Monthly Best Of on 03/28/2026




Intertwining based on the geometry of the Lorenz attractor

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 03/28/2026 and last updated on 03/28/2026 22:11:56 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



A tridimensional field made of the Menger Sponge -iteration 5-
1-10365 reference(s)		A tridimensional field
2-9532 reference(s)		A tridimensional field
3-1753 reference(s)		The eroded Menger Sponge -iteration 3-
4-421 reference(s)
A tridimensional field made of a tridimensional cubic mesh
5-279 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
6-159 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
7-146 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
8-143 reference(s)
The random walk of photons escaping the Sun
9-135 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
10-127 reference(s)		Autostereogram of the CMAP
11-125 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [1.2x10^15,1.3x10^15]-
12-121 reference(s)
Fractal piano keyboard
13-114 reference(s)		The first four iterations of the construction of the von Koch snowflake
14-112 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
15-110 reference(s)		Untitled 0671
16-108 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
17-107 reference(s)		The Lorenz attractor
18-101 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
19-100 reference(s)		Autostereogram with an hidden volcano
20-99 reference(s)
The smooth integers: the prime factor product -the radical function- of the integer numbers
21-99 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
22-99 reference(s)		Visualization of the Proth-Gilbreath Conjecture process for G(Pi(1.0025x10^15))=806.
23-95 reference(s)		Empty
24-94 reference(s)
Visualization of the Proth-Gilbreath Conjecture process for G(Pi(6.0213x10^27))=1935.
25-94 reference(s)		Happy new year 2000
26-93 reference(s)		Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
27-93 reference(s)		Artistic view of the prime numbers
28-92 reference(s)
Visualization of the Proth-Gilbreath Conjecture process for G(Pi(6.150x10^15))=800.
29-89 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
30-89 reference(s)		The generalized Ulam spiral
31-88 reference(s)		Visualization of the Proth-Gilbreath Conjecture process for G(Pi(1.0025x10^15))=806.
32-88 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
33-87 reference(s)		The abelian -commutative- group defined on elliptic curves
34-87 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
35-87 reference(s)		Color palette 'cercle.W2'
36-86 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
37-86 reference(s)		Visualization of the Proth-Gilbreath Conjecture process for G(Pi(6.150x10^15))=800.
38-84 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
39-84 reference(s)		LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
40-84 reference(s)
An amazing cross-section inside the Menger Sponge -iteration 5-
41-83 reference(s)		A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
42-83 reference(s)		Visualization of the Proth-Gilbreath Conjecture process
43-83 reference(s)		The generalized Ulam spiral displaying 100 numbers
44-82 reference(s)
The Jeener-Klein triple bottle
45-81 reference(s)		N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Pluto point of view-
46-80 reference(s)		A 4-cube -an hypercube-
47-80 reference(s)		A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
48-79 reference(s)
The Menger Sponge -iteration 5-
49-79 reference(s)		Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
50-79 reference(s)		Quantum vacuum fluctuations
51-78 reference(s)		The construction process of the Sierpinski Carpet
52-78 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
53-78 reference(s)		Elliptical trajectory of a planet around a star with perihelion advance (very exaggerated)
54-77 reference(s)		Tridimensional visualizations of the Verhulst dynamics
55-76 reference(s)		Visualization of the Proth-Gilbreath Conjecture process for G(Pi(1.2125x10^15))=811.
56-76 reference(s)
Visualization of the Proth-Gilbreath Conjecture process for G(Pi(1.6931x10^15))=969.
57-76 reference(s)		The Universe at the heart of a Calabi-Yau manifold
58-75 reference(s)		Iterations in the complex plane
59-75 reference(s)		The Continuum Hypothesis (CH)
60-75 reference(s)
Tridimensional Hilbert Curve -iterations 1 to 3-
61-75 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
62-75 reference(s)		The velocity vectors -with a common origin- of the 9 planets of the Solar System during one plutonian year
63-74 reference(s)		Visualization of the Proth-Gilbreath Conjecture process for G(Pi(1.2125x10^15))=811.
