Monthly Best Of on 06/28/2025




Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-

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, Help and Search [Plan du Site, Aide et Recherche]]
[The Y2K Bug [Le bug de l'an 2000]]
[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 06/28/2025 and last updated on 06/28/2025 22:14:15 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-621 reference(s)		Empty
2-146 reference(s)		The generalized Ulam spiral displaying 100 numbers
3-143 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
4-126 reference(s)
Tridimensional Hilbert Curve -iteration 4-
5-118 reference(s)		The random walk of photons escaping the Sun
6-117 reference(s)		The execution of a very simple program on a Turing Machine
7-116 reference(s)		The execution of a very simple program on a Turing Machine
8-105 reference(s)
A distorded -for the sake of display- 5-cube -an hyperhypercube-
9-105 reference(s)		Monument Valley at sunrise
10-99 reference(s)		Artistic view of the prime numbers
11-99 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
12-97 reference(s)
A regular 4-gon -a square-
13-97 reference(s)		The Universe at the heart of a Calabi-Yau manifold
14-96 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
15-95 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
16-95 reference(s)
Autostereogram with an hidden volcano
17-94 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
18-94 reference(s)		The first four iterations of the construction of the von Koch snowflake
19-93 reference(s)		LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
20-93 reference(s)
A tridimensional intertwining made of a random tridimensional binary tree inside a sphere
21-92 reference(s)		Bidimensional Hilbert Curve -iteration 5-
22-91 reference(s)		Autostereogram with an hidden volcano
23-90 reference(s)		Hypercube
24-90 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
25-90 reference(s)		The Menger Sponge -iteration 5-
26-89 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-
27-89 reference(s)		The Klein bottle
28-89 reference(s)
Quantum vacuum fluctuations
29-88 reference(s)		Quark and gluon structure of a nucleon
30-88 reference(s)		Fractal Self-Portrait -'Décalcomanie', a Tribute to René Magritte-
31-88 reference(s)		Mountains and fog
32-87 reference(s)
The execution of a very simple program on a Turing Machine
33-85 reference(s)		A regular 3-gon -an equilateral triangle-
34-85 reference(s)		The Lorenz attractor
35-85 reference(s)		Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
36-84 reference(s)
The generalized Ulam spiral
37-84 reference(s)		A random Menger Sponge -iteration 5-
38-84 reference(s)		Happy new year 2000
39-84 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
40-84 reference(s)
A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
41-83 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
42-83 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
43-83 reference(s)		A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 5-
44-82 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
45-82 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
46-82 reference(s)		Causal set obtained by means of an homogeneous random meshing of a cube
47-82 reference(s)		The execution of a very simple program on a Turing Machine
48-81 reference(s)
A tridimensional intertwining made of the Menger Sponge -iteration 5- inside a sphere
49-81 reference(s)		The foggy Babel Tower -a Tribute to Brueghel the Elder-
50-81 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
51-81 reference(s)		Heterogeneous -tridimensional anti-gaussian field- random meshing of a cube
52-81 reference(s)
An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
53-81 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 5-
54-80 reference(s)		Quantum vacuum fluctuations
55-80 reference(s)		The execution of a very simple program on a Turing Machine
56-80 reference(s)
A tridimensional intertwining made of the Menger Sponge -iteration 5- inside a sphere
57-80 reference(s)		Untitled 0265 -a Tribute to Vassily Kandinsky-
58-80 reference(s)		A fractal Möbius strip
59-80 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
60-80 reference(s)
The random walk of photons escaping the Sun
61-79 reference(s)		Quark and gluon structure of a nucleon
62-79 reference(s)		The execution of a very simple program on a Turing Machine
63-78 reference(s)		A Tridimensional Hilbert-like Curve defined with {X1(...),Y1(...),Z1(...)} -iteration 1-
64-78 reference(s)
The Goldbach Conjecture
65-78 reference(s)		A random triangular tiling of the plane
66-77 reference(s)		Autostereogram with an hidden ring and ghost bows
67-77 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-
68-77 reference(s)
A tridimensional intertwining made of an amazing cross-section inside the Menger Sponge -iteration 5- inside a sphere
69-76 reference(s)		The 32 vertices of a 5-cube
70-76 reference(s)		Tridimensional display (bird's-eye view)of the density of particles during a bidimensional diffusion process
71-76 reference(s)		Victor Vasarely meets Piet Mondrian
72-75 reference(s)
A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
73-75 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 5-
74-75 reference(s)		A 4-cube -an hypercube-
75-75 reference(s)		Universe or Multiverse -The fractal Universe-?
