Monthly Best Of on 08/28/2026




The Pythagoras' theorem -a right angled triangle-

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 08/28/2026 and last updated on 08/28/2026 22:09:11 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Autostereogram of a quaternionic Julia set -tridimensional cross-section-
1-240 reference(s)		The eroded Menger Sponge -iteration 3-
2-210 reference(s)		Artistic view of the prime numbers
3-195 reference(s)		The random walk of photons escaping the Sun
4-172 reference(s)
An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
5-172 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
6-169 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
7-161 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
8-152 reference(s)
A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives. More than 50 years of progress in computer science -hardware and software-
9-149 reference(s)		The Lorenz attractor
10-146 reference(s)		The tiling of a 6x10 rectangle by means of the 12 different pentominos
11-137 reference(s)		Jean-François Colonna (on 11/17/1994)with its fractal mountains
12-133 reference(s)
Quantum vacuum fluctuations
13-131 reference(s)		The Menger Sponge -iteration 5-
14-130 reference(s)		Mountains and fog
15-125 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
16-124 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
17-123 reference(s)		Fractal piano keyboard
18-122 reference(s)		The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
19-121 reference(s)		Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
20-120 reference(s)
Artistic view of gravitational waves
21-119 reference(s)		A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
22-118 reference(s)		N-body problem integration (N=2)displaying a perfect Keplerian orbit
23-116 reference(s)		Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
24-115 reference(s)
Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 1.083.984 galaxies)obtained by means of a non deterministic fractal process
25-115 reference(s)		Hypercubic lattice
26-113 reference(s)		The foggy Babel Tower -a Tribute to Brueghel the Elder-
27-112 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)
28-112 reference(s)
Tridimensional Hilbert Curve -iteration 4-
29-112 reference(s)		Artistic view of the Big Bang
30-111 reference(s)		The Mathematics are the key of the Multiverse
31-111 reference(s)		Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier-
32-111 reference(s)
Anaglyph -blue=right, red=left- of the quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
33-111 reference(s)		Voronoi diagrams
34-110 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-
35-110 reference(s)		Fractal Self-Portrait -'Décalcomanie', a Tribute to René Magritte-
36-110 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [3*10^14,4*10^14]-
37-110 reference(s)		Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
38-109 reference(s)		Paradoxal structure based on the geometry of the Bonan-Jeener-Klein triple bottle
39-109 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-
40-109 reference(s)
A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of 'pi' (141592...)-base 10- with 33.333 time steps
41-108 reference(s)		Gravitation and space-time curvature
42-108 reference(s)		The level 3 cluster made of 8 'Spectre' level 2 clusters with display of all the key-points making quadrilaterals (8 small and a big one)
43-107 reference(s)		Quark and gluon structure of a nucleon
44-107 reference(s)
Animation and accumulation of a quaternionic Julia island
45-107 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 5-
46-106 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 100215...-
47-106 reference(s)		Untitled 0193
48-105 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)
49-105 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
50-105 reference(s)		Mountains at sunrise
51-104 reference(s)		A type 'B6-XYZ' pseudo-random walk defined by means of the 48 first 'decimals' of the transcendental Champernowne number -using all base 4 integer numbers-: 0.{1 2 3 4 5 1 0 1 1 1 2 1 3 1 4 1 5 2 0 2 1 2 2 2 3 2 4 2 5 3 0 3 1 3 2 3 3 3 4 3 5 4 0 4 1 4 2 4}
52-103 reference(s)
An hexagonal tiling of the hyperbolic Poincaré disk -iteration 5-
53-103 reference(s)		Untitled 0192
54-103 reference(s)		Botticelli anomaly on the Moon
55-103 reference(s)		The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
56-103 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
57-103 reference(s)		Visualization of the Proth-Gilbreath Conjecture process
58-103 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
59-103 reference(s)		24 evenly distributed points on a sphere by means of simulated annealing
60-102 reference(s)
A double spherical cross-section inside the Menger Sponge -iteration 5-
61-102 reference(s)		A spherical cross-section inside the Menger Sponge -iteration 5-
62-102 reference(s)		Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
63-102 reference(s)		An aperiodic Penrose tiling of the plane
64-101 reference(s)
The Sierpinski Carpet -iteration 5-
65-101 reference(s)		Monument Valley at sunrise
66-101 reference(s)		The same bidimensional scalar field displayed with 4 different color palettes
67-101 reference(s)		Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers-
68-101 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
69-101 reference(s)		A random tiling of a square domain using 'generalized dominoes' made of a random number of squares
70-101 reference(s)		Tridimensional display of the Riemann Zeta function inside [-10.0,+20.0]x[-15.0,+15.0] (bird's-eye view)
71-100 reference(s)		Where is the Universe?
