Monthly Best Of on 07/28/2023




A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,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 07/28/2023 and last updated on 11/14/2023 17:50:40 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Artistic view of the prime numbers
1-105 reference(s)		 A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
2-102 reference(s)		 A Ball described by means of an 'open' 3-foil torus knot -iteration 4-
3-79 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
4-70 reference(s)
Jean-François COLONNA (on 11/17/1994)with its fractal mountains
5-69 reference(s)		 The random walk of photons escaping the Sun
6-67 reference(s)		 The Klein bottle described by means of a Bidimensional non continous Hilbert-like Curve -iteration 5-
7-65 reference(s)		 The Sierpinski carpet -iteration 1 to 5-
8-64 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
9-64 reference(s)		 A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
10-63 reference(s)		 The generalized Ulam spiral
11-63 reference(s)		 The Bonan-Jeener-Klein triple bottle
12-63 reference(s)
Autostereogram of the CMAP
13-62 reference(s)		 The Ulam spiral displaying 2025 numbers
14-62 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
15-60 reference(s)		 Happy new year 2000
16-60 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
17-59 reference(s)		 The Universe at the heart of a Calabi-Yau manifold
18-58 reference(s)		 A Ball described by means of a Tridimensional Hilbert Curve -iteration 4-
19-58 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Pluto point of view-
20-57 reference(s)
From Pluto to the Sun (non linear scales)
21-56 reference(s)		 The Piet Mondrian quadridimensional Calabi-Yau manifold -2D, 3D or 4D?-
22-56 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
23-56 reference(s)		 A Tridimensional Hilbert-like Curve defined with {X2(...),Y2(...),Z2(...)} -iteration 2-
24-55 reference(s)
Fractal Self-Portrait -a Tribute to René Magritte-
25-54 reference(s)		 64 elementary bidimensional binary cellular automata with 1 white starting central point
26-54 reference(s)		 Universe or Multiverse -The fractal Universe-?
27-53 reference(s)		 A Ball described by means of a Tridimensional Hilbert-like Curve -iteration 4-
28-53 reference(s)
The Goldbach conjecture
29-53 reference(s)		 The Syracuse conjecture for U(0)={5,10,15,20,...,1310720}
30-51 reference(s)		 Two multiplexed autostereograms by means of a pi/2 rotation
31-51 reference(s)		 Quark and gluon structure of a nucleon
32-51 reference(s)
Untitled 0613
33-50 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
34-50 reference(s)		 Autostereogram with an hidden ring and ghost bows
35-50 reference(s)		 Iterations in the complex plane: the computation of the Mandelbrot set
36-50 reference(s)
A one sheet hyperboloid of revolution -negative curvature-
37-49 reference(s)		 An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
38-49 reference(s)		 The Sierpinski carpet -iteration 3-
39-48 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
40-47 reference(s)
Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
41-47 reference(s)		 The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
42-47 reference(s)		 The Piet Mondrian Hypercube -2D, 3D or 4D?-
43-47 reference(s)		 The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 7-
44-47 reference(s)
Along the border of the Mandelbrot set
45-46 reference(s)		 The journey of an Earth-like virtuel planet (green)in the Solar System -point of view of the virtual planet-
46-46 reference(s)		 Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
47-46 reference(s)		 The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 5-
48-46 reference(s)
Tridimensional representation of an hexadecadimensional Calabi-Yau manifold with pseudo-random projection
49-46 reference(s)		 Untitled 0611
50-46 reference(s)		 Tridimensional representation of an octodimensional Calabi-Yau manifold with pseudo-random projection
51-46 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
52-46 reference(s)
A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to the Mandelbrot set border -iteration 5-
53-45 reference(s)		 Bidimensional zoom in on the Mandelbrot set
54-45 reference(s)		 The Lorenz attractor
55-45 reference(s)		 Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
56-44 reference(s)
From Pluto to the Sun -extrapolation 2-
57-44 reference(s)		 A Ball described by means of an hypercube -iteration 4-
58-44 reference(s)		 The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 6-
59-44 reference(s)		 Untitled 0610
60-44 reference(s)
An aperiodic Penrose tiling of the plane
61-43 reference(s)		 Botticelli anomaly on the Moon
62-43 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-
