Monthly Best Of on 09/28/2026




A tridimensional interpolation between a fractal structure and a cubic mesh

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

[Site Map and Help [Plan du Site et Aide]]
[The Y2K Bug [Le bug de l'an 2000]]
[Are we ready for the Year 2038 [Notre informatique est-elle prête pour l'An 2038]?]
[Real Numbers don't exist in Computers and Floating Point Computations aren't safe. [Les Nombres Réels n'existent pas dans les Ordinateurs et les Calculs Flottants ne sont pas sûrs.]]
[Please, visit A Virtual Machine for Exploring Space-Time and Beyond, the place where you can find more than 10.000 pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 09/28/2026 and last updated on 09/28/2026 22:11:04 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Tridimensional fractal cross -iteration 5-
1-450 reference(s)		Introduction à l'emploi des calculateurs électroniques, ENST, 1967
2-202 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
3-186 reference(s)		60 evenly distributed points on a sphere by means of simulated annealing
4-182 reference(s)
The truncated regular Icosahedron or again the spherical Fullerene Molecule containing 60 Carbon atoms
5-180 reference(s)		The eroded Menger Sponge -iteration 3-
6-174 reference(s)		Untitled 0672
7-171 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our 'familiar' (euclidian)quadridimensional space-time?-
8-162 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our 'familiar' (randomly distorded)quadridimensional space-time?-
9-161 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our 'familiar' (randomly distorded)quadridimensional space-time?-
10-155 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our 'familiar' (randomly distorded)quadridimensional space-time?-
11-153 reference(s)		Hypercubic lattice
12-142 reference(s)
A quoi servent les Mathématiques?
13-141 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-
14-137 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
15-137 reference(s)		Artistic view of the prime numbers
16-136 reference(s)
The Lorenz attractor
17-134 reference(s)		The random walk of photons escaping the Sun
18-130 reference(s)		The Menger Sponge -iteration 5-
19-130 reference(s)		Quantum vacuum fluctuations
20-118 reference(s)
The Goldbach Conjecture for the even numbers from 6 to 1564
21-118 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
22-117 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 100215...-
23-115 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
24-113 reference(s)
Artistic view of gravitational waves
25-111 reference(s)		Jean-François Colonna (on 11/17/1994)with its fractal mountains
26-111 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our 'familiar' (euclidian)quadridimensional space-time?-
27-111 reference(s)		Tridimensional display of the Riemann Zeta function inside [-10.0,+60.0]x[-35.0,+35.0] (bird's-eye view)
28-110 reference(s)
Randomly distorded Hypercubic lattice
29-110 reference(s)		Fractal piano keyboard
30-109 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 5-
31-107 reference(s)		Empty
32-106 reference(s)
The Goldbach Conjecture -the Goldbach Comet- for the even numbers from 6 to 6244
33-106 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of one of the 2339 pentominos 6x10 puzzle
34-105 reference(s)		Mountains and fog
35-105 reference(s)		The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
36-103 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)
37-102 reference(s)		Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
38-102 reference(s)		Tridimensional display of the particle trajectories of bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
39-101 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [1*10^14,2*10^14]-
40-99 reference(s)
An aperiodic Penrose tiling of the plane -a Tribute to Piet Mondrian and Roger Penrose-
41-98 reference(s)		A slide rule
42-97 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}
43-97 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
44-97 reference(s)
The tiling of a 6x10 rectangle by means of the 12 different pentominos
45-97 reference(s)		Fractal Self-Portrait -'Décalcomanie', a Tribute to René Magritte-
46-97 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 64 first prime numbers-
47-97 reference(s)		Le cinéma assisté par ordinateur, LA RECHERCHE, 09/1987, cover
48-97 reference(s)
The first four iterations of the construction of the von Koch snowflake
49-96 reference(s)		Artistic view of the space-time structure at the Planck scale in the context of the super-string theory
50-95 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
51-95 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
52-94 reference(s)
Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers-
53-94 reference(s)		The generalized Ulam spiral
54-93 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 rotation about the X axis -tridimensional cross-section-
55-93 reference(s)		IMAGE ET ORDINATEUR, PHOTO-REVUE, 05/1976, cover
56-93 reference(s)
An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
57-93 reference(s)		Numerical value table
58-92 reference(s)		Mountains and fog
59-92 reference(s)		Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
60-92 reference(s)
The execution of a very simple program on a Turing Machine
61-91 reference(s)		A punched paper tape
62-91 reference(s)		The Goldbach Conjecture -the Goldbach Comet- for the even numbers from 6 to 411678
63-91 reference(s)		Untitled 0673
64-91 reference(s)
Mountains and light cloud dynamics -this sequence being periodical-
65-90 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-
66-90 reference(s)		Visualization of the Proth-Gilbreath Conjecture process for G(Pi(1.0025x10^15))=806.
