Monthly Best Of on 03/28/2025




A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-

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 03/28/2025 and last updated on 03/29/2025 19:27:06 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-543 reference(s)		Along the border of the Mandelbrot set
2-167 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
3-130 reference(s)		The Simpson paradox
4-108 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
5-104 reference(s)		Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-
6-103 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
7-102 reference(s)		The first four iterations of the construction of the von Koch snowflake
8-100 reference(s)
Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-
9-99 reference(s)		The Klein bottle
10-94 reference(s)		Pseudo-octonionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-
11-90 reference(s)		A distorded -for the sake of display- 5-cube -an hyperhypercube-
12-90 reference(s)
Autostereogram with an hidden volcano
13-88 reference(s)		Along the border of the Mandelbrot set
14-87 reference(s)		Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-
15-86 reference(s)		France covered with digits
16-84 reference(s)
An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
17-83 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-
18-82 reference(s)		Artistic view of the prime numbers
19-82 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
20-81 reference(s)
Autostereogram of 8 color-multiplexed quaternionic Julia sets -tridimensional cross-sections-
21-80 reference(s)		The Sierpinski Carpet -iteration 3-
22-80 reference(s)		Fractal Self-Portrait -a Tribute to René Magritte-
23-80 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
24-79 reference(s)
Fractal diffusion front in a bidimensional medium obtained by means of a random walk process
25-79 reference(s)		The random walk of photons escaping the Sun
26-78 reference(s)		The Menger Sponge -iteration 5-
27-78 reference(s)		Foggy island
28-78 reference(s)
Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
29-77 reference(s)		Tridimensional fractal Self-Portrait
30-77 reference(s)		The Universe at the heart of a Calabi-Yau manifold
31-75 reference(s)		The generalized Ulam spiral
32-75 reference(s)
The Sierpinski Carpet -iteration 1 to 5-
33-73 reference(s)		Tridimensional representation of a hexadimensional Calabi-Yau manifold
34-73 reference(s)		Double random triangulation of the volume of a sphere -8x8x8-
35-72 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
36-71 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
37-70 reference(s)		Random quadrangulation of the surface of a torus -18x18-
38-69 reference(s)		Regular quadrangulation of the surface of a cylinder -18x18-
39-68 reference(s)		Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
40-68 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-
41-67 reference(s)		Autostereogram of the CMAP
42-66 reference(s)		The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
43-66 reference(s)		The Piet Mondrian quadridimensional Calabi-Yau manifold -2D, 3D or 4D?-
44-66 reference(s)
The Klein bottle
45-64 reference(s)		A quaternionic Julia set -tridimensional cross-section-
46-64 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
47-64 reference(s)		Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
48-63 reference(s)
The Sierpinski Carpet -iteration 4-
49-62 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-
50-62 reference(s)		The Ptolemaic system with a moving equant -grey circle above the Earth- with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend-
51-62 reference(s)		The Ptolemaic system with equant -grey circle above the Earth- with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend-
52-62 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
53-62 reference(s)		Kasner billiard: Time-dependent billiard (from negative curvatures to positive curvature)with one accelerated particle
54-61 reference(s)		Tridimensional fractal structure
55-61 reference(s)		An equilateral triangle
56-61 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
57-61 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
58-61 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
59-61 reference(s)		Untitled 0637
60-61 reference(s)
Simulation of 'from Pluto to the Sun' with pure uniform circular motions (linear scales)
61-60 reference(s)		A parallelepipedic extended Menger Sponge -iteration 2-
62-60 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-
63-60 reference(s)		The random walk of photons escaping the Sun
64-59 reference(s)
Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
65-59 reference(s)		From 'geocentrism' to 'heliocentrism'
66-59 reference(s)		A set of 4x3 stereograms of the Tridimensional Hilbert Curve -iteration 3-