63-43 reference(s)		 A distorded -for the sake of display- 5-cube -an hyperhypercube-
64-43 reference(s)
Bidimensional brownian motion
65-43 reference(s)		 Untitled 0127
66-42 reference(s)		 The Continuum Hypothesis (CH)
67-42 reference(s)		 The abelian -commutative- group defined on elliptic curves
68-42 reference(s)
Tridimensional visualization of the ABC conjecture
69-42 reference(s)		 Autostereogram with an hidden volcano
70-41 reference(s)		 Autostereogram with an hidden volcano
71-41 reference(s)		 The 1.000 first digits -base 10- of 'pi' displayed on a circle -very bad point of view-
72-41 reference(s)
Empty
73-41 reference(s)		 Autostereogram with an hidden volcano and 64 self-portraits
74-41 reference(s)		 Hypercube
75-41 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
76-41 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
77-41 reference(s)		 The ABC conjecture
78-41 reference(s)		 Artistic view of the Big Bang
79-40 reference(s)		 The Boy surface in motion
80-40 reference(s)
An octogonal tiling of the hyperbolic Poincaré disk -iteration 5-
81-40 reference(s)		 Sunny Monument Valley
82-40 reference(s)		 The foggy Babel Tower -a Tribute to Brueghel the Elder-
83-40 reference(s)		 The Node, The Garden of Rama -a Tribute to Arthur C. Clarke and Gentry Lee-
84-40 reference(s)
From Pluto to the Sun -extrapolation 2-
85-40 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)
86-40 reference(s)		 An amazing cross-section inside the Menger sponge -iteration 5-
87-40 reference(s)		 Untitled 0612
88-40 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
89-40 reference(s)		 Bidimensional Hilbert Curve -iteration 5-
90-40 reference(s)		 The first four iterations of the construction of the von Koch snowflake
91-39 reference(s)		 The 'sharp' Golden Triangle
92-39 reference(s)
The Ulam spiral with display of the first twin prime numbers ('2-twin' prime numbers)
93-39 reference(s)		 The 126.646 first digits -base 6- of 'pi' displayed as an 'absolute' tridimensional random walk
94-39 reference(s)		 A cylinder -a bidimensional manifold-
95-39 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
96-39 reference(s)
The 64 first lines of the Pascal's Triangle
97-38 reference(s)		 From 'geocentrism' to 'heliocentrism'
98-38 reference(s)		 A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
99-38 reference(s)		 Some elementary symbols used to built labyrinths -with a big black ghost structure at pi/4-
100-38 reference(s)
Jean-François COLONNA
101-38 reference(s)		 Definition of a tangent -yellow- by means of a secant -orange-
102-38 reference(s)		 The random walk of photons escaping the Sun
103-37 reference(s)		 Fractal diffusion front in a bidimensional medium obtained by means of identical interacting particles
104-37 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-
105-37 reference(s)		 From Pluto to the Sun -extrapolation 2- (non linear scales)
106-37 reference(s)		 The Menger sponge -iteration 5-
107-37 reference(s)		 The 'S' elementary symbol used to built labyrinths
108-37 reference(s)
Cantor's diagonal argument
109-37 reference(s)		 The 288.982 first digits of the 'prime' Champernowne number (=0.2 3 5 7 11 13 17 19 23 29...)displayed as an 'absolute' bidimensional random walk using the square root of the distance to the origin
110-37 reference(s)		 Untitled 0609
111-37 reference(s)		 The 64 first lines of the Pascal's Triangle
112-36 reference(s)
Quark and gluon structure of a nucleon
113-36 reference(s)		 The velocity vectors -with a common origin- of the 9 planets of the Solar System during one plutonian year
114-36 reference(s)		 A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
115-36 reference(s)		 Black dots on a square lattice
116-36 reference(s)
A fractal Möbius strip
117-36 reference(s)		 The normal field of a shell (Jeener surface 1)
118-36 reference(s)		 Untitled 0616
119-36 reference(s)		 Untitled 0608
120-36 reference(s)
Rotation about the Y (vertical)axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms
121-36 reference(s)		 display of Ph(Zeta)inside [-50.0,+50.0]x[-50.0,+50.0]
122-35 reference(s)		 The construction process of the von Koch curve -the starting point: a segment-
123-35 reference(s)		 About the length of the von Koch curve
124-35 reference(s)
A pay slip
125-35 reference(s)		 Untitled 0085
126-35 reference(s)		 An Archimedes spiral displaying 1000 numbers
127-35 reference(s)		 The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
128-35 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
1493 reference(s)		 2-ChatGPT.01.Fra
381 reference(s)
3-An2000.01.Fra
236 reference(s)		 4-demo_14
170 reference(s)
5-Stereogrammes_AutoStereogrammes.01
123 reference(s)		 6-LesCourbesRemplissantes.02.Fra
123 reference(s)
7-help.
