Monthly Best Of on 07/28/2021




Recursive intertwining

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

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(CMAP28 WWW site: this page was created on 07/28/2021 and last updated on 11/14/2023 17:50:11 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Tridimensional display of the Riemann Zeta function inside [-10.0,+20.0]x[-15.0,+15.0] (bird's-eye view)
1-47 reference(s)		 Untitled 0004
2-47 reference(s)		 The Universe at the heart of a Calabi-Yau manifold
3-43 reference(s)		 Dynamics of the even distribution of 6 points on a sphere -an Octahedron- by means of simulated annealing
4-43 reference(s)
Artistic view of the prime numbers
5-41 reference(s)		 The random walk of photons escaping the Sun
6-40 reference(s)		 Monument Valley at sunrise with light cloud dynamics -this sequence being periodical-
7-40 reference(s)		 The bidimensional John Conway's life game
8-40 reference(s)
Quaternionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-
9-40 reference(s)		 Tridimensional texture animation by means of the Generalized Product
10-39 reference(s)		 The Möbius strip
11-39 reference(s)		 Bidimensional geometrical texture animation
12-38 reference(s)
The 'exponential' spreading of a tridimensional epidemic -the COVID-19 coronavirus?- without confinement -1430 particles-, with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-
13-38 reference(s)		 The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- with partial confinement -201 particles-, with a zero death rate and a 50% infection, starting with just one infected person -red particle on bottom left picture-
14-38 reference(s)		 The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with a zero death rate and with a 50% infection, starting with just one infected person -red particle on bottom left picture-
15-38 reference(s)		 The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- with partial confinement -201 particles-, with a zero death rate and a 100% infection, starting with just one infected person -red particle on bottom left picture-
16-38 reference(s)
The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-
17-38 reference(s)		 Bidimensional quasi-symmetrical fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
18-38 reference(s)		 Tridimensional display of the particle density of a bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle
19-38 reference(s)		 A bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle
20-38 reference(s)
Bidimensional rectangular billiard with a central obstacle and an initial flow of rotating particles
21-38 reference(s)		 Dynamics of the even distribution of 24 points on a sphere by means of simulated annealing
22-38 reference(s)		 Bidimensional texture animation by means of the Generalized Product
23-38 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-
24-38 reference(s)
From Mars to the Sun
25-38 reference(s)		 Tridimensional zoom in on the Mandelbrot set
26-38 reference(s)		 Bidimensional zoom in on the Mandelbrot set with display of the arguments
27-38 reference(s)		 The front of a forest fire -white- obtained by means of a bidimensional random walk process (bird's-eye view, zoom in on the first steps)
28-38 reference(s)
Fractal diffusion front in a bidimensional medium obtained by means of a random walk process (zoom in on the first steps)
29-38 reference(s)		 Autostereogram with an hidden volcano
30-33 reference(s)		 A 4-cube -an hypercube-
31-33 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
32-27 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
33-27 reference(s)		 Quantum vacuum fluctuations
34-26 reference(s)		 64 elementary bidimensional binary cellular automata with 1 white starting central point
35-26 reference(s)		 Autostereogram with an hidden volcano
36-24 reference(s)
Pseudo Olympic Rings
37-23 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
38-23 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
39-22 reference(s)		 Ducks and friends
40-22 reference(s)
Black dots on a square lattice
41-22 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
42-22 reference(s)		 The Sierpinski carpet -iteration 1 to 5-
43-21 reference(s)		 'Le bouquet tout fait' -a Tribute to René Magritte and Sandro Botticelli-
44-20 reference(s)
The first four iterations of the construction of the von Koch snowflake
45-19 reference(s)		 Untitled 0374
46-19 reference(s)		 The generalized Ulam spiral displaying 100 numbers
47-18 reference(s)		 Autostereogram with an hidden volcano
48-17 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
49-17 reference(s)		 Untitled 0375
50-17 reference(s)		 A fractal vegetal structure
51-16 reference(s)		 A tridimensional distorted cubic mesh defined by means of three tridimensional fields
52-16 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
53-16 reference(s)		 Artistic view of a quadridimensional Calabi-Yau manifold
54-16 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
55-16 reference(s)		 Autostereogram with an hidden volcano