67-59 reference(s)		64 elementary bidimensional binary cellular automata with 1 white starting central point
68-59 reference(s)
The numerical reversibility of the bidimensional billiard -192 particles-
69-58 reference(s)		A Peano 'fractal plane' defined by means of three bidimensional fields
70-58 reference(s)		The construction of the Klein bottle described by means of a Bidimensional Hilbert Curve -iteration 7-
71-58 reference(s)		A 4-cube -an hypercube-
72-58 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
73-58 reference(s)		A regular 7-gon -an heptagon-
74-57 reference(s)		Black dots on a square lattice
75-57 reference(s)		The Ptolemaic system without equant with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend- centered on the Earth -blue sphere-
76-57 reference(s)
Along the border of the Mandelbrot set
77-56 reference(s)		The numerical irreversibility of the bidimensional billiard -1376 particles-
78-56 reference(s)		From Pluto to the Sun (non linear scales)
79-56 reference(s)		Hypercube
80-56 reference(s)
An aperiodic Penrose tiling of the plane -a Tribute to Piet Mondrian and Roger Penrose-
81-55 reference(s)		The Sierpinski Carpet -iteration 1-
82-55 reference(s)		The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
83-55 reference(s)		The tridimensional Ising Model with 2-state spins, temperature=0.1 and random initial conditions
84-55 reference(s)
Sixteen interlaced fractal torus
85-55 reference(s)		Tridimensional representation of our familiar tridimensional space
86-55 reference(s)		A 'conic' cross-section inside the Menger Sponge -iteration 5-, 'Ô temps tes pyramides' -a Tribute to Jorge Luis Borges-
87-54 reference(s)		Simple random triangulation of the surface of a torus -18x18-
88-54 reference(s)
The Lorenz attractor
89-54 reference(s)		A fractal Möbius strip
90-54 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
91-54 reference(s)		LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
92-54 reference(s)
The 64 first lines of the Pascal's Triangle
93-53 reference(s)		The Sierpinski Carpet -iteration 2-
94-53 reference(s)		The Sierpinski Carpet -iteration 3-
95-53 reference(s)		Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
96-53 reference(s)
From Pluto to the Sun (linear scales)
97-53 reference(s)		A parallelepipedic extended Menger Sponge -iteration 4-
98-53 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 5-
99-53 reference(s)		The Legendre Conjecture with 0 < n < 51 and display of Prime Number alignments
100-53 reference(s)
The construction of the bidimensional Hilbert Curve -iteration 3-
101-53 reference(s)		The Bonan-Jeener-Klein triple bottle
102-53 reference(s)		The Ulam spiral displaying 2025 numbers
103-52 reference(s)		The generalized Ulam spiral displaying 1024 numbers
104-52 reference(s)
The K-smooth integers on a generalized Ulam spiral
105-52 reference(s)		A missed journey from the Earth to Mars starting on 01/01/1950 AD, velocity=10.000 m/s
106-52 reference(s)		The Legendre Conjecture with 0 < n < 201
107-52 reference(s)		1-foil torus knot -obvious knot- on its torus and its asociated Möbius strip
108-52 reference(s)
Artistic view of the Big Bang
109-51 reference(s)		Untitled 0631
110-51 reference(s)		The interpolation between two simple geometrical periodical structures
111-51 reference(s)		Cauliflowers, seaweeds, shells,...
112-51 reference(s)
The generalized Ulam spiral displaying 100 numbers
113-51 reference(s)		An extended Menger Sponge -iteration 5-
114-51 reference(s)		The Menger Sponge -iteration 5-
115-51 reference(s)		Bidimensional zoom in on the Mandelbrot set
116-51 reference(s)
Tridimensional visualization of the Verhulst dynamics with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
117-51 reference(s)		A one sheet hyperboloid of revolution -negative curvature-
118-51 reference(s)		Fractal quaternionic shell
119-51 reference(s)		Fractal diffusion front in a bidimensional medium obtained by means of a random walk process
120-51 reference(s)
Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold
121-51 reference(s)		A 'pyramidal' cross-section inside the Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-, 'Ô temps tes pyramides' -a Tribute to Jorge Luis Borges-
122-50 reference(s)		A half-random extended Menger Sponge -iteration 4-
123-50 reference(s)		A half-random extended Menger Sponge -iteration 2-
124-50 reference(s)
Computation of the Lorenz attractor on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors)
125-50 reference(s)		2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
126-50 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
127-50 reference(s)		A set of 4x3 stereograms of a tridimensional fractal structure
128-50 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
2004 reference(s)		2-help.