67-90 reference(s)		Art and Science, 1971-1991, page 45
68-90 reference(s)
The Mathematics are the key of the Multiverse
69-89 reference(s)		A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
70-89 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
71-88 reference(s)		Botticelli anomaly on the Moon
72-88 reference(s)
Artistic view of the Big Bang
73-87 reference(s)		The execution of a very simple program on a Turing Machine
74-87 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
75-87 reference(s)		Untitled 0155 -a Tribute to Yves Tanguy-
76-87 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
77-87 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
78-87 reference(s)		The two 500 KB disk drives of a 1972 Télémécanique T1600 computer
79-86 reference(s)		Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier-
80-86 reference(s)
The generalized Ulam spiral displaying 1024 numbers
81-86 reference(s)		The foggy Babel Tower -a Tribute to Brueghel the Elder-
82-86 reference(s)		More and more craters on the Moon
83-86 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-
84-86 reference(s)
Randomly distorded Hypercubic lattice
85-86 reference(s)		Light clouds at sunset
86-86 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
87-86 reference(s)		Monument Valley at sunrise
88-85 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)
89-85 reference(s)		Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
90-85 reference(s)		Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms
91-85 reference(s)		The Ulam spiral
92-84 reference(s)
The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
93-84 reference(s)		From Pluto to the Sun (non linear scales)
94-84 reference(s)		A half-random extended Menger Sponge -iteration 3-
95-84 reference(s)		Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
96-84 reference(s)
Tridimenional display of the Goldbach Conjecture
97-84 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [1.2x10^15,1.3x10^15]-
98-84 reference(s)		A shell (Jeener surface 1)in motion
99-84 reference(s)		Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 637.312 galaxies)obtained by means of a non deterministic fractal process
100-84 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-
101-83 reference(s)		A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -90.000 digits, -base 10- with 30.000 time steps
102-83 reference(s)		N-body problem integration (N=2)displaying a perfect Keplerian orbit
103-83 reference(s)		An extended Menger Sponge -iteration 7- displaying the 211.210.335 first digits -base 2- of 'pi'
104-83 reference(s)
Untitled 0265 -a Tribute to Vassily Kandinsky-
105-83 reference(s)		A cylinder -a bidimensional manifold-
106-83 reference(s)		Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
107-82 reference(s)		The pythagorician knotted rope
108-82 reference(s)
A full-random extended Menger Sponge -iteration 5-
109-82 reference(s)		Jean-François Colonna in the style of Pieter Bruegel der elder by ChatGPT
110-82 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 613247...-
111-82 reference(s)		The regular Icosahedron, one of the 5 Platonic Solids
112-82 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
113-82 reference(s)		Jean-François Colonna in the style of Jan van Eyck by ChatGPT
114-81 reference(s)		The truncated regular Icosahedron or again the spherical Fullerene Molecule containing 60 Carbon atoms
115-81 reference(s)		Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
116-81 reference(s)
The configuration entropy of a set of n=64 particles
117-81 reference(s)		Art and Science, 1971-1991, page 13
118-81 reference(s)		Along the border of the Mandelbrot set
119-80 reference(s)		The Sierpinski Carpet -iteration 4-
120-80 reference(s)
Zoom in on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
121-80 reference(s)		Zoom in on light clouds
122-80 reference(s)		LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
123-80 reference(s)		N-body problem integration (N=2)displaying a perfect Keplerian orbit (an ellipse)
124-79 reference(s)
An extended Menger Sponge -iteration 5-
125-79 reference(s)		A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
126-79 reference(s)		The Birth of the Universe
127-79 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 256 prime numbers following 100000...-
128-79 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
3848 reference(s)		2-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.DIAPO
490 reference(s)
3-DuModeleALaPriseDeDecision.UnExempleNonIteratif.01
435 reference(s)		4-Vcatalogue.11
407 reference(s)
5-MorePages.Ang.
