Monthly Best Of on 07/28/2025




Tridimensional fractal structure in a tridimensional torus

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 07/28/2025 and last updated on 07/28/2025 22:11:24 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-648 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
2-105 reference(s)		Autostereogram of the CMAP
3-102 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-
4-96 reference(s)
The random walk of photons escaping the Sun
5-93 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-
6-90 reference(s)		Autostereogram with an hidden volcano
7-90 reference(s)		A distorded -for the sake of display- 5-cube -an hyperhypercube-
8-90 reference(s)
Monument Valley at sunrise
9-89 reference(s)		The Menger Sponge -iteration 5-
10-88 reference(s)		Artistic view of the prime numbers
11-88 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
12-87 reference(s)
The Sierpinski Carpet -iteration 1 to 5-
13-86 reference(s)		A tridimensional intertwining made of a random tridimensional binary tree inside a sphere
14-85 reference(s)		Artistic view of a tridimensional display of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
15-84 reference(s)		A Tridimensional Hilbert-like Curve defined with {X1(...),Y1(...),Z1(...)} -iteration 1-
16-84 reference(s)
Bidimensional cross-sections of the Klein bottle
17-83 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-
18-82 reference(s)		A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
19-81 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-
20-80 reference(s)
Tridimensional display of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
21-79 reference(s)		The generalized Ulam spiral
22-78 reference(s)		Tridimensional Hilbert Curve -iteration 4-
23-78 reference(s)		The Mystic Island based on the level 3 cluster made of 8 'Spectre' level 2 clusters
24-77 reference(s)
A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
25-77 reference(s)		Autostereogram of 8 color-multiplexed quaternionic Julia sets -tridimensional cross-sections-
26-74 reference(s)		A fractal torus
27-74 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
28-73 reference(s)
An amazing cross-section inside the Menger Sponge -iteration 5-
29-73 reference(s)		The Lorenz attractor
30-72 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-
31-71 reference(s)		Mapping on a sphere of a finite subset of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
32-71 reference(s)
The first four iterations of the construction of the von Koch snowflake
33-71 reference(s)		Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
34-70 reference(s)		An half-random extended Menger Sponge -iteration 3-
35-70 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
36-70 reference(s)
A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
37-69 reference(s)		The first four iterations of the construction of the von Koch snowflake
38-69 reference(s)		A tridimensional intertwining made of the Menger Sponge -iteration 5- inside a sphere
39-69 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
40-69 reference(s)
The Klein bottle
41-69 reference(s)		A random Menger Sponge -iteration 5-
42-69 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-
43-68 reference(s)		An extended Menger Sponge -iteration 3-
44-68 reference(s)
Untitled 0642
45-67 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
46-67 reference(s)		The Syracuse Conjecture for U(0)={1,2,3,4,...,128} -monodimensional display of the parities-
47-67 reference(s)		A tridimensional intertwining made of the Menger Sponge -iteration 5- inside a sphere
48-67 reference(s)
A Tridimensional Hilbert-like Curve defined with {X4(...),Y4(...),Z4(...)} -iteration 4-
49-66 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
50-66 reference(s)		Tridimensional display of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
51-65 reference(s)		A sphere -positive curvature-
52-65 reference(s)
24 evenly distributed points on a sphere by means of simulated annealing
53-65 reference(s)		A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
54-65 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
55-65 reference(s)		Mapping on the Möbius strip of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
56-64 reference(s)
Mapping on the Möbius strip of a finite subset of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
57-64 reference(s)		A periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
58-64 reference(s)		A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 5-
59-64 reference(s)		From 'geocentrism' to 'heliocentrism'
60-64 reference(s)
The Klein bottle
61-64 reference(s)		A periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
62-63 reference(s)		Quantum vacuum fluctuations
63-63 reference(s)		True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
64-63 reference(s)
A tridimensional fractal manifold defined by means of three tridimensional fields
65-63 reference(s)		The journey of an Earth-like planet (dark blue)from Pluto (grey) to the Sun (yellow)
