Monthly Best Of on 06/28/2022




The K-smooth integers on a Bidimensional Hilbert Curve -iteration 4-

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 06/28/2022 and last updated on 10/03/2024 17:04:32 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Table mountain
1-36 reference(s)		Artistic view of the prime numbers
2-30 reference(s)		The random walk of photons escaping the Sun
3-24 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
4-22 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
5-21 reference(s)		Waltzing Monument Valley (bird's-eye view)
6-20 reference(s)		Distorsion of the Menger Sponge -iteration 3-
7-20 reference(s)		Monument Valley at sunrise with light cloud dynamics -this sequence being periodical-
8-19 reference(s)
Sixteen interlaced fractal torus
9-19 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
10-19 reference(s)		Distorsion of the Bonan-Jeener-Klein double bottle
11-19 reference(s)		Happy new year 2000
12-18 reference(s)
Quaternionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-
13-17 reference(s)		Zoom in on mountains (with 3D clipping, bird's-eye view)
14-17 reference(s)		Distorsion of a sphere
15-16 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
16-16 reference(s)
Cauliflowers, seaweeds, shells,...
17-15 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
18-15 reference(s)		A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
19-15 reference(s)		A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
20-15 reference(s)
Untitled 0004
21-15 reference(s)		A dynamics of a random intertwining
22-15 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
23-14 reference(s)		A tridimensional field
24-14 reference(s)
Distorsion of a sphere
25-14 reference(s)		A perfect bidimensional piston with following initial conditions: still piston, high temperature particles at left and low temperature particles at right, in a bidimensional box submitted to a vertical field of gravity
26-14 reference(s)		Botticelli anomaly on the Moon
27-14 reference(s)		The foggy Babel Tower -a Tribute to Brueghel the Elder-
28-14 reference(s)
The Menger Sponge -iteration 5-
29-14 reference(s)		A fractal Möbius strip
30-14 reference(s)		Erosion of a bidimensional random (with small and large scale correlations)medium
31-14 reference(s)		Distorsion of the Bonan-Jeener-Klein double bottle
32-14 reference(s)
The Jeener-Klein triple bottle
33-14 reference(s)		The construction process of the von Koch curve -iteration 2: four equilateral triangles-
34-13 reference(s)		Along the border of the Mandelbrot set
35-13 reference(s)		Autostereogram with an hidden volcano
36-13 reference(s)
Untitled 0597
37-13 reference(s)		Dynamics of a bidimensional fractal structure
38-13 reference(s)		Earthquake with multifractal mountains
39-13 reference(s)		Erosion of a bidimensional random island
40-13 reference(s)
The Universe at the heart of a Calabi-Yau manifold
41-12 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
42-12 reference(s)		Autostereogram with an hidden volcano
43-12 reference(s)		The Road to Chaos -06/19/2022-
44-12 reference(s)
Tridimensional fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
45-12 reference(s)		A regular 7-gon -an heptagon-
46-12 reference(s)		A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 7-foil torus knot -iteration 3-
47-12 reference(s)		Untitled 0137 -'Jour de Lenteur', a Tribute to Yves Tanguy-
48-12 reference(s)
Quark and gluon structure of a nucleon
49-12 reference(s)		Distorsion of the Möbius strip
50-12 reference(s)		A tridimensional billiard starting with a Menger Sponge -iteration 2-
51-12 reference(s)		A pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-'the children round' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
52-12 reference(s)
The Lorenz attractor
53-12 reference(s)		Erosion of a bidimensional random (with large scale correlations)island
54-12 reference(s)		The Jeener-Klein triple bottle
55-12 reference(s)		Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
56-11 reference(s)
A tridimensional field
57-11 reference(s)		Autostereogram with an hidden ring and ghost bows
58-11 reference(s)		Tridimensional fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
