An amazing cross-section inside an extended Menger Sponge -iteration 5-
90-60 reference(s)		An extended Menger Sponge -iteration 5-
91-60 reference(s)		Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
92-60 reference(s)
Tridimensional zoom in on the Mandelbrot set
93-60 reference(s)		An elementary monodimensional binary cellular automaton -110- with 49 white starting points -on the bottom line-
94-60 reference(s)		Artistic view of gravitational waves
95-59 reference(s)		The Eratosthene sieve displaying 10x10 numbers
96-59 reference(s)
2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')-tridimensional cross-section-
97-59 reference(s)		A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} -iteration 1-
98-59 reference(s)		Untitled 0272
99-59 reference(s)		An amazing cross-section inside the complement of the Menger Sponge -iteration 2-
100-59 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
101-59 reference(s)		Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
102-59 reference(s)		Rotation about the X axis of the Lorenz attractor (1000 iterations), computed simultaneously on two different computers
103-59 reference(s)		Bidimensional Hilbert Curve -iteration 1-
104-59 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
105-59 reference(s)		An aperiodic Penrose tiling of the plane -a Tribute to Piet Mondrian and Roger Penrose-
106-58 reference(s)		An aperiodic Penrose tiling of the plane
107-58 reference(s)		Autostereogram with an hidden volcano
108-58 reference(s)
2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')-tridimensional cross-section-
109-58 reference(s)		A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
110-58 reference(s)		2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')-tridimensional cross-section-
111-58 reference(s)		A regular 5-gon -a pentagon-
112-58 reference(s)
An amazing cross-section inside an extended Menger Sponge -iteration 4-
113-58 reference(s)		An amazing cross-section inside an extended Menger Sponge -iteration 1-
114-58 reference(s)		An extended Menger Sponge -iteration 5-
115-58 reference(s)		The Menger Sponge -iteration 4-
116-58 reference(s)
Close-up on a foggy pseudo-quaternionic Mandelbrot set with a (1/O)^3 conformal transformation in the octonionic space -tridimensional cross-section-
117-58 reference(s)		A pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
118-58 reference(s)		Larsen effect
119-58 reference(s)		A one sheet hyperboloid of revolution -negative curvature-
120-58 reference(s)
Hypercube
121-58 reference(s)		Tridimensional display of the 'EinStein' aperiodic 'Spectre' tiling
122-57 reference(s)		Fractal 'celestial body' based on a torus
123-57 reference(s)		An interpolation between the Bonan-Jeener-Klein triple bottle and a 'double sphere' defined by means of three sets of bidimensional fields
124-57 reference(s)
A Peano 'fractal plane' defined by means of three bidimensional fields
125-57 reference(s)		Artistic view of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
126-57 reference(s)		A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
127-57 reference(s)		N-body problem integration (N=2)displaying a perfect Keplerian orbit (an ellipse)
128-57 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
1520 reference(s)		2-help.
552 reference(s)
3-Exposition_EcolePolytechnique_CentenaireNaissanceBenoitMandelbrot_202410_202411_202412
449 reference(s)		4-xi_____INCLUDES_bas.I.
340 reference(s)
5-Web_Mail.01.vv
287 reference(s)		6-xiii_____ImagesF.ext.
204 reference(s)
7-xrv_____champs_5.1A.I.
172 reference(s)		8-Galerie_ParticleSystems.FV
167 reference(s)
9-xci_____acces.K.
161 reference(s)		10-xrv_____particule.10.K.
158 reference(s)
11-xiirC_____.nota.t.
156 reference(s)		12-xrC_____CompressionDeCompression_Compression.01.vv.c.
148 reference(s)
13-xci_____valeurs.03.I.
133 reference(s)		14-xrk_____attractor.11.I.
131 reference(s)
15-xci_____vraies_C.K.
128 reference(s)		16-xrk_____attractor.12.I.
126 reference(s)
17-xci_____valeurs_inte.K.
125 reference(s)		18-xrv_____ARITHMET.21.I.
124 reference(s)
19-xrv_____ARITHMET.1d.I.
124 reference(s)		20-Stereogrammes_AutoStereogrammes.01
124 reference(s)
21-mail.01.vv
123 reference(s)		22-xrv_____ARITHMET.22.I.
118 reference(s)
23-xi_____INCLUDES_min.I.
118 reference(s)		24-Commentaires_ModeleIsingTriDimensionnel.01
113 reference(s)
25-xrv_____particule.41.I.
110 reference(s)		26-xci_____init.K.
110 reference(s)
27-xrk_____attractor.18.I.
108 reference(s)		28-xiii_____quad_image.ext.
106 reference(s)
29-xci_____seuil.K.
106 reference(s)		30-ComplexiteStructurelleClassements.11
106 reference(s)
31-xiirv_____.nota.t.
103 reference(s)		32-xci_____sequence.01.I.
102 reference(s)
33-xci_____gauss.K.
102 reference(s)		34-demo_14
100 reference(s)
35-xrs_____project2D.11.K.
98 reference(s)		36-xci_____neutre.K.
98 reference(s)
37-xrk_____integr.1B.vv.I.
97 reference(s)		38-xrs_____surfaces.12.I.
96 reference(s)
39-xci_____montagne.01.K.
96 reference(s)		40-xci_____normalise.01.K.
94 reference(s)
41-LOG_xiMc.11
94 reference(s)		42-xci_____complement.K.
93 reference(s)
43-xci_____format.01.K.
