Monthly Best Of on 09/28/2022




A random bidimensional fractal tree and the self-similarity

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 09/28/2022 and last updated on 11/14/2023 17:50:29 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Intertwining
1-176 reference(s)		 Artistic view of the prime numbers
2-137 reference(s)		 Coalescence of 40832 particles -black holes?- inside a tridimensional parallelepipedic billiard
3-94 reference(s)		 The smooth integers
4-86 reference(s)
The random walk of photons escaping the Sun
5-81 reference(s)		 An arbitrary surface (Jeener surface 2)in motion
6-79 reference(s)		 Autostereogram with an hidden volcano
7-77 reference(s)		 The Satanic Verses -a Tribute to Salman Rushdie-
8-74 reference(s)
A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
9-73 reference(s)		 Autostereogram with an hidden ring and ghost bows
10-73 reference(s)		 Happy new year 2000
11-67 reference(s)		 The generalized Ulam spiral
12-66 reference(s)
Untitled 0604 -a Tribute to Yves Klein-
13-65 reference(s)		 A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
14-63 reference(s)		 The Jeener-Klein triple bottle
15-61 reference(s)		 The smooth integers: the prime factor product -the radical function- of the integer numbers
16-60 reference(s)
The Sierpinski carpet -iteration 1 to 5-
17-59 reference(s)		 Bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity
18-59 reference(s)		 A tridimensional fractal manifold defined by means of three tridimensional fields
19-59 reference(s)		 Untitled 0599 -a Tribute to Robert & Sonia Delaunay-
20-59 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
21-58 reference(s)		 Distorsion of the Bonan-Jeener-Klein double bottle
22-57 reference(s)		 The 'tangent' of a sphere
23-56 reference(s)		 A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
24-56 reference(s)
Jean-François COLONNA (on 11/17/1994)with its fractal mountains
25-56 reference(s)		 Sixteen interlaced fractal torus
26-55 reference(s)		 Intertwining based on the geometry of the Lorenz attractor
27-55 reference(s)		 Untitled 0602 -a Tribute to Jean-Michel Atlan-
28-55 reference(s)
Bidimensional display of 31 Rational Numbers by means of the Stern-Brocot Tree
29-54 reference(s)		 The Road to Chaos -06/19/2022-
30-54 reference(s)		 A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
31-54 reference(s)		 A pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
32-54 reference(s)
The Universe at the heart of a Calabi-Yau manifold
33-53 reference(s)		 Pseudo Olympic Rings
34-53 reference(s)		 Monument Valley at sunrise
35-53 reference(s)		 A tridimensional billiard starting with a Menger sponge -iteration 2-
36-53 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
37-53 reference(s)		 Distorsion of a sphere
38-52 reference(s)		 Bidimensional display of 255 Rational Numbers by means of the Stern-Brocot Tree
39-51 reference(s)		 The Road to Chaos -06/19/2022-
40-51 reference(s)
Cloudy Monument Valley
41-51 reference(s)		 The Menger sponge -iteration 5-
42-51 reference(s)		 Self-Portrait -'This is not an apple', a Tribute to René Magritte-
43-51 reference(s)		 Psychedelic hypercube
44-51 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
45-51 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-
46-50 reference(s)		 Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
47-50 reference(s)		 Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
48-50 reference(s)
The Lorenz attractor
49-50 reference(s)		 An aperiodic Penrose tiling of the plane
50-49 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
51-49 reference(s)		 Tridimensional fractal Self-Portrait
52-49 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
53-48 reference(s)		 Untitled 0597
54-48 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
55-48 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
56-47 reference(s)
24 evenly distributed points on a sphere by means of simulated annealing
57-47 reference(s)		 Fractal Self-Portrait -'Décalcomanie', a Tribute to René Magritte-
58-47 reference(s)		 The Radical of the integer numbers from 2 to 257
59-47 reference(s)		 The smooth integers: the prime factor product -the radical function- of the integer numbers
60-46 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
61-46 reference(s)		 The first four iterations of the construction of the von Koch snowflake
62-45 reference(s)		 The 'hyperbolic tangent' of a sphere