72-100 reference(s)
A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of 'pi' (141592...)with 492 more digits defining a helix -base 10- with 33.497 time steps
73-100 reference(s)		The generalized Ulam spiral displaying 100 numbers
74-100 reference(s)		Empty
75-100 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [2*10^14,3*10^14]-
76-100 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [1*10^14,2*10^14]-
77-100 reference(s)		The execution of a very simple program on a Turing Machine
78-99 reference(s)		A sphere -positive curvature-
79-99 reference(s)		Untitled 0191
80-99 reference(s)
Mountains and fog
81-99 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)
82-99 reference(s)		An extended Menger Sponge -iteration 2-
83-99 reference(s)		The Menger Sponge -iteration 2-
84-99 reference(s)
The Lorenz attractor
85-99 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
86-99 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 32 first prime numbers-
87-99 reference(s)		An aperiodic Penrose tiling of the plane
88-98 reference(s)
A pseudo-periodical triangular tiling of the plane
89-98 reference(s)		Gravitation and space-time curvature
90-98 reference(s)		Zoom in on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
91-98 reference(s)		A foggy pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) and with a rotation about the Y axis -tridimensional cross-section-
92-98 reference(s)
Untitled 0671
93-98 reference(s)		Untitled 0668
94-98 reference(s)		A 4-cube -an hypercube-
95-98 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-
96-98 reference(s)
The Jeener-Klein triple bottle
97-98 reference(s)		Elliptical trajectory of a planet around a star with perihelion advance (very exaggerated)
98-98 reference(s)		An aperiodic Penrose tiling of the plane -a Tribute to Piet Mondrian and Roger Penrose-
99-97 reference(s)		The 'sharp' Golden Triangle
100-97 reference(s)
An extended Menger Sponge -iteration 2-
101-97 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [1.2x10^15,1.3x10^15]-
102-97 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-
103-96 reference(s)		An aperiodic Penrose tiling of the plane
104-96 reference(s)
The random walk of photons escaping the Sun
105-96 reference(s)		Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
106-96 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
107-96 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) and with a 0 to pi rotation about the X axis -tridimensional cross-section-
108-96 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 64 first prime numbers-
109-96 reference(s)		A shell (Jeener surface 1)in motion
110-96 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
111-96 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-
112-95 reference(s)
A tridimensional pseudo-random walk -spherical coordinates- defined by means of the 999 first decimals of the Champernowne number (1 2 3 4 5 6 7 8 9 10 11 12...)-base 10- with 333 time steps
113-95 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
114-95 reference(s)		A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -90.000 digits, -base 10- with 30.000 time steps
115-95 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) -yellow body point of view-
116-95 reference(s)
Artistic view of the Solar System viewed from a virtual planet
117-95 reference(s)		Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
118-95 reference(s)		Rotation about the X axis of the Lorenz attractor (1000 iterations), computed simultaneously on two different computers
119-95 reference(s)		Tridimensional Hilbert Curve -iterations 1 to 3-
120-95 reference(s)
The DNA of Mathematics -the 60 first digits of 'pi' and 'e'-
121-95 reference(s)		Tridimensional representation of our familiar tridimensional space
122-95 reference(s)		The Jeener hypocycloidal snail
123-95 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-
124-95 reference(s)
Tridimensional display of the Riemann Zeta function inside [-10.0,+60.0]x[-35.0,+35.0] (bird's-eye view)
125-94 reference(s)		Along the border of the Mandelbrot set
126-94 reference(s)		Numerical value table
127-94 reference(s)		The bidimensional brownian motion of 891 light and small particles
128-94 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
3758 reference(s)		2-MorePages.Ang.