92 reference(s)		44-xcg_____MIN2.01.K.
90 reference(s)
45-xci_____nombres.K.
89 reference(s)		46-xci_____genere.K.
87 reference(s)
47-An2000.01.Fra
87 reference(s)		48-AVirtualSpaceTimeTravelMachine.Fra
87 reference(s)
49-Informations_GoodNewsAndBadNews.01.Fra
85 reference(s)		50-Informations_GoodNewsAndBadNews.01.Ang
84 reference(s)
51-ChatGPT.11.Fra
84 reference(s)		52-xrv_____dimensionnement.01.vv.I.
82 reference(s)
53-MouvementBrownien.01.Fra
82 reference(s)		54-xcg_____MIN3.01.K.
81 reference(s)
55-xrv_____normalise.01.K.
80 reference(s)		56-xig_____fonct.vv.def.
80 reference(s)
57-Vcatalogue.11
80 reference(s)		58-xci_____luminance.01.K.
78 reference(s)
59-xci_____convol.01.K.
78 reference(s)		60-DEuclideAuGPS.01.Fra
78 reference(s)
61-xrs_____surfaces.13.I.
77 reference(s)		62-xci_____substitue.K.
77 reference(s)
63-xrs_____surfaces.11.I.
76 reference(s)		64-Fractal.01
76 reference(s)
65-xci_____scale.K.
75 reference(s)		66-MouvementBrownien.01.Ang
75 reference(s)
67-xci_____valeurs.02.I.
74 reference(s)		68-copyright.01.
74 reference(s)
69-xrv_____champs_5.41.I.
73 reference(s)		70-NombresEtLumiere.02.vv.Ang
73 reference(s)
71-UlamSpiral.01.Fra
72 reference(s)		72-Fractal.21
72 reference(s)
73-xrs_____surfaces.21.I.
71 reference(s)		74-xci_____valeurs_alea.K.
70 reference(s)
75-xci_____multi_02.01.K.
70 reference(s)		76-xcg_____MAX3.01.K.
70 reference(s)
77-xrv_____extrema.01.K.
69 reference(s)		78-FloatingPointNumbers.01.Ang
69 reference(s)
79-xrv_____neutre.K.
68 reference(s)		80-xrs_____surfaces.41.I.
68 reference(s)
81-Informations_AboutPicturesAnimationsAndFiles.01.Ang
68 reference(s)		82-xcg_____ADD2.01.K.
67 reference(s)
83-xrk_____attractor.1A.I.
66 reference(s)		84-xi_____INCLUDES_all.I.
66 reference(s)
85-xrs_____surfaces.22.I.
65 reference(s)		86-xci_____fract_2D.01.K.
65 reference(s)
87-SurfaceProjector.01.Ang
65 reference(s)		88-Galerie_NumbersAndLight.FV
65 reference(s)
89-DeLAxiomeDesParallelesAuGPS.01.Fra
65 reference(s)		90-AProposSite.01.Fra
65 reference(s)
91-xci_____valeurs.01.I.
64 reference(s)		92-xci_____cache.K.
64 reference(s)
93-DeLAxiomeDesParallelesAuGPS.01.Ang
64 reference(s)		94-DEuclideAuGPS.01.Ang
64 reference(s)
95-xci_____filtre.01.K.
63 reference(s)		96-IrreversibiliteDuTempsNumerique.01.Fra
63 reference(s)
97-FloatingPointNumbers.01.Fra
63 reference(s)		98-xci_____and.K.
61 reference(s)
99-MathematiquesPhysiqueFractales.02
61 reference(s)		100-ChatGPT.01.Ang
61 reference(s)
101-xcg_____ARIT.01.I.
60 reference(s)		102-ComplexiteStructurelleClassements.01
60 reference(s)
103-xrC_____CompressionOptimale.01.vv.c.
59 reference(s)		104-xrC_____ChaineOctetsUniformesAlternees_1024x1024.08.vv.I.
59 reference(s)
105-xiirf_____.nota.t.
59 reference(s)		106-VCcatalogue.11
59 reference(s)
107-DecimalesPi_100000.vv
59 reference(s)		108-xrv_____AXPB.01.K.
58 reference(s)
109-HughEverettMultiverse.01.Fra
58 reference(s)		110-Galerie_CollaborativeWorks..FV
58 reference(s)
111-AnimFractal.01.
58 reference(s)		112-xci_____passe_bande.K.
57 reference(s)
113-NDimensionalDeterministicFractalSets.01.Fra
57 reference(s)		114-Galerie_DeterministicFractalGeometry.FV
57 reference(s)
115-AQuoiServentLesMathematiques.01
57 reference(s)		116-xrC_____DeCompressionOptimale.01.vv.c.
56 reference(s)
117-xiii_____di_image.fon.
56 reference(s)		118-xci_____dilate.01.K.
56 reference(s)
119-xci_____accumule.01.K.
56 reference(s)		120-ximd_____operator.1.fon.
55 reference(s)
121-ximcf_____iterations.ext.
55 reference(s)		122-xcg_____MAX2.01.K.
55 reference(s)
123-avirtualspacetimetravelmachine.ang
55 reference(s)		124-NDimensionalDeterministicFractalSets.01.Ang
55 reference(s)
125-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
55 reference(s)		126-Informations_AboutPicturesAnimationsAndFiles.01.Fra
55 reference(s)
127-HughEverettMultiverse.01.Ang
55 reference(s)		128-Fractal.11
55 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.