64-74 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 120662...-
65-74 reference(s)		Hell on Earth -a Tribute to the seventeen victims of the attacks in January 2015, Paris-
66-74 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-
67-74 reference(s)		Recursive subdivision of the Golden Rectangle by means of the Golden Ratio -phi-
68-73 reference(s)
The Ulam spiral with display of the first twin prime numbers ('2-twin' prime numbers)
69-73 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
70-73 reference(s)		The random walk of photons escaping the Sun
71-72 reference(s)		Quaternionic butterfly with extended arithmetics -a Tribute to Laurent Schwartz-
72-72 reference(s)
Iterations in the complex plane: the computation of the Mandelbrot set
73-72 reference(s)		Hypercube
74-72 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 121288...-
75-72 reference(s)		Tridimensional fractal structure -the space-time foam?-
76-72 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
77-72 reference(s)		The Bonan-Jeener-Klein triple bottle
78-72 reference(s)		A perfect bidimensional fractal tree and the self-similarity
79-71 reference(s)		A tridimensional intertwining made of a tridimensional cubic mesh inside a sphere
80-71 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
81-71 reference(s)		Tridimensional Hilbert Curve -iteration 2-
82-71 reference(s)		Bidimensional localization of a point P its distances to the three vertices of a triangle ABC being known, the four points being coplanar
83-71 reference(s)		Visualization of the Proth-Gilbreath Conjecture process for G(Pi(6.150x10^15))=800.
84-71 reference(s)
An elementary monodimensional binary cellular automaton -86- with 1 white starting point -bottom middle-
85-71 reference(s)		Along the border of the Mandelbrot set
86-70 reference(s)		Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
87-70 reference(s)		Fractal Self-Portrait -a Tribute to René Magritte-
88-70 reference(s)
Iterations in the complex plane
89-70 reference(s)		Visualization of the Proth-Gilbreath Conjecture process
90-70 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 100215...-
91-70 reference(s)		Tridimensional representation of our familiar tridimensional space
92-70 reference(s)
Artistic view of gravitational waves
93-69 reference(s)		Iterations in the complex plane
94-69 reference(s)		The bidimensional Ising Model with 2-state spins, temperature=0.2 and random initial conditions
95-69 reference(s)		The abelian -commutative- group defined on elliptic curves
96-69 reference(s)
From Pluto to the Sun -extrapolation 1- (non linear scales)
97-68 reference(s)		Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers-
98-68 reference(s)		The infinite climb of the quadruple impossible staircase
99-68 reference(s)		A childish Sun
100-67 reference(s)
A regular 7-gon -an heptagon-
101-67 reference(s)		Color palette 'cercle.35'
102-67 reference(s)		N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
103-67 reference(s)		The quaternionic Mandelbrot set - using the pseudo-addition and the pseudo-multiplication in C- -tridimensional cross-section-
104-67 reference(s)
Larsen effect
105-67 reference(s)		Tridimensional Hilbert Curve -iteration 1-
106-67 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 120662...-
107-67 reference(s)		Fractal diffusion front in a bidimensional medium obtained by means of a random walk process
108-67 reference(s)
Rotation about the Y (vertical)axis of the u=v line on the Bonan-Jeener-Klein triple bottle and a strip, that can also be viewed as a set of 4x3 stereograms
109-67 reference(s)		The extended Bertrand paradox
110-67 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-
111-66 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
112-66 reference(s)
The multiplicative persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-
113-66 reference(s)		Iterations in the complex plane
114-66 reference(s)		Iterations in the complex plane
115-66 reference(s)		A point P and a triangle ABC, the distances from P to the three vertices of the triangle being known and the four points being coplanar
116-66 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 613247...-
117-66 reference(s)		Tridimensional accumulation of 512 correlated bidimensional brownian motions -1000 time steps-
118-66 reference(s)		The 64 first lines of the Pascal's Triangle
119-65 reference(s)		The pseudo-quaternionic fractal set obtained when computing the roots of Q^3=1 using Newton's method with translation along the third axis of the pseudo-quaternionic space (a 'NewtonBulb') -tridimensional cross-section-
120-65 reference(s)
The Ulam spiral
121-65 reference(s)		The Ulam spiral displaying 2025 numbers
122-65 reference(s)		An hexagonal tiling of the hyperbolic Poincaré disk -iteration 5-
123-65 reference(s)		A Tridimensional Hilbert-like Curve defined with {X2(...),Y2(...),Z2(...)} and based on an 'open' 3-foil torus knot -iteration 2-
124-65 reference(s)
Fractal landscape
125-65 reference(s)		The complement of the Menger Sponge -iteration 2-
126-65 reference(s)		Random quadrangulation of the volume of a torus -18x18x18-
127-65 reference(s)		Iterations in the complex plane
128-65 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
3349 reference(s)		2-Vcatalogue.11
732 reference(s)
3-An2000.01.Fra
537 reference(s)		4-copyright.01.