380 reference(s)		6-galerie_nondeterministicfractalgeometrynaturalphenomenonsynthesis.fv
326 reference(s)
7-IAGenerativesImages.01.Fra.DIAPO
291 reference(s)		8-ChatGPT.11.Ang
281 reference(s)
9-ChatGPT.11.Fra
270 reference(s)		10-IAGenerativesImages.01.Fra
250 reference(s)
11-Fractal.21
190 reference(s)		12-Galerie_DeterministicFractalGeometry.DIAPO
189 reference(s)
13-mail.01.vv
186 reference(s)		14-An2000.01.Fra
181 reference(s)
15-ChatGPT.01.Fra
180 reference(s)		16-help.
175 reference(s)
17-DroitDeReponse.01.Fra
173 reference(s)		18-MorePages.Fra.
172 reference(s)
19-EntrelacsIntertwinings.01.Ang.DIAPO
171 reference(s)		20-MOSA.JFC.F1.F2.20031207
166 reference(s)
21-xiirv_____.nota.t.
165 reference(s)		22-Galerie_ArtisticCreation.FV
165 reference(s)
23-NombresPremiers_10000.vv
164 reference(s)		24-Galerie_DeterministicFractalGeometry.FV
163 reference(s)
25-An2038.01.Ang
163 reference(s)		26-DEuclideAuGPS.01.Ang
162 reference(s)
27-AVirtualSpaceTimeTravelMachine.VersionComplete.Fra
159 reference(s)		28-Galerie_ImagesDidactiques.DIAPO
157 reference(s)
29-Fractal.01
150 reference(s)		30-aquoiserventlesmathematiques.01
149 reference(s)
31-LOG_xiMc.11
148 reference(s)		32-demo_14
147 reference(s)
33-Galerie_NewPictures.FV
145 reference(s)		34-Galerie_NumberTheory.FV
144 reference(s)
35-IAGenerativesImages.01.Ang
143 reference(s)		36-Stereogrammes_AutoStereogrammes.01
141 reference(s)
37-Proth_Gilbreath_Conjecture.01.Ang
140 reference(s)		38-MouvementBrownien.01.Fra
139 reference(s)
39-AVirtualSpaceTimeTravelMachine.VersionComplete.Ang
139 reference(s)		40-ulamspiral.01.fra
136 reference(s)
41-Galerie_GeneralitiesVisualization.FV
136 reference(s)		42-BilletDHumeur_IntelligenceArtificielle.01.Fra
136 reference(s)
43-DEuclideAuGPS.01.Fra
135 reference(s)		44-ImpossibleStructures.01.Ang
132 reference(s)
45-copyright.01.
131 reference(s)		46-Multivers.01.Fra
130 reference(s)
47-Galerie_CollaborativeWorks..FV
130 reference(s)		48-xrC_____OBJC.A3Q__1_______.11.DFractale.t.
129 reference(s)
49-An2038.01.Fra
129 reference(s)		50-Galerie_ParticleSystems.DIAPO
128 reference(s)
51-FloatingPointNumbers.01.Fra
127 reference(s)		52-ExpV_VirE.Ang
127 reference(s)
53-VisualisationDesNombres.01.Ang
126 reference(s)		54-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
126 reference(s)
55-NDimensionalDeterministicFractalSets.01.Ang
125 reference(s)		56-Claude.01.Ang
125 reference(s)
57-Galerie_BestOf.FV
124 reference(s)		58-DecimalesPi_100000.vv
124 reference(s)
59-Claude.01.Fra
124 reference(s)		60-xiirc_____.nota.t.
122 reference(s)
61-LeParadoxeDeFermi.01.Fra
121 reference(s)		62-xiac_____.nota.t.
