Monthly Best Of on 08/28/2025




Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-

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 08/28/2025 and last updated on 08/28/2025 22:10:33 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-610 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
2-143 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
3-106 reference(s)		The Many World Theory of Hugh Everett
4-97 reference(s)
The random walk of photons escaping the Sun
5-96 reference(s)		Autostereogram of the CMAP
6-95 reference(s)		The generalized Ulam spiral
7-95 reference(s)		The Klein bottle
8-94 reference(s)
Mapping on a torus of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
9-91 reference(s)		Bidimensional cross-sections of the Klein bottle
10-88 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
11-88 reference(s)		Autostereogram of 8 color-multiplexed quaternionic Julia sets -tridimensional cross-sections-
12-87 reference(s)
Autostereogram with an hidden volcano
13-87 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
14-83 reference(s)		Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
15-81 reference(s)		Artistic view of the prime numbers
16-80 reference(s)
Quantum vacuum fluctuations
17-79 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
18-79 reference(s)		Untitled 0642
19-78 reference(s)		A regular 7-gon -an heptagon-
20-78 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
21-78 reference(s)		The Lorenz attractor
22-77 reference(s)		Mapping on a sphere of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
23-76 reference(s)		A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
24-76 reference(s)
A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 4-
25-76 reference(s)		Artistic view of the Big Bang
26-76 reference(s)		The first four iterations of the construction of the von Koch snowflake
27-74 reference(s)		Mapping on a torus of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
28-73 reference(s)
An arbitrary surface (Jeener surface 2)in motion
29-73 reference(s)		LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
30-73 reference(s)		Bidimensional brownian motion -the colors used (magenta,red,yellow,green,cyan)are an increasing function of the time- and its 'external border' -white-
31-73 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 4-
32-72 reference(s)
Mapping on the Klein bottle of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
33-71 reference(s)		Mapping on a torus of a finite subset of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
34-71 reference(s)		Network
35-70 reference(s)		The Menger Sponge -iteration 5-
36-70 reference(s)
Jean-François COLONNA (on 11/17/1994)with its fractal mountains
37-70 reference(s)		A periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
38-69 reference(s)		A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 5-
39-69 reference(s)		Quark and gluon structure of a nucleon
40-69 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
41-69 reference(s)		Mapping on a quadridimensional Calabi-Yau manifold of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
42-68 reference(s)		Fractal piano keyboard
43-68 reference(s)		Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
44-68 reference(s)
The Goldbach Conjecture
45-68 reference(s)		The Bertrand paradox
46-68 reference(s)		Mapping on the Möbius strip of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
47-67 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
48-67 reference(s)
A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
49-67 reference(s)		The random walk of photons escaping the Sun
50-67 reference(s)		A variable Archimedes spiral displaying 1000 numbers
51-67 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
52-67 reference(s)
A perfect bidimensional fractal tree and the self-similarity
53-66 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
54-66 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
55-66 reference(s)		Artistic view of a tridimensional display of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
56-65 reference(s)
Tridimensional display of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
57-65 reference(s)		A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 5-
58-65 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 5-
59-65 reference(s)		Tridimensional zoom in on the Mandelbrot set
60-65 reference(s)
Autostereogram -using a periodical paradoxal structure as a desguise texture- with an hidden gaussian mountain
61-65 reference(s)		Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers-
62-65 reference(s)		Fractal intertwining
63-65 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
64-65 reference(s)
Tridimensional brownian motion -the colors used (magenta,red,yellow,green,cyan)are an increasing function of the time- and the 'external border' of its bidimensional projection -white-
65-65 reference(s)		A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 4-
66-64 reference(s)		The multiplicative persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-
67-64 reference(s)		Quark and gluon structure of a nucleon
68-64 reference(s)
Quaternionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-
69-64 reference(s)		A fractal Klein bottle
70-64 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 2-
71-63 reference(s)		Bidimensional brownian motion
72-63 reference(s)
The foggy Babel Tower -a Tribute to Brueghel the Elder-
73-63 reference(s)		N-dimensional random structure
74-63 reference(s)		Regular quadrangulation of the volume of a torus -18x18x18-
75-63 reference(s)		Tridimensional fractal Self-Portrait
76-63 reference(s)
