Monthly Best Of on 02/28/2026




A tridimensional fractal manifold defined by means of three tridimensional fields -picture sharpening-

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 02/28/2026 and last updated on 02/28/2026 22:13:46 -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-
1-10370 reference(s)		A tridimensional field
2-9538 reference(s)		A tridimensional field
3-1756 reference(s)		The eroded Menger Sponge -iteration 3-
4-366 reference(s)
A tridimensional field made of a tridimensional cubic mesh
5-282 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
6-187 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 100215...-
7-169 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
8-158 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
9-144 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
10-143 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
11-135 reference(s)		The random walk of photons escaping the Sun
12-132 reference(s)
The construction of the bidimensional Hilbert Curve -iteration 3-
13-132 reference(s)		An extended Menger Sponge -iteration 3- displaying the 10.665 first values of G(Pi(x)) modulo 2 of the Proth-Gilbreath conjecture
14-123 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 100215...-
15-119 reference(s)		Elliptical trajectory of a planet around a star with perihelion advance (very exaggerated)
16-118 reference(s)
A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
17-117 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
18-113 reference(s)		Untitled 0638
19-112 reference(s)		The first four iterations of the construction of the von Koch snowflake
20-111 reference(s)
The construction of a tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
21-111 reference(s)		The construction of a tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
22-108 reference(s)		Artistic view of the prime numbers
23-108 reference(s)		Autostereogram with an hidden volcano
24-106 reference(s)
The Lorenz attractor
25-105 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
26-105 reference(s)		The construction of the bidimensional Hilbert Curve -iteration 4-
27-104 reference(s)		Untitled 0598 -a Tribute to Robert & Sonia Delaunay-
28-104 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
29-104 reference(s)		Untitled 0265 -a Tribute to Vassily Kandinsky-
30-103 reference(s)		A 4-cube -an hypercube-
31-103 reference(s)		Untitled 0636
32-102 reference(s)
Untitled 0639
33-102 reference(s)		Rings
34-101 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 100215...-
35-100 reference(s)		Empty
36-99 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [9*10^14,10^15]-
37-98 reference(s)		The construction of the tridimensional Hilbert Curve -iteration 3-
38-97 reference(s)		Untitled 0198
39-96 reference(s)		Untitled 0637
40-96 reference(s)
The generalized Ulam spiral
41-95 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [10^15,1.1x10^15]-
42-95 reference(s)		Quark and gluon structure of a nucleon
43-94 reference(s)		Happy new year 2000
44-91 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
45-91 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 5-
46-90 reference(s)		Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
47-88 reference(s)		Hypercube
48-88 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
49-88 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-
50-88 reference(s)		Recursive subdivision of the Golden Rectangle by means of the Golden Ratio -phi-
51-87 reference(s)		Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
52-87 reference(s)
Artistic view of the Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 613247...-
53-86 reference(s)		The extended Bertrand paradox
54-86 reference(s)		Bidimensional cross-sections inside the tridimensional Ising Model with 2-state spins, temperature=0.4 and random initial conditions
55-85 reference(s)		Botticelli anomaly on the Moon
56-83 reference(s)
The Menger Sponge -iteration 5-
57-83 reference(s)		Along the border of the Mandelbrot set
58-82 reference(s)		The abelian -commutative- group defined on elliptic curves
59-82 reference(s)		The Jeener-Klein triple bottle
60-81 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-
61-80 reference(s)		The Universe at the heart of a Calabi-Yau manifold
62-80 reference(s)		Artistic view of the Big Bang
63-80 reference(s)		Happy new year 2000
64-80 reference(s)
Bidimensional cross-sections inside the tridimensional Ising Model with 2-state spins, temperature=0.2 and random initial conditions
65-80 reference(s)		Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
66-80 reference(s)		The distance {Earth-Mars} -millions of kilometers- starting on 01/01/1950 AD and during seven marsian years
67-79 reference(s)		Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
68-79 reference(s)
Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
