Monthly Best Of on 01/28/2026




Anaglyph of a 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 01/28/2026 and last updated on 01/28/2026 22:11:23 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-337 reference(s)		A 4-cube -an hypercube-
2-215 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
3-161 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 512 prime numbers following 613247...-
4-155 reference(s)
An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
5-148 reference(s)		The first four iterations of the construction of the von Koch snowflake
6-146 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
7-144 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
8-144 reference(s)
The Sierpinski Carpet -iteration 1 to 5-
9-141 reference(s)		The Menger Sponge -iteration 5-
10-132 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [6*10^14,7*10^14]-
11-129 reference(s)		Artistic view of the Proth-Gilbreath Conjecture -display of the process for the 512 prime numbers following 613247...-
12-128 reference(s)
Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
13-126 reference(s)		The random walk of photons escaping the Sun
14-124 reference(s)		The abelian -commutative- group defined on elliptic curves
15-120 reference(s)		The Lorenz attractor
16-119 reference(s)
The Jeener-Klein triple bottle
17-113 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 5-
18-107 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
19-105 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
20-104 reference(s)
A perfect bidimensional fractal tree and the self-similarity
21-103 reference(s)		Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
22-102 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
23-101 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
24-100 reference(s)
The journey of an Earth-like virtuel planet (green)in the Solar System -point of view of the virtual planet-
25-99 reference(s)		Botticelli anomaly on the Moon
26-98 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 32 first prime numbers-
27-98 reference(s)		The Goldbach Conjecture -the Goldbach Comet or the Goldbach Rainbow- for the even numbers from 6 to 411678
28-97 reference(s)
The numerical irreversibility of the bidimensional billiard
29-96 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)
30-96 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
31-96 reference(s)		Quantum vacuum fluctuations
32-95 reference(s)
Bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
33-95 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-
34-95 reference(s)		A tridimensional fractal structure -a Tribute to Thierry Mauger-
35-94 reference(s)		A bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle and with display of velocity histograms
36-94 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)
37-94 reference(s)		Happy new year 2000
38-94 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
39-93 reference(s)		Mountains and light cloud dynamics -this sequence being periodical-
40-93 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)
41-93 reference(s)		Phase rotation of the wavelet transform of a bidimensional fractal field
42-93 reference(s)		Tridimensional zoom in on the Mandelbrot set
43-93 reference(s)		A random bidimensional fractal tree and the self-similarity
44-92 reference(s)
Paradoxal structure based on the geometry of the Boy surface
45-92 reference(s)		Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
46-92 reference(s)		A Part of the DNA double helix -a Tribute to Francis Crick, Rosalind Franklin and James Watson-
47-92 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
48-92 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-
49-92 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-
50-91 reference(s)		Fractal diffusion front in a bidimensional medium obtained by means of identical interacting particles
51-91 reference(s)		Quark and gluon structure of a nucleon
52-91 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
53-91 reference(s)		The execution of a very simple program on a Turing Machine
54-90 reference(s)		A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
55-90 reference(s)		Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
56-90 reference(s)
The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
57-90 reference(s)		Happy new year 2000
58-90 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
59-90 reference(s)		Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability
60-90 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-
61-89 reference(s)		A torus
62-89 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 64 first prime numbers-
63-89 reference(s)		The distance {Earth-Mars} -millions of kilometers- starting on 01/01/1950 AD and during seven marsian years
64-88 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) -orange body point of view-
65-88 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)
66-88 reference(s)		The bidimensional Ising Model after 1000 iterations, with 2-state spins, random initial conditions and for different temperatures around the critical temperature
