Monthly Best Of on 10/28/2022




A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.393069,0.197729,0,0) -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 10/28/2022 and last updated on 11/14/2023 17:50:30 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Artistic view of the prime numbers
1-131 reference(s)		 The random walk of photons escaping the Sun
2-101 reference(s)		 The Ulam spiral
3-76 reference(s)		 The K-smooth integers on a Tridimensional Hilbert Curve -iteration 3-
4-76 reference(s)
Jean-François COLONNA (on 11/17/1994)with its fractal mountains
5-75 reference(s)		 The K-smooth integers on a Bidimensional Hilbert Curve -iteration 5-
6-73 reference(s)		 The Lorenz attractor
7-73 reference(s)		 A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
8-71 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
9-70 reference(s)		 The Node, The Garden of Rama -a Tribute to Arthur C. Clarke and Gentry Lee-
10-70 reference(s)		 Autostereogram with an hidden volcano
11-69 reference(s)		 A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
12-68 reference(s)
The K-smooth integers on a generalized Ulam spiral
13-67 reference(s)		 Coalescence of 40832 particles -black holes?- inside a tridimensional parallelepipedic billiard
14-66 reference(s)		 The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
15-64 reference(s)		 Tridimensional representation of a hexadimensional Calabi-Yau manifold
16-64 reference(s)
Autostereogram with an hidden ring and ghost bows
17-63 reference(s)		 A tridimensional fractal manifold defined by means of three tridimensional fields
18-63 reference(s)		 The 2/3/5/7-smooth integers on a generalized Ulam spiral
19-62 reference(s)		 The same bidimensional scalar field displayed with 4 different color palettes
20-60 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
21-60 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
22-60 reference(s)		 The 'tangent' of a sphere
23-59 reference(s)		 Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
24-59 reference(s)
Sixteen interlaced fractal torus
25-59 reference(s)		 Along the border of the Mandelbrot set
26-58 reference(s)		 The Sierpinski carpet -iteration 1 to 5-
27-58 reference(s)		 The generalized Ulam spiral
28-58 reference(s)
Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
29-58 reference(s)		 Artistic view of the Big Bang
30-57 reference(s)		 The foggy Babel Tower -a Tribute to Brueghel the Elder-
31-57 reference(s)		 Self-Portrait -'This is not an apple', a Tribute to René Magritte-
32-56 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
33-56 reference(s)		 Untitled 0599 -a Tribute to Robert & Sonia Delaunay-
34-56 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
35-56 reference(s)		 The Road to Chaos -06/19/2022-
36-54 reference(s)
The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with cluster(s), with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-
37-54 reference(s)		 The Menger sponge -iteration 5-
38-54 reference(s)		 Rotation about the Y (vertical)axis of the CMAP logo that can also be viewed as a set of 4x3 stereograms
39-54 reference(s)		 The generalized Ulam spiral displaying 100 numbers
40-53 reference(s)
Botticelli anomaly on the Moon
41-53 reference(s)		 The smooth integers: the prime factor product -the radical function- of the integer numbers
42-53 reference(s)		 From Pluto to the Sun (non linear scales)
43-53 reference(s)		 An amazing cross-section inside the Menger sponge -iteration 5-
44-53 reference(s)
Heterogeneous -tridimensional fractal field- random meshing of a cube
45-53 reference(s)		 Archimedes mountains (bird's-eye view)
46-52 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)
47-52 reference(s)		 Pseudo Olympic Rings
48-51 reference(s)
Fractal Self-Portrait -a Tribute to René Magritte-
49-51 reference(s)		 The Universe at the heart of a Calabi-Yau manifold
50-50 reference(s)		 An aperiodic Penrose tiling of the plane
51-50 reference(s)		 Bidimensional display of 255 Rational Numbers by means of the Stern-Brocot Tree
52-50 reference(s)
The Road to Chaos -06/19/2022-
53-50 reference(s)		 Tridimensional display of the particle density of a bidimensional snowflake-like billiard
54-50 reference(s)		 Untitled 0155 -a Tribute to Yves Tanguy-
55-50 reference(s)		 The Satanic Verses -a Tribute to Salman Rushdie-
56-50 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
57-50 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
58-50 reference(s)		 The first four iterations of the construction of the von Koch snowflake
59-49 reference(s)		 Autostereogram with an hidden volcano
60-49 reference(s)
24 evenly distributed points on a sphere by means of simulated annealing
61-49 reference(s)		 Mountains and fog
62-49 reference(s)		 Quark and gluon structure of a nucleon
