Monthly Best Of on 11/28/2025




A surface between the Klein bottle and a 'double sphere' defined by means of three bidimensional fields

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 11/28/2025 and last updated on 11/28/2025 22:15:49 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-437 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
2-176 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
3-176 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
4-175 reference(s)
The Sierpinski Carpet -iteration 1 to 5-
5-143 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 64 first prime numbers-
6-130 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 256 prime numbers following 100000...-
7-129 reference(s)		Fractal Self-Portrait -a Tribute to René Magritte-
8-124 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [2,10^14]-
9-121 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
10-117 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 256 prime numbers following 100000...-
11-116 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-
12-112 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [1x10^14,2x1014]-
13-111 reference(s)		Artistic view of the prime numbers
14-111 reference(s)		Color palette 'dentscie.R8'
15-110 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
16-110 reference(s)
The Lorenz attractor
17-108 reference(s)		Monument Valley at sunrise
18-107 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
19-107 reference(s)		The first four iterations of the construction of the von Koch snowflake
20-106 reference(s)
The Syracuse Conjecture for U(0)={5,6,7,8,...,20} -bidimensional display-
21-104 reference(s)		The random walk of photons escaping the Sun
22-104 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
23-103 reference(s)		Color palette 'inter.02.13'
24-100 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-
25-98 reference(s)		Mountains and fog
26-98 reference(s)		Color palette 'turbul.13'
27-97 reference(s)		Simulation of 'from Pluto to the Sun' with pure uniform circular motions (linear scales)
28-97 reference(s)
An extended Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
29-97 reference(s)		Mapping on a sphere family of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
30-96 reference(s)		Mountains at sunrise
31-96 reference(s)		Fractal Self-Portrait -'Décalcomanie', a Tribute to René Magritte-
32-96 reference(s)
The generalized Ulam spiral
33-94 reference(s)		Happy new year 2000
34-94 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
35-93 reference(s)		Color palette 'trou_noir.C5'
36-91 reference(s)
Color palette 'gris.55'
37-89 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 32 first prime numbers-
38-89 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [2x10^14,3x1014]-
39-85 reference(s)		Quark and gluon structure of a nucleon
40-84 reference(s)
Untitled 0668
41-84 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 32 first prime numbers-
42-84 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
43-83 reference(s)		Color palette 'anaglyphe.11'
44-81 reference(s)
Quark and gluon structure of a nucleon
45-81 reference(s)		The random walk of photons escaping the Sun
46-80 reference(s)		The distance {Earth-Mars} -millions of kilometers- starting on 01/01/1950 AD and during seven marsian years
47-80 reference(s)		A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
48-80 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 32 first prime numbers-
49-80 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 128 first prime numbers-
50-79 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 256 first prime numbers-
51-79 reference(s)		Tridimensional representation of a hexadimensional Calabi-Yau manifold
52-79 reference(s)
The same bidimensional scalar field displayed with 4 different color palettes
53-77 reference(s)		Bidimensional zoom in on the Mandelbrot set with display of the arguments
54-77 reference(s)		Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers-
55-77 reference(s)		Cantor's diagonal argument
56-77 reference(s)
The abelian -commutative- group defined on elliptic curves
57-77 reference(s)		The Jeener-Klein triple bottle
58-77 reference(s)		Quantum vacuum fluctuations
59-76 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-
60-76 reference(s)
Different modes of representation of a tridimensional cross-section of a Quaternionic Julia set
61-75 reference(s)		The DNA of Mathematics -the 100 first digits of 'pi' and 'e'-
62-74 reference(s)		The DNA of Mathematics -the 480 first digits of 'pi' and '1/pi'-
63-74 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 256 first prime numbers-
64-74 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 64 first prime numbers-
65-74 reference(s)		The Universe at the heart of a Calabi-Yau manifold
66-73 reference(s)		The erosion of the Menger Sponge -iteration 3-