104 reference(s)		 8-an2000.01.fra
104 reference(s)
9-Galerie_NumberTheory.FV
103 reference(s)		 10-DecimalesDePi.01.Fra
103 reference(s)
11-Vcatalogue.11
101 reference(s)		 12-Informations_AboutPicturesAnimationsAndFiles.01.Ang
92 reference(s)
13-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
90 reference(s)		 14-catalogue.11
89 reference(s)
15-Galerie_ImagesDesMathematiques.FV
88 reference(s)		 16-GenieLogiciel_VisualisationScientifique.01.vv
87 reference(s)
17-UlamSpiral.01.Fra
82 reference(s)		 18-Galerie_ArtisticCreation.FV
79 reference(s)
19-Web_Mail.01.vv
78 reference(s)		 20-copyright.01.
77 reference(s)
21-mail.01.vv
72 reference(s)		 22-Galerie_ArtAndScience.FV
69 reference(s)
23-Fractal.01
69 reference(s)		 24-GenieLogiciel.01.Fra
68 reference(s)
25-Galerie_CelestialMechanics.FV
67 reference(s)		 26-LOG_xiMc.11
65 reference(s)
27-GoldenTriangle.01.Fra
65 reference(s)		 28-Galerie_GeneralitiesVisualization.FV
62 reference(s)
29-Fractal.21
62 reference(s)		 30-Fractal.03
59 reference(s)
31-Galerie_DeterministicFractalGeometry.FV
58 reference(s)		 32-Fractal.11
58 reference(s)
33-Informations_GoodNewsAndBadNews.01.Fra
57 reference(s)		 34-Galerie_Tributes.FV
57 reference(s)
35-AProposSite.01.Fra
57 reference(s)		 36-FloatingPointNumbers.01.Fra
56 reference(s)
37-Exposition_EcolePolytechnique_FeteDeLaScience_201910
55 reference(s)		 38-MonodimensionalCellularAutomata.01.Fra
54 reference(s)
39-Galerie_TextureSynthesis.FV
53 reference(s)		 40-DieuScience.01.Fra
52 reference(s)
41-present.01.
51 reference(s)		 42-Galerie_ParticleSystems.FV
50 reference(s)
43-Exposition_EcolePolytechnique_FeteDeLaScience_201510
49 reference(s)		 44-EntrelacsIntertwinings.01.Fra
49 reference(s)
45-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
47 reference(s)		 46-Exposition_MairieCinquiemeArrondissementParis_202001_202002
46 reference(s)
47-AVirtualSpaceTimeTravelMachine.Fra
46 reference(s)		 48-xtc_____Peano_SurjectionFractale.23.vv.c.
45 reference(s)
49-xiirv_____.nota.t.
44 reference(s)		 50-MathematiquesPhysiqueFractales.12
44 reference(s)
51-Exposition_EcolePolytechnique_AnneeMondialeDeLaPhysique_2005
44 reference(s)		 52-relai_universel.01.vv
43 reference(s)
53-ImagesDuVirtuel.01.Fra
43 reference(s)		 54-Galerie_QuantumMechanics.FV
43 reference(s)
55-Galerie_NewPictures.FV
43 reference(s)		 56-DecimalesPi_1_100.vv
43 reference(s)
57-SurfaceProjector.01.Ang
42 reference(s)		 58-RemarquesCerveau.01
42 reference(s)
59-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
42 reference(s)		 60-MathematiquesPhysiqueFractales.02.3
42 reference(s)
61-LeNoeudInfini.01.Fra
42 reference(s)		 62-RealNumbers.01.Fra
41 reference(s)
63-infinity.01.vv
40 reference(s)		 64-NDimensionalDeterministicFractalSets.01.Fra
40 reference(s)
65-LesCourbesRemplissantes.02.Ang
40 reference(s)		 66-ImagesDuVirtuel.01.Fra.FV
40 reference(s)
67-subject.01.