63-49 reference(s)		 Untitled 0597
64-49 reference(s)
Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
65-49 reference(s)		 RestrictedAccess --> 66-49 reference(s) The 64 first lines of the Pascal's Triangle -modulo 7-
67-48 reference(s)		 Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
68-48 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
69-48 reference(s)		 An aperiodic Penrose tiling of the Golden Decagon -a Tribute to Piet Mondrian and Roger Penrose-
70-47 reference(s)		 Untitled 0320
71-47 reference(s)		 Autostereogram of the CMAP
72-47 reference(s)
A punched paper tape
73-47 reference(s)		 Monument Valley at sunrise
74-47 reference(s)		 Mountains at sunrise
75-47 reference(s)		 The 126.646 first digits -base 6- of 'pi' displayed as an 'absolute' tridimensional random walk
76-47 reference(s)
Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
77-47 reference(s)		 A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
78-47 reference(s)		 Real numbers do not exist for a computer
79-47 reference(s)		 Distorsion of the Bonan-Jeener-Klein triple bottle
80-47 reference(s)
The Mathematics are the key of the Multiverse
81-46 reference(s)		 Bidimensional display of 31 Rational Numbers by means of the Stern-Brocot Tree
82-46 reference(s)		 Untitled 0604 -a Tribute to Yves Klein-
83-46 reference(s)		 The smooth integers
84-46 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-
85-46 reference(s)		 2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
86-46 reference(s)		 Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 1.083.984 galaxies)obtained by means of a non deterministic fractal process
87-46 reference(s)		 Untitled 0600 -a Tribute to Jean Arp-
88-46 reference(s)
An aperiodic Penrose tiling of the plane
89-45 reference(s)		 Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier-
90-45 reference(s)		 Fractal synthesis of mountains with vegetation and stormy clouds
91-45 reference(s)		 A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
92-45 reference(s)
Mountains and light cloud dynamics -this sequence being periodical-
93-44 reference(s)		 A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
94-44 reference(s)		 Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
95-44 reference(s)		 Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
96-44 reference(s)
The Birth of the Universe
97-44 reference(s)		 A gradient of 114299 particles obtains by means of a tridimensional diffusion process
98-44 reference(s)		 Untitled 0602 -a Tribute to Jean-Michel Atlan-
99-44 reference(s)		 Untitled 0305
100-43 reference(s)
The 'hyperbolic tangent' of a sphere
101-43 reference(s)		 Artistic view of a bidimensional texture obtained by means of the self-transformation of a fractal process
102-43 reference(s)		 A variable Archimedes spiral displaying 1000 numbers
103-43 reference(s)		 The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
104-43 reference(s)
Happy new year 2000
105-43 reference(s)		 An aperiodic Penrose tiling of the plane
106-42 reference(s)		 The 'tangent' of a sphere
107-42 reference(s)		 Self-transformation of an arbitrary geometrical texture
108-42 reference(s)
Bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity
109-42 reference(s)		 N-body problem integration (N=5)displaying four planets with symmetrical initial conditions on elliptic trajectories -'geocentric' point of view, green body-
110-42 reference(s)		 Fractal Self-Portrait -'Décalcomanie', a Tribute to René Magritte-
111-42 reference(s)		 Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers-
112-42 reference(s)
Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
113-42 reference(s)		 The Eratosthene sieve displaying 100x100 numbers
114-41 reference(s)		 Mountains and fog
115-41 reference(s)		 7-foil torus knot on its torus
116-41 reference(s)
Tridimensional fractal structure
117-41 reference(s)		 The Jeener hypocycloidal snail
118-41 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
119-41 reference(s)		 Quantum vacuum fluctuations
120-40 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
121-40 reference(s)		 The Sierpinski carpet -iteration 2-
122-40 reference(s)		 Fractal 'celestial body' based on a torus with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
123-40 reference(s)		 Distorsion of the Möbius strip
124-40 reference(s)
An arbitrary surface (Jeener surface 2)in motion
125-40 reference(s)		 A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) and with a 0 to pi rotation about the X axis -tridimensional cross-section-
126-40 reference(s)		 Black dots on a square lattice
127-40 reference(s)		 Tridimensional Hilbert Curve -iteration 3-
128-40 reference(s)




2-The 128 most referenced Pages (*):

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



1-Vcatalogue.11
679 reference(s)		 2-xiirc_____.nota.t.