69-79 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-
70-79 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-
71-78 reference(s)		The bidimensional Ising Model with 2-state spins, temperature=0.2 and random initial conditions
72-78 reference(s)
Artistic view of the Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 613247...-
73-78 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
74-78 reference(s)		Tridimensional representation of a hexadimensional Calabi-Yau manifold
75-78 reference(s)		The generalized Ulam spiral displaying 100 numbers
76-77 reference(s)
The smooth integers: the prime factor product -the radical function- of the integer numbers
77-77 reference(s)		Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
78-77 reference(s)		Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
79-77 reference(s)		The bidimensional Ising Model with 2-state spins, a centred gaussian temperature field (minimum=0.035,maximum=0.6)and regular initial conditions (a chessboard)
80-77 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
81-77 reference(s)		The 64 first lines of the Pascal's Triangle -modulo 2-
82-76 reference(s)		An aperiodic Penrose tiling of the Golden Decagon -a Tribute to Piet Mondrian and Roger Penrose-
83-76 reference(s)		N-body problem integration (N=3)displaying two planets with symmetrical initial conditions on elliptic trajectories
84-76 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
85-76 reference(s)		2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
86-76 reference(s)		Quaternionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-
87-76 reference(s)		Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
88-76 reference(s)
A fractal Möbius strip
89-76 reference(s)		Tridimensional fractal structure -the space-time foam?-
90-76 reference(s)		The execution of a very simple program on a Turing Machine
91-75 reference(s)		A tridimensional intertwining made of an extended Menger Sponge -iteration 5- inside a sphere
92-75 reference(s)
A tridimensional intertwining inside a 'tridimensional epicycloïdal' pseudo-torus
93-75 reference(s)		Jean-François COLONNA
94-75 reference(s)		The bidimensional Ising Model after 1000 iterations, with 2-state spins, random initial conditions and for different temperatures around the critical temperature
95-75 reference(s)		Quantum vacuum fluctuations
96-74 reference(s)
The same bidimensional scalar field displayed with 4 different color palettes
97-74 reference(s)		The tridimensional Ising Model with 2-state spins, temperature=0.2, random initial conditions and an increasing number of iterations -from 100 to 4000-
98-74 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 613247...-
99-74 reference(s)		A fractal Möbius strip
100-74 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
101-74 reference(s)		The construction process of the von Koch curve
102-73 reference(s)		A torus
103-73 reference(s)		Untitled 0308
104-73 reference(s)
The set of 'Y' bidimensional fields defining an interpolation between two intertwinings
105-73 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-
106-73 reference(s)		Untitled 0139
107-73 reference(s)		Iterations in the complex plane
108-73 reference(s)
Tridimensional Hilbert Curve -iteration 3-
109-73 reference(s)		64 elementary bidimensional binary cellular automata with 1 white starting central point
110-73 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 5-
111-72 reference(s)		A tridimensional intertwining made of the Menger Sponge -iteration 5- inside a sphere
112-72 reference(s)
The evolution of the sphere using the Lorenz attractor
113-72 reference(s)		Fractal 'celestial body' based on a torus with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
114-72 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
115-72 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-
116-72 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-
117-72 reference(s)		Synthesis of tridimensional textures
118-72 reference(s)		A perfect bidimensional fractal tree and the self-similarity
119-71 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-
120-71 reference(s)
The Möbius strip
121-71 reference(s)		A Douady rabbit -a complex Julia set computed with A=(-0.13,+0.77)- with display of the arguments
122-71 reference(s)		Visualization of the Proth-Gilbreath Conjecture process for G(Pi(1.0025x10^15))=806.
123-71 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 64 first prime numbers-
124-71 reference(s)
A fractal polyhedron
125-71 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
126-70 reference(s)		Quark and gluon structure of a nucleon
127-70 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)
128-70 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
3115 reference(s)		2-Vcatalogue.11
1533 reference(s)
3-xiirv_____.nota.t.