67-73 reference(s)		Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
68-73 reference(s)
The Goldbach Conjecture for the even numbers from 6 to 1564
69-73 reference(s)		A shell (Jeener surface 1)in motion
70-73 reference(s)		The Scream -a Tribute to Edvard Munch-
71-72 reference(s)		The Ulam spiral with display of the first twin prime numbers ('2-twin' prime numbers)
72-72 reference(s)
Color palette 'sunset.11'
73-72 reference(s)		A 4-cube -an hypercube-
74-72 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
75-72 reference(s)		Causal set obtained by means of an homogeneous random meshing of a cube
76-72 reference(s)
From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
77-71 reference(s)		The generalized Ulam spiral displaying 100 numbers
78-71 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-
79-71 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 5-
80-71 reference(s)
Tridimensional zoom in on the Mandelbrot set
81-71 reference(s)		The DNA of Mathematics -the 480 first digits of 'pi' and '1/pi'-
82-71 reference(s)		Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
83-71 reference(s)		Simultaneous visualization of the number of prime numbers and of the G(Pi(x)) function during the verification of the Proth-Gilbreath Conjecture
84-71 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
85-71 reference(s)		Voronoi diagrams
86-70 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 5-
87-70 reference(s)		A 'crumpled' Klein bottle defined by means of three bidimensional fields
88-70 reference(s)
A regular 7-gon -an heptagon-
89-70 reference(s)		Color palette 'mire.01'
90-70 reference(s)		The distances {Sun-Jupiter,Sun-Saturn,Sun-Uranus,Sun-Neptune} during one neptunian year
91-70 reference(s)		N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Pluto point of view-
92-70 reference(s)
The Möbius strip
93-70 reference(s)		Tridimensional visualization of the Verhulst dynamics with a tridimensional non linear transformation of the coordinates
94-70 reference(s)		The DNA of Mathematics -the 100 first digits of 'pi' and '1/pi'-
95-70 reference(s)		The Goldbach Conjecture
96-70 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 256 prime numbers following 100000...-
97-70 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 128 first prime numbers-
98-70 reference(s)		The Many World Theory of Hugh Everett
99-69 reference(s)		Color palette 'niveaux.20'
100-69 reference(s)
The velocity vectors -with a common origin- of the 9 planets of the Solar System during one plutonian year
101-69 reference(s)		The DNA of Mathematics -the 60 first digits of 'pi' and '1/pi'-
102-69 reference(s)		Tridimensional visualization of the ABC Conjecture
103-69 reference(s)		The Sierpinski Carpet -iteration 4-
104-68 reference(s)
A tridimensional fractal manifold defined by means of three tridimensional fields
105-68 reference(s)		An Archimedes spiral displaying 100 numbers
106-68 reference(s)		Botticelli anomaly on the Moon
107-68 reference(s)		Mountains at sunrise
108-68 reference(s)
A 'mixing' between a pseudo-quaternionic Mandelbrot set (a 'MandelBulb')and a tridimensional fractal structure -tridimensional cross-section-
109-68 reference(s)		The construction of the bidimensional Hilbert Curve -iteration 4-
110-68 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 256 prime numbers following 100000...-
111-68 reference(s)		A 'mixing' between a tridimensional fractal structure and a close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
112-68 reference(s)
A 4-cube -an hypercube-
113-68 reference(s)		Artistic view of the Big Bang
114-67 reference(s)		A demonstration of the Pythagoras' theorem using a very poor picture
115-67 reference(s)		The Ulam spiral displaying 2025 numbers
116-67 reference(s)
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0,1,0,0,0,0,0,0) and with a locally variable exponent between 2 and 12 -tridimensional cross-section-
117-67 reference(s)		Artistic view of the 100.000 first digits -base 10- of 'pi'
118-67 reference(s)		Color palette 'niveaux.02'
119-67 reference(s)		Color palette 'Farg1.15'
120-67 reference(s)
The smooth integers: the prime factor product -the radical function- of the integer numbers
121-67 reference(s)		From Pluto to the Sun (non linear scales)
122-67 reference(s)		The Möbius strip
123-67 reference(s)		An extended Menger Sponge -iteration 7- displaying the 211.210.335 first digits -base 2- of 'pi'
124-67 reference(s)
The 50 first digits {1,2,3,4,5,6,7,8,9,1,...} of the Champernowne number displayed on an helix -orange-
125-67 reference(s)		The 32 vertices of a 5-cube
126-67 reference(s)		A fractal Möbius strip
127-67 reference(s)		Triple impossible staircase and a paradoxal structure
128-67 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
3305 reference(s)		2-catalogue.11
241 reference(s)
3-demo_14
