Monthly Best Of on 10/28/2025




A heap (bird's-eye view)

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 10/28/2025 and last updated on 10/28/2025 22:11:18 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-445 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
2-159 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
3-156 reference(s)		The random walk of photons escaping the Sun
4-136 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
5-117 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
6-114 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
7-107 reference(s)		The Lorenz attractor
8-105 reference(s)
The Sierpinski Carpet -iteration 1 to 5-
9-104 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
10-101 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 64 first prime numbers-
11-101 reference(s)		The generalized Ulam spiral
12-99 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
13-96 reference(s)		A variable Archimedes spiral displaying 1000 numbers
14-93 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
15-92 reference(s)		Kasner billiard: Time-dependent billiard (from negative curvature to positive curvature)with one accelerated particle
16-90 reference(s)
Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
17-87 reference(s)		Botticelli anomaly on the Moon
18-86 reference(s)		'There is a war' -a Tribute to Leonard Cohen-
19-85 reference(s)		Quantum vacuum fluctuations
20-84 reference(s)
The foggy Babel Tower -a Tribute to Brueghel the Elder-
21-83 reference(s)		The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
22-82 reference(s)		Fractal Self-Portrait -a Tribute to René Magritte-
23-82 reference(s)		A quaternionic Julia set -tridimensional cross-section-
24-80 reference(s)
A regular 7-gon -an heptagon-
25-78 reference(s)		Two identical grey rectangles in front of a grey scale
26-78 reference(s)		A fractal Möbius strip
27-78 reference(s)		Artistic view of the prime numbers
28-78 reference(s)
The first four iterations of the construction of the von Koch snowflake
29-77 reference(s)		Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
30-76 reference(s)		Quark and gluon structure of a nucleon
31-76 reference(s)		Untitled 0662
32-75 reference(s)
The execution of a very simple program on a Turing Machine
33-75 reference(s)		Quark and gluon structure of a nucleon
34-75 reference(s)		Hypercube
35-75 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
36-74 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)
37-74 reference(s)		Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
38-74 reference(s)		Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
39-74 reference(s)		The DNA of Mathematics -the 100 first digits of 'pi' and '1/pi'-
40-74 reference(s)
Artistic view of the 100.000 first digits -base 10- of 'pi'
41-73 reference(s)		The distance {Earth-Mars} -millions of kilometers- starting on 01/01/1950 AD and during seven marsian years
42-73 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
43-73 reference(s)		From Pluto to the Sun (non linear scales)
44-72 reference(s)
Tridimensional display of 36 eigenstates of the Hydrogen atom (bidimensional computation)
45-72 reference(s)		A simple geometrical periodical structure
46-71 reference(s)		The Ulam spiral displaying 2025 numbers
47-71 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 5-
48-71 reference(s)
Happy new year 2000
49-71 reference(s)		The Many World Theory of Hugh Everett
50-70 reference(s)		The Sierpinski Carpet -iteration 3-
51-70 reference(s)		The execution of a very simple program on a Turing Machine
52-69 reference(s)
The generalized Ulam spiral displaying 100 numbers
53-69 reference(s)		The 256 first digits -base 10- of 'pi' on a Bidimensional Hilbert Curve -iteration 4- mapped on a sphere
54-69 reference(s)		Tridimensional zoom in on the Mandelbrot set
55-69 reference(s)		The Lorenz attractor
56-69 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [2,10^14]-
57-69 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
58-68 reference(s)		Mountains and fog
59-68 reference(s)		Fractal synthesis of mountains with vegetation and stormy clouds
60-68 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-
61-68 reference(s)		Tridimensional Hilbert Curve -iteration 3-
62-68 reference(s)		Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier and Carl Friedrich Gauss-
63-67 reference(s)		Alien
64-67 reference(s)
The Klein bottle
65-67 reference(s)		Empty
66-67 reference(s)		The Birth of the Universe
67-67 reference(s)		A monodimensional 'quasi-continuous' cellular automaton
68-67 reference(s)
An aperiodic Penrose tiling of the plane -the extended paradoxal demoniac Rubik's Cube-
69-66 reference(s)		Bidimensional closed self-avoiding brownian motion on an ellipsoide
70-66 reference(s)		The particle trajectories of bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to an attractive central field of gravity