67-88 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [7*10^14,8*10^14]-
68-88 reference(s)
Tridimensional visualization of a bidimensional turbulent flow
69-88 reference(s)		Rotation about the Y (vertical)axis of the Jeener-Klein triple bottle that can also be viewed as a set of 4x3 stereograms
70-88 reference(s)		Tridimensional display of the 'EinStein' aperiodic 'Spectre' tiling
71-87 reference(s)		Coalescence of 40832 particles -black holes?- inside a tridimensional parallelepipedic billiard -a static, non relativistic and bounded universe- with display of the dynamics of the mass histogram, during 204.8 time units
72-87 reference(s)
Tridimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity
73-87 reference(s)		The pythagorician knotted rope -a Tribute to Pythagore-
74-87 reference(s)		Artistic view of gravitational waves
75-87 reference(s)		The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 6-
76-87 reference(s)
Quark and gluon structure of a nucleon
77-87 reference(s)		Pi/2 rotation about the X axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')-tridimensional cross-section-
78-87 reference(s)		From Pluto to the Sun (non linear scales)
79-86 reference(s)		A set of 4x3 stereograms of a close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
80-86 reference(s)
The bidimensional Ising Model with 2-state spins, temperature=0.2 and random initial conditions
81-86 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
82-86 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-
83-86 reference(s)		An aperiodic Penrose tiling of the plane
84-85 reference(s)
Bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity
85-85 reference(s)		Monument Valley at sunrise
86-85 reference(s)		The smooth integers
87-85 reference(s)		Free fall in the vacuum
88-85 reference(s)
The execution of a very simple program on a Turing Machine
89-84 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
90-84 reference(s)		The smooth integers: the prime factor product -the radical function- of the integer numbers
91-84 reference(s)		The tridimensional Ising Model with 2-state spins, temperature=0.1 and random initial conditions
92-84 reference(s)
Sixteen interlaced fractal torus
93-84 reference(s)		Synthesis of tridimensional textures
94-84 reference(s)		Mapping on the Bonan-Jeener double bottle of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
95-83 reference(s)		The Universe at the heart of a Calabi-Yau manifold
96-83 reference(s)
2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')-tridimensional cross-section-
97-83 reference(s)		The foggy Babel Tower -a Tribute to Brueghel the Elder-
98-83 reference(s)		From Pluto to the Sun -extrapolation 2-
99-83 reference(s)		From Pluto to the Sun -extrapolation 2- (non linear scales)
100-83 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 512 prime numbers following 613247...-
101-83 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 256 prime numbers following 100000...-
102-83 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-
103-82 reference(s)		An intertwining animation
104-82 reference(s)
The generalized Ulam spiral
105-82 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
106-82 reference(s)		Mountains and fog
107-82 reference(s)		The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
108-82 reference(s)
The velocity vectors -with a common origin- of the 9 planets of the Solar System during one plutonian year
109-82 reference(s)		The Möbius strip
110-82 reference(s)		The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
111-82 reference(s)		Artistic view of the prime numbers
112-82 reference(s)
Rotation about the Y (vertical)axis of a tridimensional representation of quadridimensional Calabi-Yau manifolds that can also be viewed as a set of 4x3 stereograms -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
113-82 reference(s)		Artistic view of the Big Bang
114-81 reference(s)		The Sierpinski Carpet -iteration 5-
115-81 reference(s)		Untitled 0638
116-81 reference(s)
A Tridimensional Hilbert-like Curve defined with {X2(...),Y2(...),Z2(...)} and based on an 'open' 3-foil torus knot -iteration 2-
117-81 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) -blue body point of view-
118-81 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-
119-81 reference(s)		Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
120-81 reference(s)
A one sheet hyperboloid of revolution -negative curvature-
121-81 reference(s)		Along the border of the Mandelbrot set
122-80 reference(s)		Intertwining
123-80 reference(s)		The evolution of the sphere using the Lorenz attractor
124-80 reference(s)
The Sierpinski Carpet -iteration 4-
125-80 reference(s)		Kasner billiard: Time-dependent billiard (from negative curvature to positive curvature)with one accelerated particle
126-80 reference(s)		Bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity
127-80 reference(s)		2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')-tridimensional cross-section-
128-80 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
2787 reference(s)		2-xiirv_____.nota.t.