423 reference(s)
3-ChatGPT.11.Fra
282 reference(s)		4-Vcatalogue.11
250 reference(s)
5-Proth_Gilbreath_Conjecture.01.Ang
235 reference(s)		6-ChatGPT.11.Ang
224 reference(s)
7-Galerie_DeterministicFractalGeometry.FV
218 reference(s)		8-xiirv_____.nota.t.
170 reference(s)
9-mail.01.vv
169 reference(s)		10-help.
167 reference(s)
11-demo_14
165 reference(s)		12-An2000.01.Fra
163 reference(s)
13-MorePages.Fra.
162 reference(s)		14-FloatingPointNumbers.01.Fra
162 reference(s)
15-GilbreathConjecture.01.Ang
156 reference(s)		16-Stereogrammes_AutoStereogrammes.01
152 reference(s)
17-ChatGPT.01.Fra
152 reference(s)		18-LOG_xiMc.11
149 reference(s)
19-An2038.01.Ang
145 reference(s)		20-Galerie_NewPictures.FV
144 reference(s)
21-An2038.01.Fra
144 reference(s)		22-NDimensionalDeterministicFractalSets.01.Ang
142 reference(s)
23-AVirtualSpaceTimeTravelMachine.VersionComplete.Fra
142 reference(s)		24-DecimalesPi_1_100.vv
138 reference(s)
25-AVirtualSpaceTimeTravelMachine.VersionComplete.Ang
137 reference(s)		26-DEuclideAuGPS.01.Ang
135 reference(s)
27-copyright.01.
132 reference(s)		28-FloatingPointNumbers.01.Ang
132 reference(s)
29-Galerie_NumberTheory.FV
130 reference(s)		30-Fractal.11
129 reference(s)
31-VisualisationDesNombres.01.Fra
128 reference(s)		32-Fractal.01
128 reference(s)
33-UlamSpiral.01.Ang
124 reference(s)		34-ExpV_VirE.11
124 reference(s)
35-ChatGPT.01.Ang
124 reference(s)		36-Galerie_PALETTES_A
123 reference(s)
37-subject.01.
122 reference(s)		38-NombresPremiers_10000.vv
122 reference(s)
39-MathematiquesPhysiqueFractales.02
122 reference(s)		40-Galerie_ImagesDesMathematiques.FV
122 reference(s)
41-HughEverettMultiverse.01.Fra
121 reference(s)		42-GoldenTriangle.01.Fra
121 reference(s)
43-ImpossibleStructures.01.Ang
120 reference(s)		44-Polynomials_RationalNumbers.01.Fra
119 reference(s)
45-present.01.
117 reference(s)		46-VAcatalogue.11
117 reference(s)
47-UlamSpiral.01.Fra
117 reference(s)		48-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
117 reference(s)
49-Exposition_EcolePolytechnique_FeteDeLaScience_202510
117 reference(s)		50-IAGenerativesImages.01.Fra
116 reference(s)
51-Fractal.21
116 reference(s)		52-Claude.01.Fra
116 reference(s)
53-BEST.20160828
116 reference(s)		54-ExpV_VirE.Ang
115 reference(s)
55-VCcatalogue.11
114 reference(s)		56-NDimensionalDeterministicFractalSets.01.Fra
113 reference(s)
57-GilbreathConjecture.01.Fra
113 reference(s)		58-Multivers.01.Fra
112 reference(s)
59-DEuclideAuGPS.01.Fra
112 reference(s)		60-Galerie_ArtisticCreation.FV
111 reference(s)
61-Galerie_ArtAndScience.FV
111 reference(s)		62-DecimalesDePi.01.Fra
110 reference(s)
63-Galerie_ArtAndScience
109 reference(s)		64-BilletDHumeur_IntelligenceArtificielle.01.Fra
109 reference(s)
65-Galeries.01.vv
108 reference(s)		66-DecimalesPi_100000.vv
108 reference(s)
67-AnimFractal.01.
108 reference(s)		68-xiirf_____.nota.t.