71-66 reference(s)		Dynamics of the even distribution of 24 points on a sphere by means of simulated annealing
72-66 reference(s)
The 16 first decimals -base 10- of 'pi' on a Bidimensional Hilbert Curve -iteration 2-
73-66 reference(s)		A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -10.000 digits, -base 10- into 021003... -16.607 digits, -base 4-
74-66 reference(s)		The distances {Sun-Jupiter,Sun-Saturn,Sun-Uranus,Sun-Neptune} during one neptunian year
75-66 reference(s)		Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')with a 1/Z conformal transformation in the complex plane -tridimensional cross-section-
76-66 reference(s)
Detail close-up of the quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.581514...,+0.635888...,0,0)and with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
77-66 reference(s)		A shell (Jeener surface 1)in motion
78-66 reference(s)		The Universe at the heart of a Calabi-Yau manifold
79-65 reference(s)		The execution of a very simple program on a Turing Machine
80-65 reference(s)
Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier and Carl Friedrich Gauss-
81-65 reference(s)		Quaternionic butterfly with extended arithmetics -a Tribute to Laurent Schwartz-
82-65 reference(s)		A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
83-65 reference(s)		Mountains and light cloud dynamics -this sequence being periodical-
84-65 reference(s)
Close-up on a foggy 'MandelBox' -tridimensional cross-section-
85-65 reference(s)		Tridimensional visualization of the Mandelbrot set with mapping of the arguments
86-65 reference(s)		2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
87-65 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
88-65 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
89-65 reference(s)		Untitled 0653
90-64 reference(s)		Tridimensional display of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
91-64 reference(s)		The execution of a very simple program on a Turing Machine
92-64 reference(s)
An aperiodic Penrose tiling of the Golden Decagon -a Tribute to Piet Mondrian and Roger Penrose-
93-64 reference(s)		The tridimensional brownian motion of 1815 particles
94-64 reference(s)		The bidimensional brownian motion of 891 particles
95-64 reference(s)		From Pluto to the Sun
96-64 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
97-64 reference(s)		An extended foggy 'MandelBox' -tridimensional cross-section-
98-64 reference(s)		1-foil torus knot -obvious knot- on its torus and its asociated Möbius strip
99-64 reference(s)		Happy new year 2000
100-64 reference(s)
Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
101-63 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-
102-63 reference(s)		Where is the Universe?
103-63 reference(s)		Artistic view of the Big Bang
104-63 reference(s)
The execution of a very simple program on a Turing Machine
105-63 reference(s)		Kasner billiard: Time-dependent billiard (from positive curvature to negative curvature)with one accelerated particle
106-63 reference(s)		One of my first programs written for a PB250 computer, fourth 1967 quarter -page 2/3-
107-63 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-
108-63 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
109-63 reference(s)		Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
110-63 reference(s)		Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers-
111-63 reference(s)		The DNA of Mathematics -the 480 first digits of 'pi' and '1/pi'-
112-63 reference(s)
A Part of the DNA double helix -a Tribute to Francis Crick, Rosalind Franklin and James Watson-
113-63 reference(s)		Tridimensional fractal Self-Portrait
114-63 reference(s)		Sixteen interlaced fractal torus
115-63 reference(s)		Tridimensional representation of a hexadimensional Calabi-Yau manifold
116-63 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-
117-63 reference(s)		The Sierpinski Carpet -iteration 5-
118-62 reference(s)		The trajectories of bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity
119-62 reference(s)		Fractal 'celestial body' based on a sphere
120-62 reference(s)
Tridimensional display of a spiral displaying 'pi' with 2.000 digits -base 10-
121-62 reference(s)		The multiplicative persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-
122-62 reference(s)		Mountains at sunrise
123-62 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-
124-62 reference(s)
From 'geocentrism' to 'heliocentrism'
125-62 reference(s)		The eye of God -an artistic view of the Solar System-
126-62 reference(s)		The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.581514...,+0.635888...,0,0)-tridimensional cross-section-
127-62 reference(s)		Iterations in the complex plane: the computation of the Mandelbrot set
128-62 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
3126 reference(s)		2-xiirv_____.nota.t.