745 reference(s)
3-Exposition_EcolePolytechnique_CentenaireNaissanceBenoitMandelbrot_202410_202411_202412
627 reference(s)		4-Web_Mail.01.vv
291 reference(s)
5-xiirC_____.nota.t.
236 reference(s)		6-Galerie_ParticleSystems.FV
191 reference(s)
7-mail.01.vv
154 reference(s)		8-Commentaires_ModeleIsingTriDimensionnel.01
151 reference(s)
9-xrC_____CompressionDeCompression_Compression.01.vv.c.
130 reference(s)		10-Stereogrammes_AutoStereogrammes.01
117 reference(s)
11-copyright.01.
115 reference(s)		12-Vcatalogue.11
115 reference(s)
13-An2000.01.Fra
113 reference(s)		14-demo_14
104 reference(s)
15-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
98 reference(s)		16-xiirv_____.nota.t.
96 reference(s)
17-IAGenerativesImages.01.Fra
95 reference(s)		18-avirtualspacetimetravelmachine.ang
94 reference(s)
19-ChatGPT.01.Fra
94 reference(s)		20-LOG_xiMc.11
92 reference(s)
21-ChatGPT.11.Fra
85 reference(s)		22-FloatingPointNumbers.01.Ang
83 reference(s)
23-Informations_GoodNewsAndBadNews.01.Fra
81 reference(s)		24-Informations_GoodNewsAndBadNews.01.Ang
81 reference(s)
25-ImagesDuVirtuel.01.Fra.FV
81 reference(s)		26-Galerie_CollaborativeWorks..FV
81 reference(s)
27-Fractal.01
80 reference(s)		28-HughEverettMultiverse.01.Fra
77 reference(s)
29-Informations_AboutPicturesAnimationsAndFiles.01.Ang
76 reference(s)		30-UlamSpiral.01.Fra
73 reference(s)
31-NDimensionalDeterministicFractalSets.01.Fra
72 reference(s)		32-AVirtualSpaceTimeTravelMachine.Fra
72 reference(s)
33-LesNombresTranscendants.01.Ang
70 reference(s)		34-IAGenerativesImages.01.Ang
69 reference(s)
35-AProposSite.01.Fra
69 reference(s)		36-SourceExemple_____xtc_____stereogra.01.c.
68 reference(s)
37-xtp_____AXmB.01.python.
67 reference(s)		38-HughEverettMultiverse.01.Ang
67 reference(s)
39-FloatingPointNumbers.01.Fra
67 reference(s)		40-Galerie_Animations.FV
66 reference(s)
41-Galerie_NumbersAndLight.FV
65 reference(s)		42-An2000.03.Fra
65 reference(s)
43-xiirf_____.nota.t.
64 reference(s)		44-xiav_____.nota.t.
64 reference(s)
45-NombresEtLumiere.01.vv.Fra
64 reference(s)		46-PerteDeLAssociativite.01.MUL3
63 reference(s)
47-ComplexiteStructurelleClassements.11
62 reference(s)		48-Informations_AboutPicturesAnimationsAndFiles.01.Fra
61 reference(s)
49-Fractal.21
61 reference(s)		50-DeepSeek.01.Fra
61 reference(s)
51-catalogue.11
58 reference(s)		52-UlamSpiral.01.Ang
58 reference(s)
53-NDimensionalDeterministicFractalSets.01.Ang
58 reference(s)		54-Galerie_IdMCNRS.FV
58 reference(s)
55-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis
57 reference(s)		56-DecimalesPi_100000.vv
57 reference(s)
57-RealNumbers.01.Fra
56 reference(s)		58-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
56 reference(s)
59-LesNombresTranscendants.01.Fra
55 reference(s)		60-LesCourbesRemplissantes.01.Fra
55 reference(s)
61-SIlVousPlaitDessineMoiLInfini.01.Fra
54 reference(s)		62-NombresPremiers_10000.vv
54 reference(s)
63-MathematiquesPhysiqueFractales.02
54 reference(s)		64-IrreversibiliteDuTempsNumerique.01.Fra
54 reference(s)
65-xrC_____CompressionOptimale.01.vv.c.