63-45 reference(s)		 The Sierpinski carpet -iteration 2-
64-45 reference(s)
Quark and gluon structure of a nucleon
65-45 reference(s)		 The Birth of the Universe
66-45 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
67-45 reference(s)		 Distorsion of a sphere
68-44 reference(s)
The generalized Ulam spiral displaying 100 numbers
69-44 reference(s)		 The foggy Babel Tower -a Tribute to Brueghel the Elder-
70-44 reference(s)		 The 126.646 first digits -base 6- of 'pi' displayed as an 'absolute' tridimensional random walk
71-44 reference(s)		 Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
72-44 reference(s)
Black dots on a square lattice
73-44 reference(s)		 A shell (Jeener surface 1)
74-44 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
75-44 reference(s)		 Distorsion of the Bonan-Jeener-Klein double bottle
76-44 reference(s)
Untitled 0600 -a Tribute to Jean Arp-
77-44 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
78-43 reference(s)		 An aperiodic Penrose tiling of the plane
79-43 reference(s)		 Tridimensional display of the particle density of a bidimensional snowflake-like billiard
80-43 reference(s)
Bidimensional abstract texture with random anthropomorphic patterns
81-43 reference(s)		 Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
82-43 reference(s)		 The Lorenz attractor
83-43 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
84-43 reference(s)
Distorsion of the Bonan-Jeener-Klein triple bottle
85-43 reference(s)		 The 'tangent' of a sphere
86-42 reference(s)		 Dynamics of the even distribution of 24 points on a sphere by means of simulated annealing
87-42 reference(s)		 The generalized Ulam spiral displaying 1024 numbers
88-42 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)
89-42 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-
90-42 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
91-42 reference(s)		 Artistic view of the Big Bang
92-41 reference(s)
The 'hyperbolic tangent' of a sphere
93-41 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
94-41 reference(s)		 8 evenly distributed points on a sphere by means of simulated annealing
95-41 reference(s)		 Distorsion of the Möbius strip
96-41 reference(s)
An amazing cross-section inside the Menger sponge -iteration 5-
97-41 reference(s)		 The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
98-41 reference(s)		 Fractal Self-Portrait -a Tribute to René Magritte-
99-41 reference(s)		 Tridimensional fractal structure
100-41 reference(s)
Along the border of the Mandelbrot set
101-40 reference(s)		 Generation of the 63x63 first Conway's surreal complex numbers
102-40 reference(s)		 A tridimensional field made of an amazing cross-section inside the Menger sponge -iteration 5-
103-40 reference(s)		 Intertwining
104-40 reference(s)
Monument Valley at sunrise
105-40 reference(s)		 The same bidimensional scalar field displayed with 4 different color palettes
106-40 reference(s)		 Untitled 0596
107-40 reference(s)		 Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
108-40 reference(s)
Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
109-40 reference(s)		 1-foil torus knot -obvious knot- on its torus and its asociated Möbius strip
110-40 reference(s)		 Fractal 7-foil torus knot
111-40 reference(s)		 A gradient of 114299 particles obtains by means of a tridimensional diffusion process
112-40 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
113-40 reference(s)		 Autostereogram with an hidden volcano
114-39 reference(s)		 Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier-
115-39 reference(s)		 Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
116-39 reference(s)
Mountains at sunrise
117-39 reference(s)		 Distorsion of the Möbius strip
118-39 reference(s)		 Distorsion of the Menger sponge -iteration 3-
119-39 reference(s)		 Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
120-39 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) -tridimensional cross-section-
121-39 reference(s)		 Hypercube
122-39 reference(s)		 The Goldbach conjecture -the Goldbach comet- for the even numbers from 6 to 6244
123-39 reference(s)		 Tridimensional fractal Self-Portrait
124-39 reference(s)
A shell (Jeener surface 1)in motion
125-39 reference(s)		 A cylinder -a bidimensional manifold-
126-39 reference(s)		 The Klein bottle
127-39 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
128-38 reference(s)