59-11 reference(s)		The quaternionic fractal set obtained when computing the roots of Q^8=1 using Newton's method with translation along the third axis of the quaternionic space -tridimensional cross-section-
60-11 reference(s)
Pseudo Olympic Rings
61-11 reference(s)		The multiplicative persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-
62-11 reference(s)		Dynamics of archimedian mountains (bird's-eye view)
63-11 reference(s)		Animation of a sunrise on mountains
64-11 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)
65-11 reference(s)		Distorsion of the Möbius strip
66-11 reference(s)		Empty
67-11 reference(s)		Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
68-11 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
69-11 reference(s)		Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')with a 1/O conformal transformation in the pseudo-octonionic space -tridimensional cross-section-
70-11 reference(s)		A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
71-11 reference(s)		Tridimensional visualization of the Verhulst dynamics
72-11 reference(s)
Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
73-11 reference(s)		Bidimensional cross-sections inside a fractal structure
74-11 reference(s)		Erosion of a bidimensional random (with large scale correlations)island
75-11 reference(s)		Erosion of a bidimensional random (with small scale correlations)island
76-11 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
77-11 reference(s)		Distorsion of the Bonan-Jeener-Klein triple bottle
78-11 reference(s)		The Bonan-Jeener-Klein triple bottle
79-11 reference(s)		An aperiodic Penrose tiling of the Golden Decagon -a Tribute to Piet Mondrian and Roger Penrose-
80-10 reference(s)
A tridimensionally distorded aperiodic Penrose tiling of the plane
81-10 reference(s)		An aperiodic Penrose tiling of the plane
82-10 reference(s)		A tridimensional intertwining
83-10 reference(s)		Distorsion of a sphere
84-10 reference(s)
The random walk of photons escaping the Sun
85-10 reference(s)		The Sierpinski Carpet -iteration 3-
86-10 reference(s)		Tridimensional fractal aggregate obtained by means of a 50% pasting process during collisions of particles submitted to an attractive central field of gravity
87-10 reference(s)		A Tridimensional Hilbert-like Curve defined with {X2(...),Y2(...),Z2(...)} -iteration 2-
88-10 reference(s)
A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 5-foil torus knot -iteration 3-
89-10 reference(s)		Mountains and fog
90-10 reference(s)		Fractal synthesis of mountains with vegetation and stormy clouds
91-10 reference(s)		Earthquake (bird's-eye view)
92-10 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-
93-10 reference(s)		From Pluto to the Sun (non linear scales)
94-10 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-
95-10 reference(s)		Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
96-10 reference(s)
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
97-10 reference(s)		Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
98-10 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-
99-10 reference(s)		The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
100-10 reference(s)
Artistic view of 128 quaternionic Julia sets -tridimensional cross-sections-
101-10 reference(s)		Artistic view of a pyramidal Menger Sponge computed by means of an 'Iterated Function System' -IFS-
102-10 reference(s)		A pyramidal Menger Sponge computed by means of an 'Iterated Function System' -IFS-
103-10 reference(s)		Tridimensional Hilbert Curve -iteration 3-
104-10 reference(s)
Artistic view of a quadridimensional Calabi-Yau manifold
105-10 reference(s)		Quantum vacuum fluctuations
106-9 reference(s)		Artistic view of the Big Bang
107-9 reference(s)		The 64 first lines of the Pascal's Triangle -modulo 2-
108-9 reference(s)
Generation of the 63x63 first Conway's surreal complex numbers
109-9 reference(s)		Autostereogram with an hidden volcano
110-9 reference(s)		The 'hyperbolic tangent' of a sphere
111-9 reference(s)		The 'hyperbolic tangent' of a sphere
112-9 reference(s)
Victor Vasarely meets Piet Mondrian
113-9 reference(s)		Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
114-9 reference(s)		A Lissajous surface
115-9 reference(s)		Tridimensional fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
116-9 reference(s)