The Piet Mondrian quadridimensional Calabi-Yau manifold -2D, 3D or 4D?-
77-63 reference(s)		Untitled 0269 -a Tribute to Piet Mondrian-
78-63 reference(s)		Mapping on the Klein bottle of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
79-62 reference(s)		A periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
80-62 reference(s)
True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
81-62 reference(s)		A Tridimensional Hilbert-like Curve defined with {X1(...),Y1(...),Z1(...)} -iteration 1-
82-62 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)
83-62 reference(s)		Happy new year 2000
84-62 reference(s)
Hypercube
85-62 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
86-62 reference(s)		A monodimensional 'quasi-continuous' cellular automaton
87-62 reference(s)		An elementary monodimensional binary cellular automaton -86- with 1 white starting point -bottom middle-
88-62 reference(s)
A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 5-
89-61 reference(s)		Monument Valley à la David Hockney
90-61 reference(s)		Fractal Self-Portrait -a Tribute to René Magritte-
91-61 reference(s)		Autostereogram with an hidden volcano and 64 self-portraits
92-61 reference(s)
A one sheet hyperboloid of revolution -negative curvature-
93-61 reference(s)		Bidimensional brownian motion -the colors used (magenta,red,yellow,green,cyan)are an increasing function of the time- and its 'external border' -white-
94-61 reference(s)		The Jeener-Klein triple bottle
95-61 reference(s)		The extended Bertrand paradox
96-61 reference(s)
The tower -a Tribute to Vladimir Tatline-
97-61 reference(s)		Mapping on the Möbius strip of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
98-60 reference(s)		Artistic view of a tridimensional display of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
99-60 reference(s)		Tridimensional display of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
100-60 reference(s)
A periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
101-60 reference(s)		A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
102-60 reference(s)		Vibrations 0003
103-60 reference(s)		The execution of a very simple program on a Turing Machine
104-60 reference(s)
A plane -zero curvature-
105-60 reference(s)		A set of 4x3 stereograms displaying a tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -90.000 digits, -base 10- with 30.000 time steps
106-60 reference(s)		The Continuum Hypothesis (CH)
107-60 reference(s)		A set of 4x3 stereograms of a fractal 3-foil torus knot
108-60 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
109-60 reference(s)		Bidimensional brownian motion -the colors used (magenta,red,yellow,green,cyan)are an increasing function of the time- and its 'external border' -white- with display of the evolution of the distance to the origin -grey, from left to right-
110-60 reference(s)		Artistic view of a tridimensional display of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
111-59 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
112-59 reference(s)
Autostereogram with an hidden volcano
113-59 reference(s)		The evolution of the bidimensional field defining the three coordinates of a sphere using the Lorenz attractor
114-59 reference(s)		16 earth-like planets initially on the same keplerian trajectory
115-59 reference(s)		N-body problem integration (N=2)displaying a perfect Keplerian orbit
116-59 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
117-59 reference(s)		The Goldbach Conjecture
118-59 reference(s)		A distorded -for the sake of display- 5-cube -an hyperhypercube-
119-59 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
120-59 reference(s)
A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 5-
121-58 reference(s)		Intertwining
122-58 reference(s)		The random walk of photons escaping the Sun
123-58 reference(s)		The construction process of the Sierpinski Carpet
124-58 reference(s)
Fractal natural form
125-58 reference(s)		An hexagonal tiling of the hyperbolic Poincaré disk -iteration 5-
126-58 reference(s)		The additive persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-
127-58 reference(s)		Mountains and fog
128-58 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
5281 reference(s)		2-Web_Mail.01.vv
245 reference(s)
3-Exposition_EcolePolytechnique_FeteDeLaScience_202510
191 reference(s)		4-demo_14
182 reference(s)
5-Vcatalogue.11
136 reference(s)		6-An2000.01.Fra
126 reference(s)
7-mail.01.vv
116 reference(s)		8-Stereogrammes_AutoStereogrammes.01
111 reference(s)
9-help.
110 reference(s)		10-Fractal.01
104 reference(s)
11-LOG_xiMc.11
102 reference(s)		12-ChatGPT.01.Ang
97 reference(s)
13-ChatGPT.11.Fra
93 reference(s)		14-Fractal.11
88 reference(s)
15-copyright.01.
87 reference(s)		16-DecimalesDePi.01.Fra
87 reference(s)
17-Fractal.21
85 reference(s)		18-FloatingPointNumbers.01.Fra
85 reference(s)
19-catalogue.11
84 reference(s)		20-ChatGPT.01.Fra
83 reference(s)
21-DecimalesPi_100000.vv
80 reference(s)		22-AProposSite.01.Fra
79 reference(s)
23-IAGenerativesImages.01.Fra
78 reference(s)		24-relai_universel.01.vv
75 reference(s)
25-Kepler.02.
75 reference(s)		26-Pcatalogue.11
74 reference(s)
27-MorePages.Ang.
73 reference(s)		28-FloatingPointNumbers.01.Ang
72 reference(s)
29-xiirv_____.nota.t.
71 reference(s)		30-Fractal.02
71 reference(s)
31-an2000.01.fra
69 reference(s)		32-Bard.01.Fra
69 reference(s)
33-UlamSpiral.01.Fra
68 reference(s)		34-ExpV_VirE.Ang
68 reference(s)
35-LesCourbesRemplissantes.01.Fra
67 reference(s)		36-ChatGPT.11.Ang
67 reference(s)
37-ArtScience.01
67 reference(s)		38-infinity.02.vv
66 reference(s)
39-infinity.01.vv
66 reference(s)		40-Le_Chat.01.Ang
66 reference(s)
41-Galerie_ArtisticCreation
66 reference(s)		42-xiirf_____.nota.t.