306 reference(s)
3-xiirv_____.nota.t.
231 reference(s)		 4-An2000.01.Fra
201 reference(s)
5-AVirtualSpaceTimeTravelMachine.Ang
191 reference(s)		 6-xiirs_____.nota.t.
182 reference(s)
7-help.
169 reference(s)		 8-demo_14
165 reference(s)
9-mail.01.vv
128 reference(s)		 10-Informations_AboutPicturesAnimationsAndFiles.01.Ang
117 reference(s)
11-copyright.01.
115 reference(s)		 12-Galerie_NewPictures.FV
110 reference(s)
13-Informations_GoodNewsAndBadNews.01.Ang
109 reference(s)		 14-Stereogrammes_AutoStereogrammes.01
99 reference(s)
15-PerteDeLAssociativite.01
96 reference(s)		 16-xiac_____.nota.t.
95 reference(s)
17-Galerie_NumberTheory.FV
95 reference(s)		 18-Galerie_ImagesDesMathematiques.FV
91 reference(s)
19-Galerie_ArtisticCreation.FV
88 reference(s)		 20-AProposSite.01.Fra
83 reference(s)
21-MonodimensionalCellularAutomata.01.Fra
82 reference(s)		 22-Galerie_GeneralitiesVisualization.FV
82 reference(s)
23-OrdinateursEtCalculs.01.Ang
81 reference(s)		 24-AVirtualSpaceTimeTravelMachine.Fra
80 reference(s)
25-Galerie_TextureSynthesis.FV
78 reference(s)		 26-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
78 reference(s)
27-LOG_xiMc.11
77 reference(s)		 28-NombresEtLumiere.01.vv.Fra
76 reference(s)
29-NDimensionalDeterministicFractalSets.01.Fra
76 reference(s)		 30-FloatingPointNumbers.01.Fra
76 reference(s)
31-GenieLogiciel_VisualisationScientifique.01.vv
75 reference(s)		 32-EntrelacsIntertwinings.01.Ang
73 reference(s)
33-Galerie_ArtAndScience.FV
71 reference(s)		 34-EntrelacsIntertwinings.01.Fra
71 reference(s)
35-present.01.
70 reference(s)		 36-MathematiquesPhysiqueFractales.12
69 reference(s)
37-Galerie_DeterministicFractalGeometry.FV
69 reference(s)		 38-xias_____.nota.t.
68 reference(s)
39-UlamSpiral.01.Fra
68 reference(s)		 40-SurfaceProjector.01.Ang
66 reference(s)
41-GoldenTriangle.01.Fra
66 reference(s)		 42-Galerie_DeterministicChaos.FV
65 reference(s)
43-Fractal.01
65 reference(s)		 44-FloatingPointNumbers.01.Ang
64 reference(s)
45-Fractal.11
61 reference(s)		 46-NatureDesMathematiques.01.vv.Fra
60 reference(s)
47-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
60 reference(s)		 48-ImpossibleStructures.01.Fra
60 reference(s)
49-Galerie_ParticleSystems.FV
59 reference(s)		 50-MathematiquesPhysiqueFractales.02
58 reference(s)
51-Informations_GoodNewsAndBadNews.01.Fra
58 reference(s)		 52-Galerie_QuantumMechanics.FV
58 reference(s)
53-Galerie_CelestialMechanics.FV
57 reference(s)		 54-DuModeleALImage.02.Fra
56 reference(s)
55-Autostereograms.01.
56 reference(s)		 56-Galerie_Tributes.FV
55 reference(s)
57-xiav_____.nota.t.
54 reference(s)		 58-SurfaceProjector.01.Fra
54 reference(s)
59-Galerie_Astrophysics.FV
54 reference(s)		 60-Fractal.21
54 reference(s)
61-ExpV_VirE.11
54 reference(s)		 62-xiak_____.nota.t.