Rotation about the Y (vertical)axis of a tridimensional fractal aggregate that can also be viewed as a set of 4x3 pseudo-stereograms
117-9 reference(s)		Alien
118-9 reference(s)		The Borromean Rings
119-9 reference(s)		An interpolation between the quadruple Jeener bottle and the octuple Jeener bottle defined by means of three bidimensional fields
120-9 reference(s)
Fractal 'celestial body' based on a sphere with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
121-9 reference(s)		Sunny Monument Valley
122-9 reference(s)		Foggy Archimedes mountains
123-9 reference(s)		Mountains with slight linear structures and discontinuities (bird's-eye view)
124-9 reference(s)
The fractal Moon
125-9 reference(s)		Untitled 0155 -a Tribute to Yves Tanguy-
126-9 reference(s)		N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
127-9 reference(s)		Tridimensional Mondrian -a Tribute to Piet Mondrian-
128-9 reference(s)




2-The 128 most referenced Pages (*):

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



1-An2000.01.Fra
242 reference(s)		2-Galerie_GeneralitiesVisualization.FV
223 reference(s)
3-Galerie_ArtisticCreation.FV
176 reference(s)		4-Galerie_NumberTheory.FV
161 reference(s)
5-demo_14
144 reference(s)		6-Vcatalogue.11
136 reference(s)
7-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
125 reference(s)		8-MonodimensionalCellularAutomata.01.Ang
124 reference(s)
9-Galerie_CelestialMechanics.FV
118 reference(s)		10-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
118 reference(s)
11-Galerie_ParticleSystems.FV
117 reference(s)		12-Galerie_SelfPortraits.FV
110 reference(s)
13-Commentaires_DefinitionPseudoQuaternions.01
108 reference(s)		14-Galerie_DeterministicFractalGeometry.FV
103 reference(s)
15-Galerie_GeneralitiesVisualization.DIAPO.0101
101 reference(s)		16-AVirtualSpaceTimeTravelMachine.Ang
98 reference(s)
17-VirtualChaos.01.Fra
97 reference(s)		18-Fractal.01
95 reference(s)
19-Informations_GoodNewsAndBadNews.01.Fra
94 reference(s)		20-UlamSpiral.01.Fra
92 reference(s)
21-Galerie_ArtAndScience.FV
92 reference(s)		22-Galerie_TextureSynthesis.FV
91 reference(s)
23-Galerie_QuantumMechanics.FV
90 reference(s)		24-EntrelacsIntertwinings.01.Fra
89 reference(s)
25-MathematiquesPhysiqueFractales.12
88 reference(s)		26-AVirtualSpaceTimeTravelMachine.Fra
87 reference(s)
27-MorePages.Ang.
86 reference(s)		28-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
85 reference(s)
29-EntrelacsIntertwinings.01.Ang.DIAPO.0574
82 reference(s)		30-EntrelacsIntertwinings.01.Ang.DIAPO.0476
81 reference(s)
31-EntrelacsIntertwinings.01.Ang.DIAPO.0273
81 reference(s)		32-PatrimoineHumanite.02.Ang
80 reference(s)
33-GoldenTriangle.01.Fra
80 reference(s)		34-Fractal.11
79 reference(s)
35-EnsembleDesGaleries.DIAPO.0566
79 reference(s)		36-CompressionDeCompression_ComplexiteStructurelle.CDCM2_R.01
79 reference(s)
37-ArtScience.11.Ang.DIAPO.0023
79 reference(s)		38-SurfaceProjector.01.Fra
77 reference(s)
39-Galerie_ArtisticCreation.DIAPO.0010
77 reference(s)		40-EntrelacsIntertwinings.01.Ang.DIAPO.0189
77 reference(s)
41-EnsembleDesGaleries.DIAPO.0638
77 reference(s)		42-EnsembleDesGaleries.DIAPO.0189
77 reference(s)
43-LOG_xiMc.11
76 reference(s)		44-ExpV_VirE.01.Fra
76 reference(s)
45-EnsembleDesGaleries.DIAPO.0600
76 reference(s)		46-EnsembleDesGaleries.DIAPO.0413
76 reference(s)
47-Commentaires_Hyperboloide.01
76 reference(s)		48-Stereogrammes_AutoStereogrammes.01
75 reference(s)
49-FloatingPointNumbers.01.Fra
75 reference(s)		50-EntrelacsIntertwinings.01.Ang.DIAPO.0572
75 reference(s)
51-EntrelacsIntertwinings.01.Ang.DIAPO.0066
75 reference(s)		52-EntrelacsIntertwinings.01.Ang.DIAPO.0062
75 reference(s)
53-EnsembleDesGaleries.DIAPO.0564
75 reference(s)		54-DieuScience.01.Fra
75 reference(s)
55-Galerie_ArtAndScience.DIAPO.0003
74 reference(s)		56-EntrelacsIntertwinings.01.Ang.DIAPO.0469
74 reference(s)
57-EntrelacsIntertwinings.01.Ang.DIAPO.0195
74 reference(s)		58-EntrelacsIntertwinings.01.Ang.DIAPO.0186
74 reference(s)
59-AProposSite.01.Fra
74 reference(s)		60-help.
73 reference(s)
61-Galerie_SensitivityToRoundingOffErrors.FV
73 reference(s)		62-Galerie_GeneralitiesVisualization.DIAPO.0153
73 reference(s)
63-FloatingPointNumbers.01.Ang
73 reference(s)		64-EntrelacsIntertwinings.01.Ang.DIAPO.0202
73 reference(s)
65-EnsembleDesGaleries.DIAPO.0602
73 reference(s)		66-copyright.01.