107 reference(s)
69-Claude.01.Ang
106 reference(s)		70-SurfaceProjector.01.Ang
105 reference(s)
71-SourceExemple_____xrq_____hydrogene.61.K.
105 reference(s)		72-MathematiquesPhysiqueFractales.02.1.13
105 reference(s)
73-xiirs_____.nota.t.
104 reference(s)		74-Polynomials_RationalNumbers.01.Ang
103 reference(s)
75-LesElucubrationsMathematiquesDeChatGPT.01.Fra
103 reference(s)		76-VisualisationDesNombres.01.Ang
102 reference(s)
77-create.03.
101 reference(s)		78-T_PerteDeLAssociativite.01_ProblemesNombresFlottants.03.0001
101 reference(s)
79-Proth_Gilbreath_Conjecture.01.Fra
101 reference(s)		80-Autostereograms.01.
101 reference(s)
81-stereogrammes_autostereogrammes.01
99 reference(s)		82-LesCourbesRemplissantes.01.Fra
99 reference(s)
83-CantorSet_SierpinskiCarpet_MengerSponge.01.Ang
99 reference(s)		84-T_PerteDeLAssociativite.01_ProblemesNombresFlottants.02.0001
97 reference(s)
85-IAGenerativesImages.01.Ang
97 reference(s)		86-Exposition_EcolePolytechnique_FeteDeLaScience_201910
97 reference(s)
87-AVirtualSpaceTimeTravelMachine.Fra
97 reference(s)		88-PerteDeLAssociativite.01
96 reference(s)
89-OrdinateursEtCalculs.01.Fra
96 reference(s)		90-LeParadoxeDeFermi.01.Fra
96 reference(s)
91-LeParadoxeDeFermi.01.Ang
96 reference(s)		92-Galerie_GeneralitiesVisualization.FV
96 reference(s)
93-DieuScience.01.Fra
96 reference(s)		94-MathematiquesPhysiqueFractales.02.1.12
95 reference(s)
95-LesCourbesRemplissantes.01.Ang
95 reference(s)		96-Le_Chat.01.Fra
95 reference(s)
97-MouvementBrownien.01.Fra
94 reference(s)		98-LesCourbesRemplissantes.02.Ang
94 reference(s)
99-Galerie_BestOf.FV
94 reference(s)		100-EntrelacsIntertwinings.01.Fra
94 reference(s)
101-NatureDesMathematiques.01.vv.Fra
93 reference(s)		102-LesNombresTranscendants.01.Fra
93 reference(s)
103-GoldenTriangle.01.Ang
93 reference(s)		104-GenieLogiciel.01.Fra
93 reference(s)
105-DroitDeReponse.01.Fra
93 reference(s)		106-OrdinateursEtCalculs.01.Ang
92 reference(s)
107-Galerie_NumbersAndLight.FV
92 reference(s)		108-Galerie_CelestialMechanics
92 reference(s)
109-BEST.20150928
92 reference(s)		110-WelcomeToMars.01.Fra
91 reference(s)
111-SurfaceProjector.01.Fra
91 reference(s)		112-PerteDeLAssociativite.01.VerhulstDefinition
91 reference(s)
113-Pcatalogue.11
91 reference(s)		114-MathematiquesPhysiqueFractales.12
91 reference(s)
115-BEST.20000517
91 reference(s)		116-PerteDeLAssociativite.01.VerhulstCalculs
90 reference(s)
117-Informations_AboutPicturesAnimationsAndFiles.01.Ang
90 reference(s)		118-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
90 reference(s)
119-xiirk_____.nota.t.
89 reference(s)		120-RealNumbers.01.Fra
89 reference(s)
121-RealNumbers.01.Ang
89 reference(s)		122-MonodimensionalCellularAutomata.01.Ang
89 reference(s)
123-LesCourbesRemplissantes.02.Fra
89 reference(s)		124-LeCinquantenaireDuCMAP.01.vv.Fra
89 reference(s)
125-LaBeauteDesMathematiques.01.Ang
89 reference(s)		126-Galerie_TextureSynthesis
89 reference(s)
127-BEST.20230528
89 reference(s)		128-BEST.20130328
89 reference(s)

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




Copyright © Jean-François Colonna, -2026.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, -2026.