Monthly Best Of on 09/28/2024




Iterations in the complex plane

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 09/28/2024 and last updated on 10/03/2024 17:04:58 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-619 reference(s)		Tridimensional display of an Archimedes spiral displaying 'pi' with 200 digits -base 10-
2-141 reference(s)		Artistic view of the prime numbers
3-138 reference(s)		The Many World Theory of Hugh Everett
4-135 reference(s)
Autostereogram with an hidden volcano
5-109 reference(s)		Autostereogram with an hidden volcano
6-101 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
7-98 reference(s)		The random walk of photons escaping the Sun
8-92 reference(s)
The generalized Ulam spiral
9-92 reference(s)		An extended Menger Sponge -iteration 5- displaying the 100 first digits -base 2- of the Champernowne number (=0.1 10 11 100 101 110 111 1000...)-using all base 2 integer numbers- periodically repeated in order to obtain 1.539.972 digits
10-90 reference(s)		64 elementary bidimensional binary cellular automata with 1 white starting central point
11-88 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
12-85 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
13-85 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
14-85 reference(s)		Tridimenional display of the Goldbach conjecture
15-82 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
16-82 reference(s)
Autostereogram of the CMAP
17-80 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
18-78 reference(s)		The Goldbach conjecture
19-78 reference(s)		The first four iterations of the construction of the von Koch snowflake
20-76 reference(s)
Pseudo Olympic Rings
21-76 reference(s)		Two orthogonal 'hourglasses' moving relative to each other
22-76 reference(s)		Black dots on a square lattice
23-76 reference(s)		The Jeener-Klein triple bottle
24-74 reference(s)
The Universe at the heart of a Calabi-Yau manifold
25-73 reference(s)		Autostereogram with an hidden ring and ghost bows
26-72 reference(s)		Isle of the Dead -a Tribute to Arnold Böcklin-
27-72 reference(s)		24 evenly distributed points on a sphere by means of simulated annealing
28-71 reference(s)
A distorded -for the sake of display- 5-cube -an hyperhypercube-
29-71 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
30-70 reference(s)		The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
31-69 reference(s)		Simple random triangulation of the surface of a torus -18x18-
32-68 reference(s)
The relief -modulus- of the function exp(1/z)defined by means of three bidimensional fields
33-68 reference(s)		The Piet Mondrian quadridimensional Calabi-Yau manifold -2D, 3D or 4D?-
34-68 reference(s)		The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
35-67 reference(s)		The 64 first lines of the Pascal's Triangle
36-66 reference(s)
Happy birthday
37-66 reference(s)		Quark and gluon structure of a nucleon
38-66 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
39-64 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
40-64 reference(s)
The Ulam spiral displaying 2025 numbers
41-63 reference(s)		N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Pluto point of view-
42-62 reference(s)		An extended Menger Sponge -iteration 5- using the 246.078 first digits -base 2- of a self-portrait
43-62 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
44-62 reference(s)
The Sierpinski Carpet -iteration 1 to 5-
45-61 reference(s)		A regular 7-gon -an heptagon-
46-61 reference(s)		Two multiplexed autostereograms by means of a pi/2 rotation
47-60 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
48-60 reference(s)
An extended Menger Sponge -iteration 4- displaying the 134.460 digits -base 2- of the source of the Menger Sponge generator
49-60 reference(s)		Larsen effect
50-60 reference(s)		Anaglyph -blue=right, red=left- of an hypercube
51-60 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
52-60 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
53-58 reference(s)		The Syracuse conjecture for U(0)={1,2,3,4,...,128} -monodimensional display of the parities-
54-57 reference(s)		The 256 first digits -base 10- of 'pi' on a Bidimensional Hilbert Curve -iteration 4- mapped on a sphere
55-57 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-
56-57 reference(s)
An amazing cross-section inside the Menger Sponge -iteration 5-
57-57 reference(s)		The Lorenz attractor
58-57 reference(s)		The CMAP logo
59-57 reference(s)		Tridimensional display of the Riemann Zeta function inside [+0.1,+0.9]x[0,+50]
60-56 reference(s)
Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
61-56 reference(s)		An extended Menger Sponge -iteration 7- displaying the 211.210.335 first digits -base 2- of 'pi'
62-56 reference(s)		Fractal Self-Portrait -a Tribute to René Magritte-
63-56 reference(s)		Jean-François COLONNA
64-56 reference(s)
Happy new year 2000
65-56 reference(s)		The Ulam spiral
66-55 reference(s)		A fractal Möbius strip
67-55 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
68-55 reference(s)
Tridimensional visualization of the ABC conjecture
69-55 reference(s)		Tridimensional display of the Riemann Zeta function inside [-10.0,+20.0]x[-15.0,+15.0] (bird's-eye view)