72 reference(s)
67-Fractal.21
72 reference(s)		68-EntrelacsIntertwinings.01.Ang.DIAPO.0162
72 reference(s)
69-EntrelacsIntertwinings.01.Ang
72 reference(s)		70-OrdinateursEtCalculs.01.Ang
71 reference(s)
71-Galerie_BestOf.DIAPO.0021
71 reference(s)		72-EntrelacsIntertwinings.01.Ang.DIAPO.0455
71 reference(s)
73-EntrelacsIntertwinings.01.Ang.DIAPO.0188
71 reference(s)		74-EnsembleDesGaleries.DIAPO.0559
71 reference(s)
75-Commentaires_InterlacedEpicycloidalJeenerBottle.01
71 reference(s)		76-Autostereograms.01.
71 reference(s)
77-ArithmetiqueEtOrdinateur.01.vv.Fra
71 reference(s)		78-present.01.
70 reference(s)
79-SurfaceProjector.01.Ang
70 reference(s)		80-Galerie_Tributes.FV
70 reference(s)
81-Galerie_NewPictures
70 reference(s)		82-ExpV_VirE.11
70 reference(s)
83-EntrelacsIntertwinings.01.Ang.DIAPO.0327
70 reference(s)		84-EnsembleDesGaleries.DIAPO.0406
70 reference(s)
85-BEST.20070628
70 reference(s)		86-Galerie_SignalProcessing.FV
69 reference(s)
87-Galerie_DeterministicChaos.FV
69 reference(s)		88-EntrelacsIntertwinings.01.Ang.DIAPO.0435
69 reference(s)
89-EntrelacsIntertwinings.01.Ang.DIAPO.0366
69 reference(s)		90-EntrelacsIntertwinings.01.Ang.DIAPO.0307
69 reference(s)
91-EnsembleDesGaleries.DIAPO.0386
69 reference(s)		92-An2000.01.Ang
69 reference(s)
93-MonodimensionalCellularAutomata.01.Fra
68 reference(s)		94-GenieLogiciel_VisualisationScientifique.01.vv
68 reference(s)
95-GenieLogiciel.01.Fra
68 reference(s)		96-Galerie_NewPictures.FV
68 reference(s)
97-Galerie_ImagesDidactiques.FV
68 reference(s)		98-EntrelacsIntertwinings.01.Ang.DIAPO.0500
68 reference(s)
99-RemarquesCerveau.01
67 reference(s)		100-ManyChaos.01.Ang
67 reference(s)
101-EntrelacsIntertwinings.01.Ang.DIAPO.0081
67 reference(s)		102-ArtScience.11.Ang.DIAPO.0004
67 reference(s)
103-LeNoeudInfini.01.Fra
66 reference(s)		104-Galerie_AnthropomorphicPatterns.FV
66 reference(s)
105-EnsembleDesGaleries.DIAPO.0482
66 reference(s)		106-mail.01.vv
65 reference(s)
107-NatureDesMathematiques.01.vv.Fra
65 reference(s)		108-NDimensionalDeterministicFractalSets.01.Ang
65 reference(s)
109-FaireConnaitre_FaireAimer_LesMathematiques.01.Fra
65 reference(s)		110-EnsembleDesGaleries.DIAPO.1018
65 reference(s)
111-EnsembleDesGaleries.DIAPO.0045
64 reference(s)		112-infinity.01.vv.DIAPO
63 reference(s)
113-UlamSpiral.01.Ang
63 reference(s)		114-Kepler.02.
63 reference(s)
115-Galerie_Astrophysics.FV
63 reference(s)		116-Galerie_AnthropomorphicPatterns
63 reference(s)
117-Fractal.03
63 reference(s)		118-EnsembleDesGaleries.DIAPO.0242
63 reference(s)
119-EnsembleDesGaleries.DIAPO.0088
63 reference(s)		120-PatrimoineHumanite.02.Fra
62 reference(s)
121-EntrelacsIntertwinings.01.Ang.DIAPO.0420
62 reference(s)		122-EntrelacsIntertwinings.01.Ang.DIAPO.0246
62 reference(s)
123-EntrelacsIntertwinings.01.Ang.DIAPO.0158
62 reference(s)		124-EntrelacsIntertwinings.01.Ang.DIAPO.0100
62 reference(s)
125-EnsembleDesGaleries.DIAPO.0204
62 reference(s)		126-Commentaires_SystemeSolaire.01
62 reference(s)
127-NDimensionalDeterministicFractalSets.01.Fra
61 reference(s)		128-EntrelacsIntertwinings.01.Ang.DIAPO.0536
61 reference(s)

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Copyright © Jean-François COLONNA, 2022-2024.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2022-2024.