66-63 reference(s)		An amazing generalized cross-section inside the Menger Sponge -iteration 5-
67-63 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
68-63 reference(s)
Mapping on a torus of a finite subset of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
69-62 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 5-
70-62 reference(s)		The foggy Babel Tower -a Tribute to Brueghel the Elder-
71-62 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
72-62 reference(s)
LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
73-62 reference(s)		Mapping on the Klein bottle of a finite subset of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
74-61 reference(s)		A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 4-
75-61 reference(s)		Bidimensional closed self-avoiding brownian motion on an ellipsoide
76-61 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
77-61 reference(s)		Quark and gluon structure of a nucleon
78-61 reference(s)		Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
79-61 reference(s)		The Goldbach Conjecture
80-61 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
81-61 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
82-60 reference(s)		A set of 4x3 stereograms of the quaternionic Julia set computed with A=(-0.581514...,+0.635888...,0,0)-tridimensional cross-section-
83-60 reference(s)		Tridimensional fractal Self-Portrait
84-60 reference(s)
A fractal Möbius strip
85-60 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
86-60 reference(s)		The Jeener-Klein triple bottle
87-60 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
88-60 reference(s)
Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
89-59 reference(s)		Mapping on a torus of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
90-59 reference(s)		An aperiodic Penrose tiling of the plane
91-59 reference(s)		A tridimensional intertwining made of the Menger Sponge -iteration 5- the Bonan-Jeener-Klein triple bottle
92-59 reference(s)
Mountains and fog
93-59 reference(s)		A spherical cross-section inside the Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
94-59 reference(s)		A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
95-59 reference(s)		Fractal Self-Portrait -a Tribute to René Magritte-
96-59 reference(s)
The Bonan-Jeener-Klein triple bottle
97-59 reference(s)		A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
98-58 reference(s)		Tridimensional display of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
99-58 reference(s)		A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} -iteration 3-
100-58 reference(s)
The distance {Earth-Mars} -millions of kilometers- starting on 01/01/1950 AD and during seven marsian years
101-58 reference(s)		N-body problem integration (N=10)displaying the actual Solar System during one marsian year -Earth point of view and zoom on the four first planets-
102-58 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)
103-58 reference(s)		The Goldbach Conjecture -the Goldbach Comet or the Goldbach Rainbow- for the even numbers from 6 to 411678
104-58 reference(s)
Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
105-58 reference(s)		Artistic view of a 'tridimensional epicycloïdal' pseudo-torus
106-58 reference(s)		The Piet Mondrian quadridimensional Calabi-Yau manifold -2D, 3D or 4D?-
107-58 reference(s)		Heterogeneous -tridimensional anti-gaussian field- random meshing of a cube
108-58 reference(s)
Mapping on a sphere of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
109-57 reference(s)		A periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
110-57 reference(s)		The execution of a very simple program on a Turing Machine
111-57 reference(s)		A perfect bidimensional fractal tree and the self-similarity
112-57 reference(s)
Intertwining
113-57 reference(s)		Fractal network
114-57 reference(s)		The erosion of the Menger Sponge -iteration 1-
115-57 reference(s)		A spherical cross-section inside the Menger Sponge -iteration 5-
116-57 reference(s)
Random quadrangulation of the surface of a 'crumpled' torus -18x18-
117-57 reference(s)		A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
118-57 reference(s)		7-foil torus knot on its torus
119-57 reference(s)		Bidimensional Hilbert Curve -iteration 5-
120-57 reference(s)
Fractal intertwining
121-57 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
122-57 reference(s)		A fractal Klein bottle
123-57 reference(s)		Tridimensional fractal structure
124-57 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
125-57 reference(s)		Artistic view of a tridimensional display of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
126-56 reference(s)		Artistic view of a tridimensional display of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
127-56 reference(s)		The Many World Theory of Hugh Everett
128-56 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
3878 reference(s)		2-demo_14
203 reference(s)
3-Web_Mail.01.vv
194 reference(s)		4-Vcatalogue.11
135 reference(s)
5-LOG_xiMc.11
134 reference(s)		6-FloatingPointNumbers.01.Fra
126 reference(s)
7-help.