1798 reference(s)
3-xiirc_____.nota.t.
955 reference(s)		4-xiirf_____.nota.t.
714 reference(s)
5-xiirs_____.nota.t.
517 reference(s)		6-Vcatalogue.11
430 reference(s)
7-An2000.01.Fra
216 reference(s)		8-ChatGPT.11.Ang
196 reference(s)
9-Web_Mail.01.vv
192 reference(s)		10-xiak_____.nota.t.
184 reference(s)
11-Galerie_NumberTheory.FV
160 reference(s)		12-ChatGPT.11.Fra
145 reference(s)
13-Galerie_ArtisticCreation.FV
139 reference(s)		14-GilbreathConjecture.01.Fra
135 reference(s)
15-xiia_____.nota.t.
130 reference(s)		16-xiac_____.nota.t.
129 reference(s)
17-Stereogrammes_AutoStereogrammes.01
128 reference(s)		18-ExpV_VirE.Ang
128 reference(s)
19-Galerie_DeterministicFractalGeometry.FV
126 reference(s)		20-MorePages.Ang.
125 reference(s)
21-Pcatalogue.11
120 reference(s)		22-DecimalesPi_100000.vv
119 reference(s)
23-ChatGPT.01.Fra
118 reference(s)		24-demo_14
114 reference(s)
25-help.
113 reference(s)		26-Exposition_EcolePolytechnique_FeteDeLaScience_202510
113 reference(s)
27-AVirtualSpaceTimeTravelMachine.Fra
113 reference(s)		28-UlamSpiral.01.Fra
112 reference(s)
29-Multivers.01.Fra
110 reference(s)		30-MathematiquesPhysiqueFractales.02
107 reference(s)
31-Fractal.01
106 reference(s)		32-mail.01.vv
105 reference(s)
33-Galerie_GeneralitiesVisualization.FV
105 reference(s)		34-ChatGPT.01.Ang
103 reference(s)
35-LesApprentisDieux.01
102 reference(s)		36-catalogue.11
98 reference(s)
37-Le_Chat.01.Ang
98 reference(s)		38-GilbreathConjecture.01.Ang
97 reference(s)
39-DecimalesDePi.01.Fra
97 reference(s)		40-Le_Chat.01.Fra
96 reference(s)
41-xiirk_____.nota.t.
94 reference(s)		42-Galerie_BestOf.FV
93 reference(s)
43-Galerie_ArtAndScience.FV
93 reference(s)		44-FloatingPointNumbers.01.Fra
93 reference(s)
45-GenieLogiciel.01.Fra
92 reference(s)		46-Galerie_ImagesEssentiellesDesMathematiques.FV
92 reference(s)
47-AProposSite.01.Fra
89 reference(s)		48-MorePages.Fra.
88 reference(s)
49-SIlVousPlaitDessineMoiLInfini.01.Fra
87 reference(s)		50-ImagesDuVirtuel.01.Fra.FV
87 reference(s)
51-Fractal.21
86 reference(s)		52-DeepSeek.01.Fra
86 reference(s)
53-Galerie_NewPictures.FV
85 reference(s)		54-Galerie_ImagesDesMathematiques.FV
84 reference(s)
55-Fractal.11
84 reference(s)		56-NDimensionalDeterministicFractalSets.01.Fra
83 reference(s)
57-Autostereograms.01.
83 reference(s)		58-UlamSpiral.01.Ang
82 reference(s)
59-IAGenerativesImages.01.Fra
82 reference(s)		60-FloatingPointNumbers.01.Ang
82 reference(s)
61-NombresPremiers_10000.vv
81 reference(s)		62-IAGenerativesImages.01.Ang
81 reference(s)
63-LeParadoxeDeFermi.01.Ang
80 reference(s)		64-ExpV_VirE.11
80 reference(s)
65-SurfaceProjector.01.Ang
79 reference(s)		66-LeParadoxeDeFermi.01.Fra
79 reference(s)
67-DieuScience.01.Fra
78 reference(s)		68-copyright.01.