2-The 128 most referenced Pages (*):

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



1-demo_14
135 reference(s)		 2-Galerie_NumberTheory.FV
123 reference(s)
3-Informations_GoodNewsAndBadNews.01.Ang
114 reference(s)		 4-Galerie_GeneralitiesVisualization
114 reference(s)
5-Vcatalogue.11
110 reference(s)		 6-AVirtualSpaceTimeTravelMachine.Ang
109 reference(s)
7-An2000.01.Fra
108 reference(s)		 8-Galerie_GeneralitiesVisualization.FV
102 reference(s)
9-AVirtualSpaceTimeTravelMachine.Fra
99 reference(s)		 10-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
96 reference(s)
11-EntrelacsIntertwinings.01.Fra
91 reference(s)		 12-EntrelacsIntertwinings.01.Ang
90 reference(s)
13-Galerie_ArtisticCreation.FV
89 reference(s)		 14-Galerie_ImagesDesMathematiques.FV
87 reference(s)
15-DuModeleALImage.02.Fra
83 reference(s)		 16-help.
79 reference(s)
17-ImpossibleStructures.01.Fra
77 reference(s)		 18-ImagesDuVirtuel.01.Fra.FV
70 reference(s)
19-MOSA.LYAP.33.10000.20031207
68 reference(s)		 20-Informations_GoodNewsAndBadNews.01.Fra
68 reference(s)
21-Galerie_ParticleSystems.FV
68 reference(s)		 22-FaireDeLaRecherche.01.vv
67 reference(s)
23-Galerie_NewPictures.FV
64 reference(s)		 24-infinity.01.vv
63 reference(s)
25-Galerie_CelestialMechanics.FV
63 reference(s)		 26-Fractal.01
63 reference(s)
27-subject.01.
62 reference(s)		 28-OrdinateursEtCalculs.01.Ang
62 reference(s)
29-Galerie_NewPictures
61 reference(s)		 30-Galerie_ArtAndScience.FV
58 reference(s)
31-MonodimensionalCellularAutomata.01.Fra
56 reference(s)		 32-MathematiquesPhysiqueFractales.01
55 reference(s)
33-Galerie_SelfPortraits.FV
55 reference(s)		 34-Galerie_DeterministicFractalGeometry.FV
54 reference(s)
35-AProposSite.01.Fra
54 reference(s)		 36-Galerie_TextureSynthesis.FV
52 reference(s)
37-galerie_numbertheory.fv
51 reference(s)		 38-Commentaires_Hyperboloide.01
51 reference(s)
39-Stereogrammes_AutoStereogrammes.01
49 reference(s)		 40-Galerie_DeterministicFractalGeometry.DIAPO.0032
49 reference(s)
41-ArtScience.11.Ang.DIAPO.0023
49 reference(s)		 42-UlamSpiral.01.Fra
48 reference(s)
43-EnsembleDesGaleries.DIAPO.0529
48 reference(s)		 44-Commentaires_NoeudTrefle.01
48 reference(s)
45-LOG_xiMc.11
47 reference(s)		 46-EntrelacsIntertwinings.01.Ang.DIAPO.0273
46 reference(s)
47-BEST.20090728
46 reference(s)		 48-Commentaires_InterlacedEpicycloidalJeenerBottle.01
45 reference(s)
49-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_1
44 reference(s)		 50-GoldenTriangle.01.Fra
44 reference(s)
51-CompressionDeCompression_ComplexiteStructurelle.JPEG2000_ZL.01
44 reference(s)		 52-IllusionConnaissance.01
43 reference(s)
53-HommageBenoitMandelbrot.11
43 reference(s)		 54-GenieLogiciel_VisualisationScientifique.01.vv
43 reference(s)
55-Galerie_ImagesDidactiques.FV
43 reference(s)		 56-mail.01.vv
42 reference(s)
57-NDimensionalDeterministicFractalSets.01.Fra
42 reference(s)		 58-IllusionConnaissance.02
42 reference(s)
59-EnsembleDesGaleries.DIAPO.0393
42 reference(s)		 60-copyright.01.
41 reference(s)
61-Polynomials_RationalNumbers.01.Fra
41 reference(s)		 62-Galerie_Tributes.FV
41 reference(s)
63-EntrelacsIntertwinings.01.Ang.DIAPO.0446
41 reference(s)		 64-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
41 reference(s)
65-CompressionDeCompression_ComplexiteStructurelle.CDC_D__CDC_E.01