1053 reference(s)		4-An2000.01.Fra
890 reference(s)
5-Pcatalogue.11
812 reference(s)		6-help.
740 reference(s)
7-Galerie_RCMGalerie.FV
714 reference(s)		8-mail.01.vv
624 reference(s)
9-copyright.01.
620 reference(s)		10-xiirf_____.nota.t.
539 reference(s)
11-xiirc_____.nota.t.
492 reference(s)		12-catalogue.11
416 reference(s)
13-Galerie_NumbersAndLight.FV
363 reference(s)		14-Galerie_NumberTheory.FV
358 reference(s)
15-Galerie_ArtisticCreation.FV
245 reference(s)		16-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
232 reference(s)
17-Galerie_Pi.FV
230 reference(s)		18-Galerie_DeterministicFractalGeometry.FV
230 reference(s)
19-demo_14
225 reference(s)		20-Web_Mail.01.vv
220 reference(s)
21-Galerie_ParticleSystems.FV
204 reference(s)		22-xiirs_____.nota.t.
194 reference(s)
23-Galerie_GeneralitiesVisualization.FV
194 reference(s)		24-Galerie_SelfPortraits.FV
188 reference(s)
25-MorePages.Ang.
187 reference(s)		26-present.01.
181 reference(s)
27-Proth_Gilbreath_Conjecture.01.Ang
175 reference(s)		28-Galerie_ImagesDesMathematiques.FV
167 reference(s)
29-Stereogrammes_AutoStereogrammes.01
158 reference(s)		30-Fractal.01
148 reference(s)
31-ExpV_VirE.11
148 reference(s)		32-Galerie_CelestialMechanics.FV
147 reference(s)
33-ChatGPT.11.Ang
147 reference(s)		34-Proth_Gilbreath_Conjecture.01.Fra
145 reference(s)
35-ChatGPT.11.Fra
145 reference(s)		36-Galerie_ImagesEssentiellesDesMathematiques.FV
139 reference(s)
37-Galerie_Animations.FV
139 reference(s)		38-xiac_____.nota.t.
136 reference(s)
39-Galerie_ArtAndScience.FV
136 reference(s)		40-Galerie_DeterministicChaos.FV
135 reference(s)
41-GilbreathConjecture.01.Fra
132 reference(s)		42-Galerie_ImagesDidactiques.FV
131 reference(s)
43-xiia_____.nota.t.
128 reference(s)		44-AVirtualSpaceTimeTravelMachine.Fra
128 reference(s)
45-Galerie_Astrophysics.FV
125 reference(s)		46-Fractal.11
124 reference(s)
47-AProposSite.01.Fra
120 reference(s)		48-Galerie_PALETTES_A
119 reference(s)
49-UlamSpiral.01.Fra
117 reference(s)		50-GenieLogiciel.01.Fra
117 reference(s)
51-GilbreathConjecture.01.Ang
116 reference(s)		52-xci_____TAHX.01.K.
115 reference(s)
53-Fractal.21
115 reference(s)		54-xiak_____.nota.t.
113 reference(s)
55-xci_____comH_v2d2cvl.K.
113 reference(s)		56-FloatingPointNumbers.01.Fra
113 reference(s)
57-create.03.
112 reference(s)		58-LesApprentisDieux.01
112 reference(s)
59-xci_____AutoC_NDB.vv.y.
111 reference(s)		60-LeParadoxeDeFermi.01.Fra
111 reference(s)
61-xiirk_____.nota.t.
110 reference(s)		62-NDimensionalDeterministicFractalSets.01.Ang
110 reference(s)
63-Galerie_Tributes.FV
109 reference(s)		64-ChatGPT.01.Fra
109 reference(s)
65-Galerie_QuantumMechanics.FV
108 reference(s)		66-Galerie_IdMCNRS.FV
108 reference(s)
67-FaireDesMathematiques.01.Fra
107 reference(s)		68-xrs_____CalabiYau.41.I.
106 reference(s)
69-Le_Chat.01.Ang
105 reference(s)		70-xiirv_____.PRIM.81.8..u.