76-74 reference(s)
A simple geometrical periodical structure
77-74 reference(s)		Intertwining
78-74 reference(s)		A sphere -positive curvature-
79-74 reference(s)		Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
80-74 reference(s)
An extended Menger Sponge -iteration 3-
81-74 reference(s)		Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
82-74 reference(s)		The Goldbach Conjecture for the even numbers from 6 to 1564
83-74 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
84-74 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
85-74 reference(s)		The execution of a very simple program on a Turing Machine
86-73 reference(s)		Autostereogram of the CMAP
87-73 reference(s)		The Sierpinski Carpet -iteration 3-
88-73 reference(s)
A Peano 'fractal plane' defined by means of three bidimensional fields
89-73 reference(s)		A Bidimensional Hilbert-like Curve defined with {X4(...),Y4(...)} -iteration 4-
90-73 reference(s)		A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
91-73 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
92-73 reference(s)
A circle
93-73 reference(s)		The double Jeener bottle
94-73 reference(s)		The Bonan-Jeener-Klein triple bottle
95-73 reference(s)		A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 5-
96-72 reference(s)
An aperiodic Penrose tiling of the plane
97-72 reference(s)		The 'sharp' Golden Triangle
98-72 reference(s)		A perfect bidimensional fractal tree and the self-similarity
99-72 reference(s)		A tridimensional intertwining made of a random tridimensional binary tree inside a sphere
100-72 reference(s)
A tridimensional intertwining made of an amazing cross-section inside the Menger Sponge -iteration 5- inside a sphere
101-72 reference(s)		Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
102-72 reference(s)		Animation of a sunrise on mountains
103-72 reference(s)		The Menger Sponge -iteration 3-
104-72 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) -tridimensional cross-section-
105-72 reference(s)		Artistic view of the Big Bang
106-71 reference(s)		The Klein bottle
107-71 reference(s)		The Ulam spiral with display of the first twin prime numbers ('2-twin' prime numbers)
108-71 reference(s)
A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -90.000 digits, -base 10- with 30.000 time steps
109-71 reference(s)		The K-smooth integers on a Bidimensional Hilbert Curve -iteration 4-
110-71 reference(s)		The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
111-71 reference(s)		An half-random extended Menger Sponge -iteration 3-
112-71 reference(s)
An extended Menger Sponge -iteration 7- displaying the 211.210.335 first digits -base 2- of 'pi'
113-71 reference(s)		A one sheet hyperboloid of revolution -negative curvature-
114-71 reference(s)		Fractal 3-foil torus knot
115-71 reference(s)		Fractal diffusion front in a bidimensional medium obtained by means of a random walk process
116-71 reference(s)
The abelian -commutative- group defined on elliptic curves
117-71 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
118-71 reference(s)		The self-similarity of the von Koch curve displayed by means of a zoom in with a ratio that is equal to 3
119-70 reference(s)		Self-Portrait with intertwining
120-70 reference(s)
A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the von Koch Curve -iteration 1-
121-70 reference(s)		Fractal piano keyboard
122-70 reference(s)		A parallelepipedic extended Menger Sponge -iteration 5-
123-70 reference(s)		Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
124-70 reference(s)
A blue Sponge-tree -a Tribute to Yves Klein-
125-70 reference(s)		Iterations in the complex plane: the computation of the Mandelbrot set
126-70 reference(s)		Anaglyph -blue=right, red=left- of an hypercube
127-70 reference(s)		Tridimensional fractal Self-Portrait
128-70 reference(s)




2-The 128 most referenced Pages (*):

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



1-MorePages.Ang.