41 reference(s)		 66-SurfaceProjector.01.Fra
40 reference(s)
67-Galerie_DeterministicChaos.FV
40 reference(s)		 68-NatureDesMathematiques.01.vv.Fra
39 reference(s)
69-Galerie_QuantumMechanics.FV
39 reference(s)		 70-FloatingPointNumbers.01.Fra
39 reference(s)
71-Autostereograms.01.
39 reference(s)		 72-Web_Mail.01.vv
38 reference(s)
73-Fractal.11
38 reference(s)		 74-FloatingPointNumbers.01.Ang
38 reference(s)
75-SurfaceProjector.01.Ang
37 reference(s)		 76-PerteDeLAssociativite.01
37 reference(s)
77-MorePages.Ang.
37 reference(s)		 78-Galerie_FluidMechanics.FV
37 reference(s)
79-Galerie_Astrophysics.FV
37 reference(s)		 80-MonodimensionalCellularAutomata.01.Ang
36 reference(s)
81-MathematiquesPhysiqueFractales.02
36 reference(s)		 82-ExpV_VirE.11
36 reference(s)
83-EntrelacsIntertwinings.01.Ang.DIAPO.0250
36 reference(s)		 84-EnsembleDesGaleries.DIAPO.0637
36 reference(s)
85-Informations_AboutPicturesAnimationsAndFiles.01.Ang
35 reference(s)		 86-GoldenTriangle.01.Ang
35 reference(s)
87-Galerie_SensitivityToRoundingOffErrors.FV
35 reference(s)		 88-AnimFractal.01.
35 reference(s)
89-infinity.02.vv
34 reference(s)		 90-galerie_artisticcreation.fv
34 reference(s)
91-Pcatalogue.11
34 reference(s)		 92-NDimensionalDeterministicFractalSets.01.Ang
34 reference(s)
93-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
34 reference(s)		 94-Fractal.21
34 reference(s)
95-BEST.20151228
34 reference(s)		 96-galerie_nondeterministicfractalgeometrynaturalphenomenonsynthesis.fv
33 reference(s)
97-catalogue.11
33 reference(s)		 98-DecimalesPi_1_100.vv
33 reference(s)
99-ArtScience.01
33 reference(s)		 100-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_10
32 reference(s)
101-UlamSpiral.01.Ang
32 reference(s)		 102-Multivers.01.Fra
32 reference(s)
103-ManyChaos.01.Ang
32 reference(s)		 104-LeNoeudInfini.01.Ang
32 reference(s)
105-Kepler.02.
32 reference(s)		 106-Informations_AboutPicturesAnimationsAndFiles.01.Fra
32 reference(s)
107-Exposition_EcolePolytechnique_FeteDeLaScience_201910
32 reference(s)		 108-EntrelacsIntertwinings.01.Ang.DIAPO.0011
32 reference(s)
109-EnsembleDesGaleries.DIAPO.1146
32 reference(s)		 110-Commentaires_DefinitionPseudoOctonions.01
32 reference(s)
111-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_12
31 reference(s)		 112-present.01.
31 reference(s)
113-galerie_particlesystems.fv
31 reference(s)		 114-RealNumbers.01.Fra
31 reference(s)
115-LeParadoxeDeFermi.01.Fra
31 reference(s)		 116-Galerie_SignalProcessing.FV
31 reference(s)
117-ConjectureDeSyracuse_0256.vv
31 reference(s)		 118-CompressionDeCompression_ComplexiteStructurelle.ZL.01
31 reference(s)
119-xDarchivesG__SMC__sources__utilitaires_____SI_ASSYS
30 reference(s)		 120-galerie_generalitiesvisualization.fv
30 reference(s)
121-VAcatalogue.11
30 reference(s)		 122-OrdinateurMathematiquesArt.01.Fra
30 reference(s)
123-NombresPremiers_10000.vv
30 reference(s)		 124-NombresEtLumiere.01.vv.Fra
30 reference(s)
125-LeNoeudInfini.01.Fra
30 reference(s)		 126-ImpossibleStructures.01.Ang
30 reference(s)
127-Commentaires_NKleinBottle.01
30 reference(s)		 128-OrdinateursEtCalculs.01.Fra
29 reference(s)

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




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