70-54 reference(s)		About the length of the von Koch curve
71-54 reference(s)		A pay slip
72-54 reference(s)
Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
73-54 reference(s)		Bidimensional cross-sections of the Klein bottle
74-54 reference(s)		A cylinder defined by means of three bidimensional fields
75-54 reference(s)		The tridimensional John Conway's life game with random initial conditions -0.8% of occupied cells- and 40 iterations
76-54 reference(s)
A one sheet hyperboloid of revolution -negative curvature-
77-54 reference(s)		A Ball described by means of an 'open' 3-foil torus knot -iteration 4-
78-54 reference(s)		Cantor's diagonal argument
79-54 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
80-54 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
81-54 reference(s)		The Syracuse conjecture for U(0)={2,4,6,8,...,524288}
82-53 reference(s)		An octogonal tiling of the hyperbolic Poincaré disk -iteration 5-
83-53 reference(s)		A 4-cube -an hypercube-
84-53 reference(s)
The Bonan-Jeener-Klein triple bottle
85-53 reference(s)		Autostereogram with an hidden volcano
86-52 reference(s)		Happy new year 2000
87-52 reference(s)		Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
88-52 reference(s)
Triple impossible staircase and a paradoxal structure
89-52 reference(s)		The 5x5=25 patches of the tridimensional representation of a quadridimensional Calabi-Yau manifold
90-52 reference(s)		The 64 first lines of the Pascal's Triangle -modulo 7-
91-51 reference(s)		A Peano 'fractal plane' defined by means of three bidimensional fields
92-51 reference(s)
The Liouville function displayed as a bidimensional random walk for the integer numbers from 2 to 100001
93-51 reference(s)		Tridimensional display of a spiral displaying 'pi' with 4.000 digits -base 10-
94-51 reference(s)		Quark and gluon structure of a nucleon
95-51 reference(s)		From Pluto to the Sun (non linear scales)
96-51 reference(s)
An extended Menger Sponge -iteration 3-
97-51 reference(s)		Autostereogram with an hidden volcano and 64 self-portraits
98-51 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
99-51 reference(s)		The tower -a Tribute to Vladimir Tatline-
100-51 reference(s)
An aperiodic Penrose tiling of the plane -a Tribute to Piet Mondrian and Roger Penrose-
101-50 reference(s)		The special Liouville function displayed as a bidimensional random walk for the integer numbers from 2 to 100001
102-50 reference(s)		A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -90.000 digits, -base 10- with 30.000 time steps
103-50 reference(s)		The K-smooth integers on a generalized Ulam spiral
104-50 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 4-
105-50 reference(s)		The DNA of Mathematics -the 480 first digits of 'pi' (3,141592...)and '2.pi' (6,283185...)-
106-50 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
107-50 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
108-50 reference(s)
LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
109-50 reference(s)		An aperiodic Penrose tiling of the plane
110-49 reference(s)		An aperiodic Penrose tiling of the plane
111-49 reference(s)		The Syracuse conjecture for U(0)={5,6,7,8,...,20} -bidimensional display-
112-49 reference(s)
An interpolation between the Möbius strip and a 'double sphere' defined by means of three sets of bidimensional fields
113-49 reference(s)		A variable Archimedes spiral displaying 1000 numbers
114-49 reference(s)		A set of 4x3 stereograms displaying a tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -90.000 digits, -base 10- with 30.000 time steps
115-49 reference(s)		An half-random extended Menger Sponge -iteration 3-
116-49 reference(s)
The Mandelbrot set computed for 1 to 16 iterations with display of the arguments
117-49 reference(s)		The quaternionic Julia set -degree=2- computed with A=(-0.581514...,+0.635888...,0,0)-tridimensional cross-section-
118-49 reference(s)		Fractal Self-Portrait -'Décalcomanie', a Tribute to René Magritte-
119-49 reference(s)		Hypercube
120-49 reference(s)
My own quadruple impossible staircase -a Tribute to Maurits Cornelis Escher-
121-49 reference(s)		Tridimensional display of the Riemann Zeta function inside [-10.0,+60.0]x[-35.0,+35.0] (bird's-eye view)
122-48 reference(s)		The Syracuse conjecture for U(0)={1,2,3,4,...,128} -monodimensional display-
123-48 reference(s)		Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier-
124-48 reference(s)
A tridimensional pseudo-random walk defined by means of 'pi': 141592... -100.001 digits, -base 10- into 303142... -128.509 digits, -base 6-
125-48 reference(s)		The 180 first digits of 'pi' displayed as a Labyrinth
126-48 reference(s)		The foggy Babel Tower -a Tribute to Brueghel the Elder-
127-48 reference(s)		An extended Menger Sponge -iteration 5- displaying the 991.818 first digits -base 2- of the Champernowne number (=0.1 10 11 100 101 110 111 1000...)-using all base 2 integer numbers-
128-48 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
2149 reference(s)		2-Web_Mail.01.vv
199 reference(s)
3-Stereogrammes_AutoStereogrammes.01
154 reference(s)		4-ChatGPT.01.Fra
101 reference(s)
5-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
89 reference(s)		6-demo_14
88 reference(s)
7-help.