56-15 reference(s)
The random walk of photons escaping the Sun
57-15 reference(s)		 Fractal natural form
58-15 reference(s)		 A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
59-15 reference(s)		 Random quadrangulation of the volume of a sphere -18x18x18-
60-15 reference(s)
Tridimensional display of the generalized Ulam spiral displaying 4096 numbers
61-14 reference(s)		 Happy new year 2000
62-14 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
63-14 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
64-14 reference(s)
True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
65-13 reference(s)		 Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
66-13 reference(s)		 An Archimedes spiral displaying 100000 numbers
67-13 reference(s)		 True colors autostereogram of a fractal landscape
68-13 reference(s)
Untitled 0379
69-13 reference(s)		 Artistic view of the Big Bang
70-12 reference(s)		 Along the border of the Mandelbrot set
71-12 reference(s)		 4 evenly distributed points on a sphere -a Tetrahedron- by means of simulated annealing
72-12 reference(s)
Bidimensional cross-sections of the Klein bottle
73-12 reference(s)		 A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
74-12 reference(s)		 The Lorenz attractor
75-12 reference(s)		 Happy new year 2000
76-12 reference(s)
Anaglyph -blue=right, red=left- of a tridimensional filamentous fractal structure
77-12 reference(s)		 A fractal Möbius strip
78-12 reference(s)		 The CMAP logo
79-12 reference(s)		 The Bonan-Jeener-Klein triple bottle
80-12 reference(s)
A special Klein bottle
81-12 reference(s)		 The Klein bottle
82-12 reference(s)		 An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
83-12 reference(s)		 An aperiodic Penrose tiling of the plane
84-11 reference(s)
An aperiodic Penrose tiling of the plane
85-11 reference(s)		 Two multiplexed autostereograms by means of a pi/2 rotation
86-11 reference(s)		 Autostereogram with an hidden ring and ghost bows
87-11 reference(s)		 Untitled 0057
88-11 reference(s)
An interpolation between the quadruple Jeener bottle and the octuple Jeener bottle defined by means of three bidimensional fields
89-11 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System
90-11 reference(s)		 A half-random extended Menger sponge -iteration 5-
91-11 reference(s)		 Untitled 0377
92-11 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
93-11 reference(s)		 The Jeener-Klein triple bottle
94-11 reference(s)		 The Syracuse conjecture for U(0)={5,6,7,8,...,20} -tridimensional display-
95-10 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
96-10 reference(s)
The random walk of photons escaping the Sun
97-10 reference(s)		 The Sierpinski carpet -iteration 2-
98-10 reference(s)		 The generalized Ulam spiral
99-10 reference(s)		 Snowy multifractal mountains
100-10 reference(s)
Color palette 'magenta.21'
101-10 reference(s)		 The actual Solar System viewed during 243 years from a dark blue virtual planet -this last one approximately belongs to the plane of Pluto and its distance from the Sun equals the one of Mars-
102-10 reference(s)		 5-foil torus knots
103-10 reference(s)		 Jean-François COLONNA
104-10 reference(s)
The Goldbach conjecture -the Goldbach comet- for the even numbers from 6 to 6244
105-10 reference(s)		 A fractal-fractal tree
106-10 reference(s)		 Foggy seaboard
107-10 reference(s)		 Tridimensional display of the Riemann Zeta function inside [+0.1,+0.9]x[0,+50]
108-9 reference(s)
Quantum vacuum fluctuations
109-9 reference(s)		 An aperiodic Penrose tiling of the plane
110-9 reference(s)		 A fractal vegetal structure -'the Knowledge Tree'-
111-9 reference(s)		 The self-similarity of a perfect bidimensional fractal tree
112-9 reference(s)
A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
113-9 reference(s)		 Autostereogram of 8 color-multiplexed quaternionic Julia sets -tridimensional cross-sections-
114-9 reference(s)		 Artistic view of the quaternionic fractal set obtained when computing the roots of Q^3=1 using Newton's method with translation along the third axis of the quaternionic space -tridimensional cross-section-
115-9 reference(s)		 The Ulam spiral
116-9 reference(s)
Botticelli anomaly on the Moon
117-9 reference(s)		 The Simpson paradox
118-9 reference(s)		 Synthetic picture mosaic with random points
119-9 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Pluto point of view-
120-9 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Sun point of view-
121-9 reference(s)		 An amazing cross-section inside the Menger sponge -iteration 5-
122-9 reference(s)		 Anaglyph -blue=right, red=left- of a close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
123-9 reference(s)		 Untitled 0376
124-9 reference(s)
Tridimensional display of the inflationary Universe
125-9 reference(s)		 Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
126-9 reference(s)		 Isle of the Dead -a Tribute to Arnold Böcklin-
127-9 reference(s)		 A 'bidimensional epicycloïdal' pseudo-torus
128-9 reference(s)