104 reference(s)
71-GoldenTriangle.01.Fra
104 reference(s)		72-Galerie_SensitivityToRoundingOffErrors.FV
104 reference(s)
73-xivP_d07_f2_____.PAYT.1.11..u.
102 reference(s)		74-Informations_GoodNewsAndBadNews.01.Fra
102 reference(s)
75-DecimalesDePi.01.Fra
102 reference(s)		76-xrs_____disque.19.I.
101 reference(s)
77-fractal.01
100 reference(s)		78-MathematiquesPhysiqueFractales.02
100 reference(s)
79-LesCourbesRemplissantes.02.Fra
100 reference(s)		80-xivP_d09_f2_____.REFL.c.54..u.
99 reference(s)
81-DecimalesPi_100000.vv
99 reference(s)		82-xiirv_____.PIAL.91.1.1..u.
98 reference(s)
83-MorePages.Fra.
98 reference(s)		84-LOG_xiMc.11
98 reference(s)
85-xrs_____Horner42.28.I.
97 reference(s)		86-xrC_____OBJC.B4P__1_______.11.PlansDeBits.t.
96 reference(s)
87-xiirv_____.PRIM.6n.2..u.
96 reference(s)		88-xiirv_____.GILB.11.2..u.
96 reference(s)
89-DecimalesPi_1_100.vv
96 reference(s)		90-xrC_____OBJC.E25__1_______.11.Recursive.t.
95 reference(s)
91-xiirv_____.PRIM.4.12..u.
95 reference(s)		92-xrC_____ObjetComplexe.B4T__1.vv.t.
94 reference(s)
93-NombresPremiers_10000.vv
94 reference(s)		94-Galerie_SignalProcessing.FV
94 reference(s)
95-xiii_____contours.def.
93 reference(s)		96-VCcatalogue.11
93 reference(s)
97-LeNoeudInfini.01.Fra
93 reference(s)		98-SurfaceProjector.01.Fra
92 reference(s)
99-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
92 reference(s)		100-Galerie_TextureSynthesis.FV
92 reference(s)
101-DieuScience.01.Fra
92 reference(s)		102-xiav_____.nota.t.
91 reference(s)
103-ChatGPT.01.Ang
91 reference(s)		104-xrs_____project3D.14.I.
90 reference(s)
105-xrC_____OBJC.E23__1_______.11.Ondelettes.t.
90 reference(s)		106-xrC_____OBJC.B4P__1_______.11.Ondelettes.t.
90 reference(s)
107-MathematiquesPhysiqueFractales.22
90 reference(s)		108-xrv_____TRON.01.K.
89 reference(s)
109-MouvementBrownien.01.Fra
89 reference(s)		110-xrC_____OBJC.E21__1_______.11.DFractale.t.
88 reference(s)
111-NatureDesMathematiques.01.vv.Fra
88 reference(s)		112-xiirv_____.GILB.31.1..u.
87 reference(s)
113-Le_Chat.01.Fra
87 reference(s)		114-ImagesEncadreesDisponibles.01
87 reference(s)
115-UlamSpiral.01.Ang
85 reference(s)		116-RealNumbers.01.Fra
85 reference(s)
117-IAGenerativesImages.01.Fra
85 reference(s)		118-Galerie_BestOf.FV
85 reference(s)
119-xrs_____fleur.13.I.
83 reference(s)		120-SurfaceProjector.01.Ang
83 reference(s)
121-DEuclideAuGPS.01.Ang
83 reference(s)		122-Polynomials_RationalNumbers.01.Fra
82 reference(s)
123-LesCourbesRemplissantes.01.Fra
82 reference(s)		124-ImpossibleStructures.01.Fra
82 reference(s)
125-xiird_____.ACIN.L.12..u.
81 reference(s)		126-Multivers.01.Fra
81 reference(s)
127-xiidM_____fonction.def.
80 reference(s)		128-DieuScience.01.Ang
80 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.