71106 reference(s)		2-AVirtualSpaceTimeTravelMachine.Ang
2097 reference(s)
3-xiirv_____.nota.t.
480 reference(s)		4-xi_____INCLUDES_bas.I.
360 reference(s)
5-xiirs_____.nota.t.
311 reference(s)		6-Web_Mail.01.vv
264 reference(s)
7-mail.01.vv
242 reference(s)		8-xiii_____ImagesF.ext.
237 reference(s)
9-xiirf_____.nota.t.
227 reference(s)		10-xiirc_____.nota.t.
206 reference(s)
11-demo_14
205 reference(s)		12-xrv_____champs_5.1A.I.
198 reference(s)
13-xrv_____particule.10.K.
182 reference(s)		14-xci_____acces.K.
181 reference(s)
15-xci_____valeurs.03.I.
180 reference(s)		16-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
170 reference(s)
17-Fractal.11
169 reference(s)		18-FloatingPointNumbers.01.Fra
169 reference(s)
19-xci_____vraies_C.K.
166 reference(s)		20-Galerie_DeterministicFractalGeometry.FV
160 reference(s)
21-xiirC_____.nota.t.
157 reference(s)		22-xci_____valeurs_inte.K.
156 reference(s)
23-help.
156 reference(s)		24-xci_____init.K.
153 reference(s)
25-xrv_____ARITHMET.21.I.
151 reference(s)		26-xrv_____ARITHMET.22.I.
146 reference(s)
27-xrv_____ARITHMET.1d.I.
146 reference(s)		28-xrk_____attractor.11.I.
145 reference(s)
29-Vcatalogue.11
145 reference(s)		30-Galerie_ArtAndScience.FV
145 reference(s)
31-Stereogrammes_AutoStereogrammes.01
144 reference(s)		32-Informations_AboutPicturesAnimationsAndFiles.01.Ang
140 reference(s)
33-xrk_____attractor.12.I.
139 reference(s)		34-xi_____INCLUDES_min.I.
139 reference(s)
35-xiia_____.nota.t.
134 reference(s)		36-xrv_____particule.41.I.
132 reference(s)
37-xci_____complement.K.
131 reference(s)		38-xci_____normalise.01.K.
130 reference(s)
39-xci_____seuil.K.
129 reference(s)		40-LOG_xiMc.11
129 reference(s)
41-Galerie_CollaborativeWorks..FV
129 reference(s)		42-An2000.01.Fra
129 reference(s)
43-xci_____sequence.01.I.
128 reference(s)		44-xci_____neutre.K.
128 reference(s)
45-xig_____fonct.vv.def.
125 reference(s)		46-xci_____format.01.K.
125 reference(s)
47-xiak_____.nota.t.
124 reference(s)		48-xci_____montagne.01.K.
124 reference(s)
49-xrk_____attractor.18.I.
123 reference(s)		50-xiii_____quad_image.ext.
123 reference(s)
51-xrs_____surfaces.12.I.
122 reference(s)		52-xrs_____project2D.11.K.
120 reference(s)
53-xrk_____integr.1B.vv.I.
120 reference(s)		54-xci_____gauss.K.
120 reference(s)
55-xrv_____champs_5.41.I.
119 reference(s)		56-xrv_____dimensionnement.01.vv.I.
114 reference(s)
57-xias_____.nota.t.
114 reference(s)		58-xcg_____MIN2.01.K.
114 reference(s)
59-xci_____nombres.K.
113 reference(s)		60-xrs_____surfaces.11.I.
112 reference(s)
61-ChatGPT.11.Fra
111 reference(s)		62-xci_____scale.K.
110 reference(s)
63-xcg_____MIN3.01.K.