117 reference(s)		8-ChatGPT.01.Fra
114 reference(s)
9-ChatGPT.11.Fra
106 reference(s)		10-Galerie_ArtAndScience.FV
105 reference(s)
11-Stereogrammes_AutoStereogrammes.01
104 reference(s)		12-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
103 reference(s)
13-ChatGPT.01.Ang
102 reference(s)		14-FloatingPointNumbers.01.Ang
99 reference(s)
15-DecimalesDePi.01.Fra
92 reference(s)		16-LesCourbesRemplissantes.01.Fra
91 reference(s)
17-ExpV_VirE.Ang
90 reference(s)		18-An2000.01.Fra
89 reference(s)
19-ChatGPT.11.Ang
88 reference(s)		20-IAGenerativesImages.01.Fra
87 reference(s)
21-Fractal.21
87 reference(s)		22-Multivers.01.Ang
85 reference(s)
23-DecimalesPi_100000.vv
84 reference(s)		24-Fractal.11
81 reference(s)
25-VCcatalogue.11
76 reference(s)		26-Le_Chat.01.Fra
76 reference(s)
27-catalogue.11
75 reference(s)		28-mail.01.vv
74 reference(s)
29-MorePages.Ang.
74 reference(s)		30-SIlVousPlaitDessineMoiLInfini.01.Fra
73 reference(s)
31-Galerie_DeterministicFractalGeometry.FV
73 reference(s)		32-Galerie_ArtisticCreation
73 reference(s)
33-AProposSite.01.Fra
72 reference(s)		34-Pcatalogue.11
71 reference(s)
35-NDimensionalDeterministicFractalSets.01.Fra
71 reference(s)		36-Galerie_NewPictures.FV
71 reference(s)
37-NDimensionalDeterministicFractalSets.01.Ang
70 reference(s)		38-Fractal.01
70 reference(s)
39-Le_Chat.01.Ang
69 reference(s)		40-Galerie_GeneralitiesVisualization.FV
69 reference(s)
41-VAcatalogue.11
68 reference(s)		42-OrdinateursEtCalculs.01.Ang
68 reference(s)
43-LesNombresTranscendants.01.Ang
68 reference(s)		44-Autostereograms.01.
67 reference(s)
45-SurfaceProjector.01.Ang
66 reference(s)		46-PerteDeLAssociativite.01
66 reference(s)
47-DeepSeek.01.Fra
66 reference(s)		48-OrdinateursEtCalculs.01.Fra
65 reference(s)
49-GoldenTriangle.01.Fra
65 reference(s)		50-MonodimensionalCellularAutomata.01.Fra
64 reference(s)
51-AVirtualSpaceTimeTravelMachine.Fra
64 reference(s)		52-UlamSpiral.01.Fra
63 reference(s)
53-Polynomials_RationalNumbers.01.Fra
63 reference(s)		54-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
63 reference(s)
55-Galerie_PALETTES_C
63 reference(s)		56-NombresPremiers_10000.vv
62 reference(s)
57-MathematiquesPhysiqueFractales.02
62 reference(s)		58-GenieLogiciel.01.Fra
62 reference(s)
59-Galerie_ParticleSystems.FV
62 reference(s)		60-Galerie_NumberTheory.FV
62 reference(s)
61-xci_____epaississement_3D.11.K.
61 reference(s)		62-LeNoeudInfini.01.Ang
61 reference(s)
63-Informations_AboutPicturesAnimationsAndFiles.01.Ang
61 reference(s)		64-ImagesDuVirtuel.01.Fra.FV
61 reference(s)
65-HughEverettMultiverse.01.Ang
61 reference(s)		66-xiirs_____.PSPH.31.2.1..u.
60 reference(s)
67-PatrimoineHumanite.02.Fra
60 reference(s)		68-Galerie_ArtisticCreation.FV
60 reference(s)
69-Bard.01.Fra
60 reference(s)		70-xrv_____SINX.01.K.