513 reference(s)
5-mail.01.vv
425 reference(s)		6-help.
404 reference(s)
7-catalogue.11
253 reference(s)		8-demo_14
208 reference(s)
9-xiirv_____.nota.t.
185 reference(s)		10-Web_Mail.01.vv
167 reference(s)
11-Galerie_NumberTheory.FV
161 reference(s)		12-Pcatalogue.11
158 reference(s)
13-ChatGPT.01.Fra
155 reference(s)		14-MorePages.Ang.
144 reference(s)
15-ChatGPT.11.Ang
143 reference(s)		16-xiirf_____.nota.t.
140 reference(s)
17-Galerie_DeterministicFractalGeometry.FV
139 reference(s)		18-xiirc_____.nota.t.
134 reference(s)
19-FloatingPointNumbers.01.Fra
134 reference(s)		20-ChatGPT.11.Fra
131 reference(s)
21-Stereogrammes_AutoStereogrammes.01
129 reference(s)		22-fractal.01
124 reference(s)
23-DecimalesDePi.01.Fra
124 reference(s)		24-UlamSpiral.01.Fra
122 reference(s)
25-GilbreathConjecture.01.Ang
121 reference(s)		26-NombresPremiers_10000.vv
119 reference(s)
27-Proth_Gilbreath_Conjecture.01.Ang
117 reference(s)		28-DecimalesPi_1_100.vv
117 reference(s)
29-Fractal.21
112 reference(s)		30-VAcatalogue.11
109 reference(s)
31-Proth_Gilbreath_Conjecture.01.Fra
109 reference(s)		32-Fractal.01
108 reference(s)
33-GilbreathConjecture.01.Fra
107 reference(s)		34-Galerie_ImagesDidactiques.FV
98 reference(s)
35-Fractal.11
98 reference(s)		36-GoldenTriangle.01.Fra
97 reference(s)
37-Galerie_ParticleSystems.FV
97 reference(s)		38-Le_Chat.01.Fra
95 reference(s)
39-xiirs_____.nota.t.
94 reference(s)		40-Galerie_RCMGalerie.FV
92 reference(s)
41-AVirtualSpaceTimeTravelMachine.Fra
91 reference(s)		42-IAGenerativesImages.01.Ang
90 reference(s)
43-NDimensionalDeterministicFractalSets.01.Ang
88 reference(s)		44-LOG_xiMc.11
88 reference(s)
45-Galerie_GeneralitiesVisualization.FV
87 reference(s)		46-VCcatalogue.11
85 reference(s)
47-ChatGPT.01.Ang
84 reference(s)		48-AProposSite.01.Fra
84 reference(s)
49-Galerie_ImagesDesMathematiques.FV
83 reference(s)		50-SurfaceProjector.01.Ang
82 reference(s)
51-UlamSpiral.01.Ang
81 reference(s)		52-NDimensionalDeterministicFractalSets.01.Fra
81 reference(s)
53-MathematiquesPhysiqueFractales.02
81 reference(s)		54-Galerie_ArtAndScience.FV
80 reference(s)
55-IAGenerativesImages.01.Fra
79 reference(s)		56-Galerie_Pi.FV
79 reference(s)
57-ExpV_VirE.11
79 reference(s)		58-Informations_AboutPicturesAnimationsAndFiles.01.Ang
78 reference(s)
59-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
78 reference(s)		60-MathematiquesPhysiqueFractales.22
77 reference(s)
61-Polynomials_RationalNumbers.01.Fra
75 reference(s)		62-Galerie_QuantumMechanics.FV
75 reference(s)
63-Galerie_CelestialMechanics.FV
75 reference(s)		64-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
74 reference(s)
65-LesCourbesRemplissantes.01.Fra
74 reference(s)		66-DecimalesPi_100000.vv
74 reference(s)
67-xiac_____.nota.t.