53 reference(s)
63-UlamSpiral.01.Ang
53 reference(s)		 64-MathematiquesEtRepresentations.01.vv.Ang
53 reference(s)
65-GoldenTriangle.01.Ang
52 reference(s)		 66-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
52 reference(s)
67-subject.01.
51 reference(s)		 68-RealNumbers.01.Fra
51 reference(s)
69-NDimensionalDeterministicFractalSets.01.Ang
51 reference(s)		 70-AnimFractal.01.
51 reference(s)
71-LeNoeudInfini.01.Ang
50 reference(s)		 72-Galerie_ImagesDidactiques.FV
50 reference(s)
73-Kepler.02.
49 reference(s)		 74-IllusionConnaissance.02
49 reference(s)
75-Galerie_SensitivityToRoundingOffErrors.FV
49 reference(s)		 76-ManyChaos.01.Ang
48 reference(s)
77-ImagesDuVirtuel.01.Fra.FV
48 reference(s)		 78-Galerie_BestOf.FV
48 reference(s)
79-AvantPropos.01.Fra
48 reference(s)		 80-OrdinateurMathematiquesArt.01.Fra
47 reference(s)
81-MonodimensionalCellularAutomata.01.Ang
47 reference(s)		 82-IllusionConnaissance.01
47 reference(s)
83-Galerie_SelfPortraits.FV
47 reference(s)		 84-Galerie_GeneralitiesVisualization
46 reference(s)
85-Fractal.02
46 reference(s)		 86-Commentaires_NKleinBottle.01
46 reference(s)
87-Commentaires_DefinitionPseudoQuaternions.01
46 reference(s)		 88-Web_Mail.01.vv
45 reference(s)
89-Informations_AboutPicturesAnimationsAndFiles.01.Fra
45 reference(s)		 90-Commentaires_EnsembleMandelbrotQuaternion.01
45 reference(s)
91-infinity.01.vv
44 reference(s)		 92-MathematiquesPhysiqueFractales.22
44 reference(s)
93-LeParadoxeDeFermi.01.Fra
44 reference(s)		 94-Galerie_SignalProcessing.FV
44 reference(s)
95-Exposition_EcolePolytechnique_FeteDeLaScience_201910
44 reference(s)		 96-DieuScience.01.Fra
44 reference(s)
97-SI_ASSYS
43 reference(s)		 98-RemarquesCerveau.01
43 reference(s)
99-Polynomials_RationalNumbers.01.Fra
43 reference(s)		 100-infinity.02.vv
42 reference(s)
101-MathematiquesPhysiqueFractales.02.15
42 reference(s)		 102-ImagesEncadreesDisponibles.01
42 reference(s)
103-Fractal.03
42 reference(s)		 104-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_10
41 reference(s)
105-VirtualChaos.01.Fra
41 reference(s)		 106-VAcatalogue.11
41 reference(s)
107-Pcatalogue.11
41 reference(s)		 108-PatrimoineHumanite.02.Fra
41 reference(s)
109-OrdinateursEtCalculs.01.Fra
41 reference(s)		 110-MorePages.Ang.
41 reference(s)
111-Galerie_FluidMechanics.FV
41 reference(s)		 112-create.03.
40 reference(s)
113-catalogue.11
40 reference(s)		 114-EnsembleDesGaleries.DIAPO.1031
40 reference(s)
115-EnsembleDesGaleries.DIAPO.0087
40 reference(s)		 116-Commentaires_SurfaceDeBoy.01
40 reference(s)
117-Commentaires_DefinitionPseudoOctonions.01
40 reference(s)		 118-AvantPropos.01.Ang
40 reference(s)
119-ArtEtMathematiques.01
40 reference(s)		 120-Multivers.01.Fra
39 reference(s)
121-MOSA.LYAP.33.10000.20031207
39 reference(s)		 122-ImpossibleStructures.01.Ang
39 reference(s)
123-FaireDeLaRecherche.01.vv
39 reference(s)		 124-Commentaires_FluideInstationnaireBiDimensionnelIdeal.01
39 reference(s)
125-xiaf_____.nota.t.
38 reference(s)		 126-VisualisationRelief.01.vv.Fra
38 reference(s)
127-Polynomials_RationalNumbers.01.Ang
38 reference(s)		 128-MathematiquesModeleOutilArtiste.02.Ang
38 reference(s)

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Copyright © Jean-François COLONNA, 2022-2023.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2022-2023.