59 reference(s)
71-infinity.01.vv
59 reference(s)		72-copyright.01.
59 reference(s)
73-NatureDesMathematiques.01.vv.Fra
59 reference(s)		74-Multivers.01.Fra
59 reference(s)
75-MonodimensionalCellularAutomata.01.Ang
59 reference(s)		76-Galerie_Tributes.FV
59 reference(s)
77-Galerie_ImagesDesMathematiques.FV
59 reference(s)		78-Galerie_BestOf.FV
59 reference(s)
79-DieuScience.01.Ang
59 reference(s)		80-CompressionDeCompression_ComplexiteStructurelle.CDCM1_A1.01
59 reference(s)
81-BEST.20140628
59 reference(s)		82-subject.01.
58 reference(s)
83-Informations_GoodNewsAndBadNews.01.Ang
58 reference(s)		84-xiad_____.nota.t.
57 reference(s)
85-SurfaceProjector.01.Fra
57 reference(s)		86-Exposition_EcolePolytechnique_FeteDeLaScience_201810
57 reference(s)
87-xrC_____OBJC.B4S__1_______.11.PlansDeBits.t.
56 reference(s)		88-IllusionConnaissance.02
56 reference(s)
89-Galerie_TextureSynthesis.FV
56 reference(s)		90-Galerie_Pi.FV
56 reference(s)
91-Galerie_Astrophysics.FV
56 reference(s)		92-xiirk_____.IFS2S.11.6..u.
55 reference(s)
93-xiii_____montagnes.fon.
55 reference(s)		94-xiii_____Images.def.
55 reference(s)
95-RemarquesCerveau.01
55 reference(s)		96-Notations_AppartientA.01
55 reference(s)
97-NombresEtLumiere.01.vv.Fra
55 reference(s)		98-LesCourbesRemplissantes.01.Ang
55 reference(s)
99-Informations_AboutPicturesAnimationsAndFiles.01.Fra
55 reference(s)		100-GenieLogiciel_VisualisationScientifique.01.vv
55 reference(s)
101-DecimalesPi_1_100.vv
55 reference(s)		102-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
55 reference(s)
103-xrv_____gauss.01.K.
54 reference(s)		104-xrv_____champs_5.1B.I.
54 reference(s)
105-xrC_____ObjetComplexe.B3T__1.vv.t.
54 reference(s)		106-xiirk_____.REFM.f1.2.1..u.
54 reference(s)
107-OrdinateurMathematiquesArt.01.Fra
54 reference(s)		108-NombresEtLumiere.02.vv.Ang
54 reference(s)
109-MouvementBrownien.01.Ang
54 reference(s)		110-Kepler.02.
54 reference(s)
111-IAGenerativesImages.01.Ang
54 reference(s)		112-Galerie_SignalProcessing.FV
54 reference(s)
113-Galerie_PALETTES_A
54 reference(s)		114-xci_____genere_ch.01.I.
53 reference(s)
115-LesCourbesRemplissantes.02.Fra
53 reference(s)		116-HughEverettMultiverse.01.Fra
53 reference(s)
117-Exposition_EcolePolytechnique_FeteDeLaScience_201910
53 reference(s)		118-An2000.02.Fra
53 reference(s)
119-xiirf_____.COT2.G1.1..u.
52 reference(s)		120-create.03.
52 reference(s)
121-LeParadoxeDeFermi.01.Ang
52 reference(s)		122-Galerie_DeterministicFractalGeometry
52 reference(s)
123-Galerie_CelestialMechanics.FV
52 reference(s)		124-EntrelacsIntertwinings.01.Fra
52 reference(s)
125-xrC_____OBJC.ZC3__1_______.11.PlansDeBits.t.
51 reference(s)		126-xiirv_____.STRX.11.1.cX..u.
51 reference(s)
127-xiirf_____.SIER.91.1..u.
51 reference(s)		128-Polynomials_RationalNumbers.01.Ang
51 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.