73 reference(s)		68-MouvementBrownien.01.Fra
73 reference(s)
69-Galerie_NewPictures.FV
73 reference(s)		70-OrdinateursEtCalculs.01.Fra
72 reference(s)
71-Multivers.01.Fra
72 reference(s)		72-LesCourbesRemplissantes.02.Fra
72 reference(s)
73-Galerie_ArtisticCreation.FV
72 reference(s)		74-Autostereograms.01.
72 reference(s)
75-xiak_____.nota.t.
71 reference(s)		76-SurfaceProjector.01.Fra
71 reference(s)
77-RealNumbers.01.Fra
70 reference(s)		78-Bard.01.Fra
70 reference(s)
79-MathematiquesPhysiqueFractales.02.15
68 reference(s)		80-Galerie_Astrophysics.FV
68 reference(s)
81-xiirC_____.nota.t.
67 reference(s)		82-xias_____.nota.t.
67 reference(s)
83-expv_vire.11
67 reference(s)		84-SIlVousPlaitDessineMoiLInfini.01.Fra
67 reference(s)
85-NombresEtLumiere.01.vv.Fra
67 reference(s)		86-NatureDesMathematiques.01.vv.Fra
67 reference(s)
87-LeNoeudInfini.01.Fra
67 reference(s)		88-AnimFractal.01.
67 reference(s)
89-MathematiquesPhysiqueFractales.12
66 reference(s)		90-Le_Chat.01.Ang
66 reference(s)
91-Galerie_SignalProcessing.FV
66 reference(s)		92-An2038.01.Fra
66 reference(s)
93-present.01.
65 reference(s)		94-MonodimensionalCellularAutomata.01.Fra
65 reference(s)
95-ImagesEncadreesDisponibles.01
65 reference(s)		96-Galerie_ImagesEssentiellesDesMathematiques.FV
65 reference(s)
97-Fractal.03
64 reference(s)		98-ExpV_VirE.21
64 reference(s)
99-DeepSeek.01.Fra
64 reference(s)		100-FloatingPointNumbers.01.Ang
63 reference(s)
101-An2038.01.Ang
63 reference(s)		102-MonodimensionalCellularAutomata.01.Ang
62 reference(s)
103-Informations_GoodNewsAndBadNews.01.Fra
62 reference(s)		104-Informations_GoodNewsAndBadNews.01.Ang
62 reference(s)
105-ImpossibleStructures.01.Fra
62 reference(s)		106-Galerie_Tributes.FV
62 reference(s)
107-VisSci_SciVis.01
61 reference(s)		108-Polynomials_RationalNumbers.01.Ang
61 reference(s)
109-OrdinateurMathematiquesArt.01.Fra
61 reference(s)		110-MesExpositionsPassees.01
61 reference(s)
111-ExpositionsDiverses.01.Fra
61 reference(s)		112-LesNombresTranscendants.01.Fra
60 reference(s)
113-LeParadoxeDeFermi.01.Fra
60 reference(s)		114-HughEverettMultiverse.01.Fra
60 reference(s)
115-DieuScience.01.Ang
60 reference(s)		116-Commentaires_ProblemeDesNCorps.01
60 reference(s)
117-Commentaires_NKleinBottle.01
60 reference(s)		118-Bard.01.Ang
60 reference(s)
119-xiaf_____.nota.t.
59 reference(s)		120-HughEverettMultiverse.01.Ang
59 reference(s)
121-Galerie_Animations.FV
59 reference(s)		122-ExpV_VirE.Fra
59 reference(s)
123-EntrelacsIntertwinings.01.Fra
59 reference(s)		124-DieuScience.01.Fra
59 reference(s)
125-xiav_____.nota.t.
58 reference(s)		126-infinity.01.vv
58 reference(s)
127-RemarquesCerveau.01
58 reference(s)		128-PerteDeLAssociativite.01
58 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.