2416 reference(s)
3-Vcatalogue.11
2113 reference(s)		4-xiirf_____.nota.t.
1047 reference(s)
5-xiirc_____.nota.t.
1044 reference(s)		6-An2000.01.Fra
742 reference(s)
7-xiirs_____.nota.t.
677 reference(s)		8-Pcatalogue.11
565 reference(s)
9-IAGenerativesImages.01.Fra
458 reference(s)		10-Galerie_NumberTheory.FV
439 reference(s)
11-catalogue.11
374 reference(s)		12-Galerie_DeterministicFractalGeometry.FV
353 reference(s)
13-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
345 reference(s)		14-Galerie_ArtisticCreation.FV
322 reference(s)
15-xiia_____.nota.t.
321 reference(s)		16-ChatGPT.01.Fra
318 reference(s)
17-present.01.
290 reference(s)		18-IAGenerativesImages.01.Ang
262 reference(s)
19-ChatGPT.11.Fra
253 reference(s)		20-LesApprentisDieux.01
248 reference(s)
21-Galerie_Pi.FV
248 reference(s)		22-Galerie_PALETTES_A
246 reference(s)
23-xiirk_____.nota.t.
245 reference(s)		24-MorePages.Ang.
239 reference(s)
25-ExpV_VirE.Ang
232 reference(s)		26-xiak_____.nota.t.
230 reference(s)
27-Galerie_GeneralitiesVisualization.FV
230 reference(s)		28-Web_Mail.01.vv
226 reference(s)
29-xiirC_____.nota.t.
219 reference(s)		30-Galerie_ImagesDesMathematiques.FV
210 reference(s)
31-Galerie_ParticleSystems.FV
209 reference(s)		32-xiac_____.nota.t.
208 reference(s)
33-MorePages.Fra.
207 reference(s)		34-ExpV_VirE.11
201 reference(s)
35-Exposition_EcolePolytechnique_FeteDeLaScience_202510
199 reference(s)		36-demo_14
197 reference(s)
37-create.03.
194 reference(s)		38-Galerie_CelestialMechanics.FV
194 reference(s)
39-help.
193 reference(s)		40-AVirtualSpaceTimeTravelMachine.Fra
192 reference(s)
41-Fractal.01
185 reference(s)		42-Galerie_SelfPortraits.FV
176 reference(s)
43-GenieLogiciel.01.Fra
171 reference(s)		44-Galerie_ImagesEssentiellesDesMathematiques.FV
169 reference(s)
45-Galerie_ArtAndScience.FV
161 reference(s)		46-LeParadoxeDeFermi.01.Fra
160 reference(s)
47-FloatingPointNumbers.01.Fra
160 reference(s)		48-SIlVousPlaitDessineMoiLInfini.01.Fra
159 reference(s)
49-NDimensionalDeterministicFractalSets.01.Ang
158 reference(s)		50-ChatGPT.01.Ang
158 reference(s)
51-Le_Chat.01.Fra
156 reference(s)		52-LOG_xiMc.11
154 reference(s)
53-GilbreathConjecture.01.Ang
154 reference(s)		54-BilletDHumeur_IntelligenceArtificielle.01.Fra
154 reference(s)
55-ChatGPT.11.Ang
152 reference(s)		56-Fractal.11
151 reference(s)
57-DeepSeek.01.Fra
150 reference(s)		58-VCcatalogue.11
148 reference(s)
59-Fractal.21
146 reference(s)		60-Galerie_Tributes.FV
145 reference(s)
61-NombresEtLumiere.01.vv.Fra
142 reference(s)		62-Galerie_DeterministicChaos.FV
140 reference(s)
63-DieuScience.01.Fra
140 reference(s)		64-Galerie_ImagesDidactiques.FV
139 reference(s)
65-DEuclideAuGPS.01.Ang
137 reference(s)		66-Proth_Gilbreath_Conjecture.01.Ang
136 reference(s)
67-Multivers.01.Fra
136 reference(s)		68-Stereogrammes_AutoStereogrammes.01
133 reference(s)
69-DecimalesDePi.01.Fra
133 reference(s)		70-LeParadoxeDeFermi.01.Ang
131 reference(s)
71-xiav_____.nota.t.