53 reference(s)		66-ComplexiteStructurelleClassements.01
53 reference(s)
67-Galerie_NumberTheory.FV
51 reference(s)		68-FaireDeLaRecherche.01.vv
51 reference(s)
69-ChatGPT.11.Ang
51 reference(s)		70-ArithmetiqueEtOrdinateur.01.vv.Fra
51 reference(s)
71-AQuoiServentLesMathematiques.01
51 reference(s)		72-xiirs_____.nota.t.
50 reference(s)
73-stereogrammes_autostereogrammes.01
50 reference(s)		74-xrC_____DeCompressionOptimale.01.vv.c.
49 reference(s)
75-relai_universel.01.vv
49 reference(s)		76-SurfaceProjector.01.Ang
49 reference(s)
77-DecimalesPi_1_100.vv
49 reference(s)		78-MathematiquesPhysiqueFractales.12
48 reference(s)
79-Bard.01.Fra
48 reference(s)		80-AnimFractal.01.
48 reference(s)
81-subject.01.
47 reference(s)		82-VCcatalogue.11
47 reference(s)
83-xiia_____.nota.t.
46 reference(s)		84-Notations_AppartientA.01
46 reference(s)
85-NombresEtLumiere.02.vv.Ang
46 reference(s)		86-MathematiquesPhysiqueFractales.02.15
46 reference(s)
87-Galerie_SignalProcessing.FV
46 reference(s)		88-BEST.20180528
46 reference(s)
89-MesExpositionsPassees.01
45 reference(s)		90-ManyChaos.01.Ang
45 reference(s)
91-LeParadoxeDeFermi.01.Fra
45 reference(s)		92-Downloading.01.vv
45 reference(s)
93-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
45 reference(s)		94-Commentaires_SurfaceDeBoy.01
45 reference(s)
95-AProposSite.01.Ang
45 reference(s)		96-Galerie_NewPictures.FV
44 reference(s)
97-Fractal.11
44 reference(s)		98-DieuScience.01.Ang
44 reference(s)
99-infinity.01.vv
43 reference(s)		100-create.03.
43 reference(s)
101-Multivers.01.Fra
43 reference(s)		102-MonodimensionalCellularAutomata.01.Ang
43 reference(s)
103-Galerie_ImagesEssentiellesDesMathematiques.FV
43 reference(s)		104-Galerie_FluidMechanics.FV
43 reference(s)
105-Galerie_CelestialMechanics.DIAPO.0001
43 reference(s)		106-An2000.01.Ang
43 reference(s)
107-LeCinquantenaireDuCMAP.01.vv.Fra
42 reference(s)		108-Galerie_GeneralitiesVisualization.FV
42 reference(s)
109-ConjectureDeSyracuse_0128.Parity.vv
42 reference(s)		110-RasoirDOccamEtMathematiques.01.vv.Ang
41 reference(s)
111-NatureDesMathematiques.01.vv.Fra
41 reference(s)		112-MorePages.Ang.
41 reference(s)
113-MathematiquesModeleOutilArtiste.02.Ang
41 reference(s)		114-Kepler.02.
41 reference(s)
115-GoldenTriangle.01.Fra
41 reference(s)		116-Commentaires_NKleinBottle.01
41 reference(s)
117-Commentaires_EnsembleMandelbrotQuaternion.01
41 reference(s)		118-RasoirDOccamEtMathematiques.01.vv.Fra
40 reference(s)
119-MonodimensionalCellularAutomata.01.Fra
40 reference(s)		120-MiseEnSceneDesNombres.01.vv.Ang
40 reference(s)
121-Galerie_Pi.FV
40 reference(s)		122-Galerie_ImagesDesMathematiques.FV
40 reference(s)
123-Galerie_DeterministicFractalGeometry.FV
40 reference(s)		124-EntrelacsIntertwinings.01.Fra
40 reference(s)
125-AvantPropos.01.Ang
40 reference(s)		126-present.01.
39 reference(s)
127-PatrimoineHumanite.02.Fra
39 reference(s)		128-MathematiquesEtCinematographe.01.vv
39 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.