211 reference(s)		4-Web_Mail.01.vv
211 reference(s)
5-GilbreathConjecture.01.Fra
178 reference(s)		6-Le_Chat.01.Ang
165 reference(s)
7-ChatGPT.11.Fra
148 reference(s)		8-Stereogrammes_AutoStereogrammes.01
144 reference(s)
9-GilbreathConjecture.01.Ang
144 reference(s)		10-DecimalesPi_100000.vv
138 reference(s)
11-Vcatalogue.11
135 reference(s)		12-UlamSpiral.01.Fra
133 reference(s)
13-Galerie_DeterministicFractalGeometry.DIAPO.0042
132 reference(s)		14-FloatingPointNumbers.01.Fra
130 reference(s)
15-Galerie_NewPictures.DIAPO.0040
125 reference(s)		16-Galerie_DeterministicFractalGeometry.DIAPO.0043
124 reference(s)
17-Galerie_GeneralitiesVisualization.DIAPO.0110
123 reference(s)		18-Galerie_GeneralitiesVisualization.DIAPO.0111
122 reference(s)
19-Galerie_GeneralitiesVisualization.DIAPO.0115
121 reference(s)		20-Galerie_GeneralitiesVisualization.DIAPO.0112
121 reference(s)
21-Galerie_DeterministicFractalGeometry.DIAPO.0041
121 reference(s)		22-DecimalesDePi.01.Fra
121 reference(s)
23-ChatGPT.01.Ang
121 reference(s)		24-AProposSite.01.Fra
121 reference(s)
25-Galerie_GeneralitiesVisualization.DIAPO.0120
119 reference(s)		26-Galerie_GeneralitiesVisualization.DIAPO.0119
119 reference(s)
27-Galerie_GeneralitiesVisualization.DIAPO.0109
118 reference(s)		28-Galerie_DeterministicFractalGeometry.DIAPO.0044
118 reference(s)
29-Galerie_DeterministicFractalGeometry.DIAPO.0040
118 reference(s)		30-Informations_GoodNewsAndBadNews.01.Ang
117 reference(s)
31-Galerie_NewPictures.DIAPO.0041
116 reference(s)		32-Galerie_GeneralitiesVisualization.DIAPO.0124
116 reference(s)
33-Galerie_GeneralitiesVisualization.DIAPO.0116
116 reference(s)		34-ChatGPT.01.Fra
116 reference(s)
35-Galerie_NewPictures.DIAPO.0034
115 reference(s)		36-Galerie_NewPictures.DIAPO.0031
114 reference(s)
37-Galerie_GeneralitiesVisualization.DIAPO.0121
114 reference(s)		38-Galerie_GeneralitiesVisualization.DIAPO.0117
114 reference(s)
39-Galerie_DeterministicFractalGeometry.DIAPO.0046
114 reference(s)		40-Fractal.01
114 reference(s)
41-Galerie_NewPictures.DIAPO.0033
113 reference(s)		42-Galerie_NewPictures.DIAPO.0026
113 reference(s)
43-Galerie_NewPictures.DIAPO.0025
113 reference(s)		44-Galerie_GeneralitiesVisualization.DIAPO.0123
113 reference(s)
45-Galerie_GeneralitiesVisualization.DIAPO.0113
113 reference(s)		46-Galerie_DeterministicFractalGeometry.DIAPO.0045
113 reference(s)
47-UlamSpiral.01.Ang
112 reference(s)		48-Galerie_GeneralitiesVisualization.DIAPO.0147
112 reference(s)
49-Galerie_GeneralitiesVisualization.DIAPO.0118
112 reference(s)		50-Galerie_GeneralitiesVisualization.DIAPO.0114
112 reference(s)
51-Galerie_GeneralitiesVisualization.DIAPO.0074
112 reference(s)		52-Galerie_DeterministicFractalGeometry.DIAPO.0037
112 reference(s)
53-Galerie_NewPictures.DIAPO.0035
111 reference(s)		54-Galerie_GeneralitiesVisualization.DIAPO.0127
111 reference(s)
55-Galerie_GeneralitiesVisualization.DIAPO.0126
111 reference(s)		56-Galerie_GeneralitiesVisualization.DIAPO.0108
111 reference(s)
57-Galerie_GeneralitiesVisualization.DIAPO.0106
111 reference(s)		58-Galerie_GeneralitiesVisualization.DIAPO.0080
111 reference(s)
59-Galerie_DeterministicFractalGeometry.DIAPO.0039
111 reference(s)		60-EnsembleDesGaleriesFractales.DIAPO.0104
111 reference(s)
61-Galerie_NewPictures.DIAPO.0032
110 reference(s)		62-Galerie_GeneralitiesVisualization.DIAPO.0122
110 reference(s)
63-Galerie_GeneralitiesVisualization.DIAPO.0073
110 reference(s)		64-Galerie_DeterministicFractalGeometry.DIAPO.0050
110 reference(s)
65-Galerie_DeterministicFractalGeometry.DIAPO.0038
110 reference(s)		66-Galerie_DeterministicFractalGeometry.DIAPO.0036
110 reference(s)
67-Galerie_DeterministicFractalGeometry.DIAPO.0034
110 reference(s)		68-Fractal.21
110 reference(s)
69-EnsembleDesGaleries.DIAPO.0955
110 reference(s)		70-EnsembleDesGaleries.DIAPO.0954
110 reference(s)
71-Galerie_NewPictures.DIAPO.0042
109 reference(s)		72-Galerie_NewPictures.DIAPO.0028
109 reference(s)
73-Galerie_NewPictures.DIAPO.0027
109 reference(s)		74-Galerie_GeneralitiesVisualization.DIAPO.0107
109 reference(s)
75-Galerie_GeneralitiesVisualization.DIAPO.0072
109 reference(s)		76-Galerie_GeneralitiesVisualization.DIAPO.0065
109 reference(s)
77-Galerie_GeneralitiesVisualization.DIAPO.0062
109 reference(s)		78-Galerie_GeneralitiesVisualization.DIAPO.0026
109 reference(s)
79-Galerie_DeterministicFractalGeometry.DIAPO.0047
109 reference(s)		80-Galerie_DeterministicFractalGeometry.DIAPO.0033
109 reference(s)
81-Galerie_NewPictures.DIAPO.0029
108 reference(s)		82-Galerie_GeneralitiesVisualization.DIAPO.0105
108 reference(s)
83-Galerie_GeneralitiesVisualization.DIAPO.0071
108 reference(s)		84-Galerie_GeneralitiesVisualization.DIAPO.0064
108 reference(s)
85-Galerie_GeneralitiesVisualization.DIAPO.0059
108 reference(s)		86-EnsembleDesGaleriesFractales.DIAPO.0185
108 reference(s)
87-EnsembleDesGaleries.DIAPO.0795
108 reference(s)		88-help.