126 reference(s)		72-copyright.01.
126 reference(s)
73-NDimensionalDeterministicFractalSets.01.Fra
124 reference(s)		74-mail.01.vv
123 reference(s)
75-Galerie_Animations.FV
123 reference(s)		76-ExpositionsDiverses.01.Fra
122 reference(s)
77-Galerie_SensitivityToRoundingOffErrors.FV
121 reference(s)		78-UlamSpiral.01.Ang
117 reference(s)
79-Galerie_Astrophysics.FV
117 reference(s)		80-Informations_GoodNewsAndBadNews.01.Fra
116 reference(s)
81-DroitDeReponse.01.Fra
115 reference(s)		82-DEuclideAuGPS.01.Fra
115 reference(s)
83-UlamSpiral.01.Fra
114 reference(s)		84-SurfaceProjector.01.Ang
114 reference(s)
85-LesCourbesRemplissantes.01.Fra
114 reference(s)		86-AProposSite.01.Fra
112 reference(s)
87-NatureDesMathematiques.01.vv.Fra
111 reference(s)		88-MathematiquesPhysiqueFractales.02
111 reference(s)
89-GilbreathConjecture.01.Fra
111 reference(s)		90-Galerie_TextureSynthesis.FV
110 reference(s)
91-Galerie_ArtAndScience
110 reference(s)		92-Informations_GoodNewsAndBadNews.01.Ang
109 reference(s)
93-Galerie_QuantumMechanics.FV
108 reference(s)		94-Bard.01.Fra
108 reference(s)
95-subject.01.
107 reference(s)		96-Galerie_BestOf.FV
107 reference(s)
97-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
106 reference(s)		98-GoldenTriangle.01.Ang
106 reference(s)
99-DieuScience.01.Ang
106 reference(s)		100-EntrelacsIntertwinings.01.Fra
105 reference(s)
101-MartiensEtMathematiques.01.Fra
104 reference(s)		102-LesCourbesRemplissantes.02.Fra
104 reference(s)
103-FaireDesMathematiques.01.Fra
104 reference(s)		104-GoldenTriangle.01.Fra
103 reference(s)
105-Proth_Gilbreath_Conjecture.01.Fra
102 reference(s)		106-RealNumbers.01.Fra
101 reference(s)
107-NombresPremiers_10000.vv
101 reference(s)		108-Galerie_SignalProcessing.FV
101 reference(s)
109-Kepler.02.
100 reference(s)		110-DecimalesPi_1_100.vv
100 reference(s)
111-Galerie_CollaborativeWorks..FV
99 reference(s)		112-LesCourbesRemplissantes.02.Ang
98 reference(s)
113-Galerie_NewPictures.FV
98 reference(s)		114-OrdinateurMathematiquesArt.01.Fra
97 reference(s)
115-DecimalesPi_100000.vv
97 reference(s)		116-infinity.01.vv
95 reference(s)
117-DuModeleALImage.02.Fra
95 reference(s)		118-Galerie_RCMGalerie.FV
94 reference(s)
119-AnimFractal.01.
94 reference(s)		120-VAcatalogue.11
93 reference(s)
121-MonodimensionalCellularAutomata.01.Ang
92 reference(s)		122-Fractal.03
92 reference(s)
123-xias_____.nota.t.
90 reference(s)		124-Multivers.01.Ang
90 reference(s)
125-MathematiquesPhysiqueFractales.12
90 reference(s)		126-ImagesEncadreesDisponibles.01
90 reference(s)
127-infinity.02.vv
89 reference(s)		128-PerteDeLAssociativite.01
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.