77 reference(s)
69-WelcomeToMars.01.Fra
77 reference(s)		70-RealNumbers.01.Fra
77 reference(s)
71-LOG_xiMc.11
77 reference(s)		72-WelcomeToMars.01.Ang
76 reference(s)
73-MathematiquesPhysiqueFractales.12
76 reference(s)		74-Kepler.02.
76 reference(s)
75-DieuScience.01.Ang
76 reference(s)		76-NatureDesMathematiques.01.vv.Fra
75 reference(s)
77-Informations_GoodNewsAndBadNews.01.Fra
75 reference(s)		78-ArtScience.01
75 reference(s)
79-EntrelacsIntertwinings.01.Fra
74 reference(s)		80-DecimalesPi_1_100.vv
74 reference(s)
81-Informations_GoodNewsAndBadNews.01.Ang
73 reference(s)		82-Galerie_ParticleSystems.FV
72 reference(s)
83-present.01.
71 reference(s)		84-MathematiquesPhysiqueFractales.22
71 reference(s)
85-DEuclideAuGPS.01.Fra
71 reference(s)		86-subject.01.
70 reference(s)
87-Galerie_DeterministicChaos.FV
70 reference(s)		88-Multivers.01.Ang
69 reference(s)
89-NombresEtLumiere.01.vv.Fra
68 reference(s)		90-infinity.01.vv
67 reference(s)
91-MonodimensionalCellularAutomata.01.Ang
67 reference(s)		92-Galerie_SignalProcessing.FV
67 reference(s)
93-Galerie_SelfPortraits.FV
67 reference(s)		94-DEuclideAuGPS.01.Ang
67 reference(s)
95-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
66 reference(s)		96-AnimFractal.01.
66 reference(s)
97-Galerie_Pi.FV
65 reference(s)		98-Galerie_ArtAndScience
65 reference(s)
99-FaireDeLaRecherche.01.vv
65 reference(s)		100-FaireConnaitre_FaireAimer_les_Mathematiques_en_2020.01.vv.Fra
65 reference(s)
101-RemarquesCerveau.01
64 reference(s)		102-NDimensionalDeterministicFractalSets.01.Ang
64 reference(s)
103-LesCourbesRemplissantes.02.Fra
64 reference(s)		104-Informations_AboutPicturesAnimationsAndFiles.01.Ang
64 reference(s)
105-HughEverettMultiverse.01.Ang
64 reference(s)		106-GoldenTriangle.01.Fra
64 reference(s)
107-Galerie_TextureSynthesis.FV
64 reference(s)		108-Galerie_ImagesDidactiques.FV
64 reference(s)
109-ExpositionsDiverses.01.Fra
64 reference(s)		110-MesExpositionsPassees.01
63 reference(s)
111-LesCourbesRemplissantes.01.Fra
63 reference(s)		112-ConjectureDeSyracuse_0256.vv
63 reference(s)
113-SurfaceProjector.01.Fra
62 reference(s)		114-Galerie_CelestialMechanics.FV
62 reference(s)
115-Galerie_Animations.FV
62 reference(s)		116-PerteDeLAssociativite.01
61 reference(s)
117-DuModeleALImage.02.Fra
60 reference(s)		118-MartiensEtMathematiques.01.Fra
59 reference(s)
119-ImagesDuVirtuel.01.Fra
59 reference(s)		120-Galerie_SensitivityToRoundingOffErrors.FV
59 reference(s)
121-Fractal.03
59 reference(s)		122-DeLAxiomeDesParallelesAuGPS.01.Ang
59 reference(s)
123-create.03.
58 reference(s)		124-ManyChaos.01.Ang
58 reference(s)
125-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
58 reference(s)		126-Galerie_NewPictures
58 reference(s)
127-Exposition_EcolePolytechnique_FeteDeLaScience_201810
58 reference(s)		128-Downloading.01.vv
58 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.