120 reference(s)
63-UlamSpiral.01.Ang
120 reference(s)		64-GilbreathConjecture.01.Fra
120 reference(s)
65-GenieLogiciel.01.Fra
120 reference(s)		66-Galerie_GeneralitiesVisualization.DIAPO
120 reference(s)
67-MathematiquesPhysiqueFractales.02.27
119 reference(s)		68-ImpossibleStructures.01.Fra
119 reference(s)
69-Fractal.11
119 reference(s)		70-DieuScience.01.Ang
119 reference(s)
71-DecimalesPi_1_100.vv
119 reference(s)		72-DecimalesDePi.01.Fra
119 reference(s)
73-Informations_AboutPicturesAnimationsAndFiles.01.Ang
117 reference(s)		74-Pcatalogue.11
116 reference(s)
75-ChatGPT.01.Ang
116 reference(s)		76-Spheres.01
115 reference(s)
77-DieuScience.01.Fra
115 reference(s)		78-ExpV_VirE.11
114 reference(s)
79-RemarquesCerveau.01
113 reference(s)		80-Galerie_ArtAndScience.FV
113 reference(s)
81-FloatingPointNumbers.01.Ang
113 reference(s)		82-xiak_____.nota.t.
112 reference(s)
83-Galerie_NumbersAndLight.FV
112 reference(s)		84-Polynomials_RationalNumbers.01.Fra
111 reference(s)
85-GilbreathConjecture.01.Ang
111 reference(s)		86-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
110 reference(s)
87-Galerie_PALETTES_A
110 reference(s)		88-Galerie_ImagesDesMathematiques.DIAPO
110 reference(s)
89-xiirs_____.nota.t.
109 reference(s)		90-xiirk_____.nota.t.
109 reference(s)
91-catalogue.11
109 reference(s)		92-VirtualChaos.01.Fra
109 reference(s)
93-VirtualChaos.01.Ang
109 reference(s)		94-VCcatalogue.11
109 reference(s)
95-BEST.20190728
109 reference(s)		96-CantorSet_SierpinskiCarpet_MengerSponge.01.Ang
108 reference(s)
97-xrs_____sphere.12.I.
107 reference(s)		98-SurfaceProjector.01.Ang
107 reference(s)
99-ComplexiteStructurelleClassements.01
107 reference(s)		100-MouvementBrownien.01.Ang
106 reference(s)
101-MathematiquesPhysiqueFractales.02
106 reference(s)		102-xiirf_____.nota.t.
105 reference(s)
103-MathematiquesPhysiqueFractales.02.1.13
105 reference(s)		104-LesNombresTranscendants.01.Ang
105 reference(s)
105-LeNoeudInfini.01.Ang
105 reference(s)		106-xi_____INCLUDES_bas.I.
104 reference(s)
107-create.03.
104 reference(s)		108-Proth_Gilbreath_Conjecture.01.Fra
104 reference(s)
109-xrv_____champs_5.1A.I.
103 reference(s)		110-NatureDesMathematiques.01.vv.Fra
103 reference(s)
111-NDimensionalDeterministicFractalSets.01.Fra
103 reference(s)		112-HughEverettMultiverse.01.Fra
103 reference(s)
113-Galerie_ImagesDesMathematiques.FV
103 reference(s)		114-BEST.20000517
103 reference(s)
115-xrs_____sphere.18.I.
102 reference(s)		116-xiaq_____.nota.t.
102 reference(s)
117-LesNombresTranscendants.01.Fra
102 reference(s)		118-Galerie_RCMGalerie.FV
102 reference(s)
119-xrq_____Laguerre.31.I.
101 reference(s)		120-Galerie_CelestialMechanics
101 reference(s)
121-AnimFractal.01.
101 reference(s)		122-xrs_____surfaces.12.I.
100 reference(s)
123-UlamSpiral.01.Fra
100 reference(s)		124-RealNumbers.01.Fra
100 reference(s)
125-Exposition_EcolePolytechnique_FeteDeLaScience_202510
100 reference(s)		126-ComplexiteStructurelleClassements.11
100 reference(s)
127-BEST.20160828
100 reference(s)		128-xrq_____synapse.11.I.
99 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.