110 reference(s)		64-ChatGPT.01.Fra
110 reference(s)
65-xrs_____surfaces.13.I.
109 reference(s)		66-xci_____genere.K.
109 reference(s)
67-xiirk_____.nota.t.
108 reference(s)		68-copyright.01.
107 reference(s)
69-xrv_____normalise.01.K.
106 reference(s)		70-xci_____substitue.K.
106 reference(s)
71-Multivers.01.Ang
106 reference(s)		72-ChatGPT.11.Ang
106 reference(s)
73-xrs_____surfaces.22.I.
105 reference(s)		74-xci_____valeurs.02.I.
104 reference(s)
75-xcg_____MAX3.01.K.
103 reference(s)		76-Galerie_ArtisticCreation.FV
103 reference(s)
77-xrv_____extrema.01.K.
102 reference(s)		78-Galerie_NumbersAndLight.FV
102 reference(s)
79-xiac_____.nota.t.
101 reference(s)		80-xci_____luminance.01.K.
101 reference(s)
81-xrC_____ChaineOctetsUniformesAlternees_1024x1024.08.vv.I.
100 reference(s)		82-xci_____convol.01.K.
100 reference(s)
83-xrv_____neutre.K.
99 reference(s)		84-xrs_____surfaces.41.I.
99 reference(s)
85-xrC_____images_1bit.01.vv.I.
99 reference(s)		86-xiav_____.nota.t.
98 reference(s)
87-xci_____valeurs_alea.K.
98 reference(s)		88-UlamSpiral.01.Fra
97 reference(s)
89-EntrelacsIntertwinings.01.Fra
97 reference(s)		90-xci_____valeurs.01.I.
96 reference(s)
91-VAcatalogue.11
96 reference(s)		92-xci_____multi_02.01.K.
95 reference(s)
93-IAGenerativesImages.01.Fra
95 reference(s)		94-xrs_____surfaces.21.I.
94 reference(s)
95-xrC_____DeCompressionOptimale.01.vv.c.
93 reference(s)		96-xci_____passe_bande.K.
93 reference(s)
97-xci_____dilate.01.K.
93 reference(s)		98-xci_____cache.K.
93 reference(s)
99-ChatGPT.01.Ang
93 reference(s)		100-xrC_____CompressionDeCompression_Compression.01.vv.c.
92 reference(s)
101-xrC_____images_1octet.01.vv.I.
91 reference(s)		102-xci_____fract_2D.01.K.
91 reference(s)
103-xci_____filtre.01.K.
91 reference(s)		104-Fractal.01
90 reference(s)
105-Le_Chat.01.Ang
89 reference(s)		106-DecimalesDePi.01.Fra
89 reference(s)
107-ximd_____operator.1.fon.
88 reference(s)		108-xiii_____di_image.fon.
88 reference(s)
109-present.01.
87 reference(s)		110-Commentaires_NKleinBottle.01
87 reference(s)
111-xig_____fonct.vv.fon.
86 reference(s)		112-HughEverettMultiverse.01.Fra
86 reference(s)
113-Galerie_ParticleSystems.FV
86 reference(s)		114-Fractal.21
86 reference(s)
115-xrC_____CompressionOptimale.01.vv.c.
85 reference(s)		116-AProposSite.01.Fra
85 reference(s)
117-UlamSpiral.01.Ang
84 reference(s)		118-ExpV_VirE.Ang
83 reference(s)
119-DecimalesPi_100000.vv
82 reference(s)		120-xci_____lissage.K.
81 reference(s)
121-Galerie_NewPictures.FV
81 reference(s)		122-xci_____move.K.
80 reference(s)
123-create.03.
80 reference(s)		124-xci_____genere_ch.02.I.
79 reference(s)
125-OrdinateursEtCalculs.01.Ang
79 reference(s)		126-GoldenTriangle.01.Fra
79 reference(s)
127-Galerie_ImagesDidactiques.FV
79 reference(s)		128-Galerie_GeneralitiesVisualization.FV
79 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.