39 reference(s)		 68-T_Cryptographie_Alphabet.01.vv.Fra.0001
39 reference(s)
69-Multivers.01.Fra
39 reference(s)		 70-Galerie_SignalProcessing.FV
39 reference(s)
71-ExpV_VirE.11
39 reference(s)		 72-Commentaires_HyperCubeDimensionN.01
39 reference(s)
73-OrdinateurMathematiquesArt.01.Fra
38 reference(s)		 74-Informations_GoodNewsAndBadNews.01.Ang
38 reference(s)
75-Galerie_ImagesDidactiques.FV
38 reference(s)		 76-FloatingPointNumbers.01.Ang
38 reference(s)
77-DecimalesPi_100000.vv
38 reference(s)		 78-Bard.01.Fra
38 reference(s)
79-RasoirDOccamEtMathematiques.01.vv.Fra
37 reference(s)		 80-LesCourbesRemplissantes.01.Fra
37 reference(s)
81-Kepler.02.
37 reference(s)		 82-Galerie_DeterministicChaos.FV
37 reference(s)
83-VisualisationRelief.01.vv.Fra
36 reference(s)		 84-T_MathematiquesPhysiqueFractales.02.1_NumerotationDesRationnels.01.vv.Fra.0001
36 reference(s)
85-ImagesEncadreesDisponibles.01
36 reference(s)		 86-SurfaceProjector.01.Fra
35 reference(s)
87-LesCourbesRemplissantes.01.Ang
35 reference(s)		 88-GoldenTriangle.01.Ang
35 reference(s)
89-EntrelacsIntertwinings.01.Ang
35 reference(s)		 90-Polynomials_RationalNumbers.01.Fra
34 reference(s)
91-MathematiquesPhysiqueFractales.02
34 reference(s)		 92-FaireDesMathematiques.01.Fra
34 reference(s)
93-BEST.20170828
34 reference(s)		 94-BEST.20150828
34 reference(s)
95-T_MathematiquesPhysiqueFractales.02.15_ArbreDeSternBrocot.01.vv.Fra.0002
33 reference(s)		 96-NombresPremiers_10000.vv
33 reference(s)
97-NatureDesMathematiques.01.vv.Fra
33 reference(s)		 98-Informations_AboutPicturesAnimationsAndFiles.01.Fra
33 reference(s)
99-Galerie_SensitivityToRoundingOffErrors.FV
33 reference(s)		 100-Galerie_Astrophysics.FV
33 reference(s)
101-ExpV_VirE.Fra
33 reference(s)		 102-Commentaires_DefinitionPseudoOctonions.01
33 reference(s)
103-AnimFractal.01.
33 reference(s)		 104-PerteDeLAssociativite.01
32 reference(s)
105-Notations_AppartientA.01
32 reference(s)		 106-Galerie_FluidMechanics.FV
32 reference(s)
107-Exposition_EcolePolytechnique_FeteDeLaScience_201810
32 reference(s)		 108-ChatGPT.01.Ang
32 reference(s)
109-BEST.20171028
32 reference(s)		 110-An2000.01.Ang
32 reference(s)
111-T_DuReelAuVirtuel_MetaOrdinateur.02.Fra.0003
31 reference(s)		 112-MathematiquesPhysiqueFractales.02.15
31 reference(s)
113-LeNoeudInfini.01.Ang
31 reference(s)		 114-BEST.20140128
31 reference(s)
115-Autostereograms.01.
31 reference(s)		 116-xtc_____HexagonesPremiers.01.vv.c.
30 reference(s)
117-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_1
30 reference(s)		 118-MathematiquesPhysiqueFractales.02.11
30 reference(s)
119-ManyChaos.01.Ang
30 reference(s)		 120-LeParadoxeDeFermi.01.Fra
30 reference(s)
121-IllusionConnaissance.02
30 reference(s)		 122-Galerie_BestOf.FV
30 reference(s)
123-xtc_____INCLUDES.01.I.
29 reference(s)		 124-Labyrinthes.01.Fra
29 reference(s)
125-Galerie_SelfPortraits.FV
29 reference(s)		 126-ConjectureDeSyracuse_0256.vv
29 reference(s)
127-Bard.01.Ang
29 reference(s)		 128-BEST.20170528
29 reference(s)

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




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