2-The 128 most referenced Pages (*):

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



1-demo_14
1118 reference(s)		 2-AVirtualSpaceTimeTravelMachine.Ang
427 reference(s)
3-An2000.01.Fra
357 reference(s)		 4-Galerie_NumberTheory.FV
317 reference(s)
5-help.
261 reference(s)		 6-Vcatalogue.11
261 reference(s)
7-Stereogrammes_AutoStereogrammes.01
252 reference(s)		 8-mail.01.vv
238 reference(s)
9-Galerie_GeneralitiesVisualization.FV
224 reference(s)		 10-Galerie_ArtisticCreation.FV
218 reference(s)
11-Galerie_ArtAndScience.FV
208 reference(s)		 12-RealNumbers.01.Fra
204 reference(s)
13-LOG_xiMc.11
198 reference(s)		 14-Fractal.01
198 reference(s)
15-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
197 reference(s)		 16-Galerie_ParticleSystems.FV
193 reference(s)
17-Fractal.21
188 reference(s)		 18-FloatingPointNumbers.01.Ang
186 reference(s)
19-FloatingPointNumbers.01.Fra
182 reference(s)		 20-Galerie_DeterministicFractalGeometry.FV
181 reference(s)
21-EntrelacsIntertwinings.01.Ang
180 reference(s)		 22-SurfaceProjector.01.Fra
175 reference(s)
23-logiciel
172 reference(s)		 24-demo
172 reference(s)
25-demo14
171 reference(s)		 26-demo.14
171 reference(s)
27-an2000
171 reference(s)		 28-nombresreels
169 reference(s)
29-copyright.01.
169 reference(s)		 30-realnumbers
168 reference(s)
31-genielogiciel
168 reference(s)		 32-SurfaceProjector.01.Ang
167 reference(s)
33-Galerie_NewPictures.FV
167 reference(s)		 34-Galerie_CelestialMechanics.FV
167 reference(s)
35-EntrelacsIntertwinings.01.Fra
167 reference(s)		 36-AVirtualSpaceTimeTravelMachine.Fra
166 reference(s)
37-AProposSite.01.Fra
165 reference(s)		 38-GoldenTriangle.01.Fra
161 reference(s)
39-Galerie_QuantumMechanics.FV
159 reference(s)		 40-AnimFractal.01.
158 reference(s)
41-MonodimensionalCellularAutomata.01.Ang
156 reference(s)		 42-Fractal.11
156 reference(s)
43-ImpossibleStructures.01.Fra
153 reference(s)		 44-ImpossibleStructures.01.Ang
152 reference(s)
45-VirtualChaos.01.Fra
149 reference(s)		 46-MorePages.
149 reference(s)
47-MathematiquesPhysiqueFractales.02
147 reference(s)		 48-Galerie_TextureSynthesis.FV
145 reference(s)
49-UlamSpiral.01.Fra
143 reference(s)		 50-Informations_AboutPicturesAnimationsAndFiles.01.Ang
143 reference(s)
51-NDimensionalDeterministicFractalSets.01.Ang
142 reference(s)		 52-Galerie_ImagesDesMathematiques.FV
142 reference(s)
53-Informations_GoodNewsAndBadNews.01.Fra
140 reference(s)		 54-BEST.20140828
140 reference(s)
55-GenieLogiciel.01.Fra
138 reference(s)		 56-ExpV_VirE.11
138 reference(s)
57-Commentaires_EnsembleJuliaOctonion.01
138 reference(s)		 58-ImagesDuVirtuel.01.Fra.FV
137 reference(s)
59-GenieLogiciel_VisualisationScientifique.01.vv
137 reference(s)		 60-Galerie_Tributes.FV
137 reference(s)
61-Galerie_SignalProcessing.FV
137 reference(s)		 62-Informations_GoodNewsAndBadNews.01.Ang
136 reference(s)
63-Galerie_ParticleSystems
136 reference(s)		 64-HommageBenoitMandelbrot.21
135 reference(s)
65-Galerie_AnthropomorphicPatterns.FV
134 reference(s)		 66-Galerie_SensitivityToRoundingOffErrors.FV
133 reference(s)
67-NDimensionalDeterministicFractalSets.01.Fra