65 reference(s)
43-VCcatalogue.11
65 reference(s)		44-Multivers.01.Fra
65 reference(s)
45-HughEverettMultiverse.01.Ang
65 reference(s)		46-Galerie_NewPictures.FV
65 reference(s)
47-xiirk_____.nota.t.
64 reference(s)		48-MorePages.
63 reference(s)
49-xiirs_____.nota.t.
62 reference(s)		50-MonodimensionalCellularAutomata.01.Fra
62 reference(s)
51-xiia_____.nota.t.
61 reference(s)		52-Le_Chat.01.Fra
61 reference(s)
53-Informations_AboutPicturesAnimationsAndFiles.01.Ang
61 reference(s)		54-DeepSeek.01.Fra
61 reference(s)
55-xiirc_____.nota.t.
60 reference(s)		56-MathematiquesPhysiqueFractales.02.22
60 reference(s)
57-Galerie_SignalProcessing.FV
60 reference(s)		58-Galerie_NumbersAndLight.FV
60 reference(s)
59-subject.01.
59 reference(s)		60-demo_14.FV
59 reference(s)
61-create.03.
59 reference(s)		62-NDimensionalDeterministicFractalSets.01.Ang
59 reference(s)
63-ManyChaos.01.Fra
59 reference(s)		64-JFC
59 reference(s)
65-present.01.
58 reference(s)		66-SurfaceProjector.01.Fra
58 reference(s)
67-SurfaceProjector.01.Ang
58 reference(s)		68-Spheres.01
58 reference(s)
69-LesCourbesRemplissantes.02.Fra
58 reference(s)		70-Galerie_NumberTheory.FV
58 reference(s)
71-Fractal.03
58 reference(s)		72-DuModeleALImage.02.Fra
58 reference(s)
73-Bard.01.Ang
58 reference(s)		74-xiav_____.nota.t.
57 reference(s)
75-xias_____.nota.t.
57 reference(s)		76-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_1
57 reference(s)
77-Galeries.01.vv
57 reference(s)		78-NDimensionalDeterministicFractalSets.01.Fra
56 reference(s)
79-LesNombresTranscendants.01.Ang
56 reference(s)		80-HughEverettMultiverse.01.Fra
56 reference(s)
81-Galerie_DeterministicFractalGeometry.FV
56 reference(s)		82-Galerie_ArtisticCreation.FV
56 reference(s)
83-VAcatalogue.11
55 reference(s)		84-RealNumbers.01.Fra
55 reference(s)
85-ImagesDuVirtuel.01.Fra.FV
55 reference(s)		86-Downloading.01.vv
55 reference(s)
87-xiak_____.nota.t.
54 reference(s)		88-xiac_____.nota.t.
54 reference(s)
89-VisSci_SciVis.01
54 reference(s)		90-Multivers.01.Ang
54 reference(s)
91-IAGenerativesImages.01.Fra.DIAPO.0001
54 reference(s)		92-Galerie_Tributes.FV
54 reference(s)
93-Ariane501.01.Fra
54 reference(s)		94-An2000.06.Fra
54 reference(s)
95-nombresreels
53 reference(s)		96-demo14
53 reference(s)
97-demo.14
53 reference(s)		98-NombresPremiers_10000.vv
53 reference(s)
99-MouvementBrownien.01.Ang
53 reference(s)		100-LeNoeudInfini.01.Ang
53 reference(s)
101-Autostereograms.01.
53 reference(s)		102-AVirtualSpaceTimeTravelMachine.Fra
53 reference(s)
103-real.01.vv.
52 reference(s)		104-VisitesGaleriesEnfouies.01.Ang
52 reference(s)
105-OrdinateurMathematiquesArt.01.Fra
52 reference(s)		106-MouvementBrownien.01.Fra
52 reference(s)
107-LumiereVirtuelleParadoxale.01
52 reference(s)		108-LeNoeudInfini.01.Fra
52 reference(s)
109-Galerie_NumberTheory
52 reference(s)		110-Galerie_GeneralitiesVisualization.FV
52 reference(s)
111-Galerie_ArtAndScience.FV
52 reference(s)		112-EntrelacsIntertwinings.01.Ang
52 reference(s)
113-AProposSite.01.Ang
52 reference(s)		114-Polynomials_RationalNumbers.01.Fra
51 reference(s)
115-GoldenTriangle.01.Fra
51 reference(s)		116-Galerie_QuantumMechanics.FV
51 reference(s)
117-Galerie_Pi.FV
51 reference(s)		118-DecimalesPi_1_100.vv
51 reference(s)
119-OrdinateursEtCalculs.01.Fra
50 reference(s)		120-NombresEtLumiere.02.vv.Ang
50 reference(s)
121-Informations_GoodNewsAndBadNews.01.Ang
50 reference(s)		122-IllusionConnaissance.02
50 reference(s)
123-Galerie_NewPictures
50 reference(s)		124-ExpV_VirE.01.Ang
50 reference(s)
125-xiirC_____.nota.t.
49 reference(s)		126-cerveau.01.vv.
49 reference(s)
127-Tcatalogue.11
49 reference(s)		128-RemarquesCerveau.01
49 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.