107 reference(s)
89-Galerie_NewPictures.DIAPO.0047
107 reference(s)		90-Galerie_NewPictures.DIAPO.0030
107 reference(s)
91-Galerie_NewPictures.DIAPO.0023
107 reference(s)		92-Galerie_GeneralitiesVisualization.DIAPO.0131
107 reference(s)
93-Galerie_GeneralitiesVisualization.DIAPO.0130
107 reference(s)		94-Galerie_GeneralitiesVisualization.DIAPO.0092
107 reference(s)
95-Galerie_GeneralitiesVisualization.DIAPO.0086
107 reference(s)		96-Galerie_GeneralitiesVisualization.DIAPO.0081
107 reference(s)
97-Galerie_GeneralitiesVisualization.DIAPO.0075
107 reference(s)		98-Galerie_GeneralitiesVisualization.DIAPO.0033
107 reference(s)
99-Galerie_DeterministicFractalGeometry.DIAPO.0049
107 reference(s)		100-EnsembleDesGaleriesFractales.DIAPO.0274
107 reference(s)
101-EnsembleDesGaleriesFractales.DIAPO.0230
107 reference(s)		102-EnsembleDesGaleriesFractales.DIAPO.0029
107 reference(s)
103-EnsembleDesGaleriesFractales.DIAPO.0027
107 reference(s)		104-EnsembleDesGaleries.DIAPO.0957
107 reference(s)
105-Galerie_NewPictures.DIAPO.0037
106 reference(s)		106-Galerie_NewPictures.DIAPO.0036
106 reference(s)
107-Galerie_GeneralitiesVisualization.DIAPO.0125
106 reference(s)		108-Galerie_GeneralitiesVisualization.DIAPO.0102
106 reference(s)
109-Galerie_GeneralitiesVisualization.DIAPO.0099
106 reference(s)		110-Galerie_GeneralitiesVisualization.DIAPO.0091
106 reference(s)
111-Galerie_GeneralitiesVisualization.DIAPO.0070
106 reference(s)		112-Galerie_GeneralitiesVisualization.DIAPO.0067
106 reference(s)
113-Galerie_GeneralitiesVisualization.DIAPO.0063
106 reference(s)		114-Galerie_GeneralitiesVisualization.DIAPO.0061
106 reference(s)
115-Galerie_GeneralitiesVisualization.DIAPO.0060
106 reference(s)		116-Galerie_GeneralitiesVisualization.DIAPO.0028
106 reference(s)
117-Galerie_DeterministicFractalGeometry.DIAPO.0051
106 reference(s)		118-Galerie_DeterministicFractalGeometry.DIAPO.0048
106 reference(s)
119-EnsembleDesGaleriesFractales.DIAPO.0271
106 reference(s)		120-EnsembleDesGaleriesFractales.DIAPO.0184
106 reference(s)
121-EnsembleDesGaleries.DIAPO.0203
106 reference(s)		122-EnsembleDesGaleries.DIAPO.0063
106 reference(s)
123-Galerie_NewPictures.DIAPO.0058
105 reference(s)		124-Galerie_NewPictures.DIAPO.0043
105 reference(s)
125-Galerie_NewPictures.DIAPO.0039
105 reference(s)		126-Galerie_GeneralitiesVisualization.DIAPO.0183
105 reference(s)
127-Galerie_GeneralitiesVisualization.DIAPO.0151
105 reference(s)		128-Galerie_GeneralitiesVisualization.DIAPO.0149
105 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.