132 reference(s)		 68-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
132 reference(s)
69-MonodimensionalCellularAutomata.01.Fra
132 reference(s)		 70-Kepler.02.
132 reference(s)
71-Autostereograms.01.
132 reference(s)		 72-catalogue.11
131 reference(s)
73-NatureDesMathematiques.01.vv.Fra
131 reference(s)		 74-ImagesDuVirtuel.01.Fra
131 reference(s)
75-MOSA.LYAP.33.10000.20031207
130 reference(s)		 76-ExpV_VirE.Ang
130 reference(s)
77-BEST.20110128
130 reference(s)		 78-PatrimoineHumanite.02.Fra
129 reference(s)
79-OrdinateurMathematiquesArt.01.Fra
129 reference(s)		 80-LeParadoxeDeFermi.01.Fra
129 reference(s)
81-Galerie_DeterministicChaos.FV
129 reference(s)		 82-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
129 reference(s)
83-CompressionDeCompression_ComplexiteStructurelle.CDCM2_CDC_D__CDC_E.01
129 reference(s)		 84-Galerie_NewPictures
128 reference(s)
85-MathematiquesPhysiqueFractales.12
127 reference(s)		 86-Galerie_ImagesDidactiques.FV
127 reference(s)
87-Galerie_BestOf.FV
127 reference(s)		 88-Galerie_Astrophysics.FV
127 reference(s)
89-MathematiquesPhysiqueFractales.02.26
126 reference(s)		 90-Exposition_EcolePolytechnique_FeteDeLaScience_201910
126 reference(s)
91-Web_Mail.01.vv
125 reference(s)		 92-FaireDeLaRecherche.01.vv
125 reference(s)
93-EnsembleDesGaleries.DIAPO.0012
125 reference(s)		 94-GoldenTriangle.01.Ang
124 reference(s)
95-Exposition_MairieCinquiemeArrondissementParis_202001_202002
124 reference(s)		 96-DieuScience.01.Fra
124 reference(s)
97-UlamSpiral.01.Ang
123 reference(s)		 98-subject.01.
122 reference(s)
99-SourceExemple_____xrq_____hydrogene.61.K.
122 reference(s)		 100-MathematiquesPhysiqueFractales.02.27
122 reference(s)
101-LeParadoxeDeFermi.01.Ang
122 reference(s)		 102-Fractal.03
122 reference(s)
103-ExpV_VirE.21
122 reference(s)		 104-Commentaires_DefinitionQuaternions.01
122 reference(s)
105-BEST.20170928
122 reference(s)		 106-BEST.20130528
122 reference(s)
107-xrC_____OBJC.RB___1_______.11.PlansDeBits.t.
121 reference(s)		 108-present.01.
121 reference(s)
109-infinity.01.vv
121 reference(s)		 110-VirtualChaos.01.Ang
121 reference(s)
111-PerteDeLAssociativite.01.ADD3
121 reference(s)		 112-PerteDeLAssociativite.01
121 reference(s)
113-OrdinateursEtCalculs.01.Ang
121 reference(s)		 114-LesApprentisDieux.01
121 reference(s)
115-DieuScience.01.Ang
121 reference(s)		 116-Commentaires_DefinitionPseudoQuaternions.01
121 reference(s)
117-Galerie_ArtisticCreation
120 reference(s)		 118-An2000.01.Ang
120 reference(s)
119-HommageBenoitMandelbrot.11
119 reference(s)		 120-Galerie_DeterministicFractalGeometry
119 reference(s)
121-Spheres.01
118 reference(s)		 122-MathematiquesPhysiqueFractales.22
118 reference(s)
123-Commentaires_DefinitionComplexes.01
118 reference(s)		 124-IllusionConnaissance.02
117 reference(s)
125-DecimalesPi_1_100.vv
117 reference(s)		 126-ArtEtMathematiques.01
117 reference(s)
127-Pcatalogue.11
116 reference(s)		 128-Galerie_SalonDAutomne.FV
116 reference(s)

And now, enjoy visiting A Virtual Space-Time Travel Machine.




Copyright © Jean-François COLONNA, 2021-2023.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2021-2023.