87 reference(s)		8-NDimensionalDeterministicFractalSets.01.Fra
87 reference(s)
9-mail.01.vv
85 reference(s)		10-UlamSpiral.01.Fra
80 reference(s)
11-catalogue.11
77 reference(s)		12-NombresPremiers_10000.vv
77 reference(s)
13-Informations_GoodNewsAndBadNews.01.Fra
73 reference(s)		14-IAGenerativesImages.01.Fra
73 reference(s)
15-Galerie_Pi.FV
73 reference(s)		16-Galerie_NewPictures.FV
73 reference(s)
17-AProposSite.01.Fra
73 reference(s)		18-Fractal.21
72 reference(s)
19-Fractal.01
71 reference(s)		20-FloatingPointNumbers.01.Fra
71 reference(s)
21-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
68 reference(s)		22-Galerie_GeneralitiesVisualization.FV
68 reference(s)
23-An2000.01.Fra
68 reference(s)		24-EntrelacsIntertwinings.01.Ang
63 reference(s)
25-Polynomials_RationalNumbers.01.Fra
62 reference(s)		26-PerteDeLAssociativite.01
62 reference(s)
27-ExpV_VirE.11
62 reference(s)		28-ImagesDuVirtuel.01.Fra.FV
61 reference(s)
29-LOG_xiMc.11
59 reference(s)		30-Fractal.03
57 reference(s)
31-ChatGPT.01.Ang
57 reference(s)		32-Exposition_EcolePolytechnique_FeteDeLaScience_201910
56 reference(s)
33-DecimalesDePi.01.Fra
56 reference(s)		34-Vcatalogue.11
55 reference(s)
35-DecimalesPi_1_100.vv
55 reference(s)		36-GoldenTriangle.01.Fra
54 reference(s)
37-Fractal.11
54 reference(s)		38-copyright.01.
53 reference(s)
39-MathematiquesPhysiqueFractales.22
53 reference(s)		40-AvantPropos.01.Ang
53 reference(s)
41-Autostereograms.01.
53 reference(s)		42-relai_universel.01.vv
52 reference(s)
43-NombresEtLumiere.01.vv.Fra
52 reference(s)		44-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
52 reference(s)
45-LeParadoxeDeFermi.01.Ang
52 reference(s)		46-Galerie_DeterministicFractalGeometry.FV
51 reference(s)
47-MathematiquesModeleOutilArtiste.02.Ang
50 reference(s)		48-IllusionConnaissance.02
50 reference(s)
49-Multivers.01.Fra
49 reference(s)		50-MorePages.Ang.
49 reference(s)
51-Galerie_QuantumMechanics.FV
49 reference(s)		52-EntrelacsIntertwinings.01.Fra
49 reference(s)
53-LesApprentisDieux.01
48 reference(s)		54-Galerie_SelfPortraits.FV
48 reference(s)
55-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis
48 reference(s)		56-fractal.01
47 reference(s)
57-ImagesDuVirtuel.01.Fra
47 reference(s)		58-Galerie_NumberTheory.FV
47 reference(s)
59-Polynomials_RationalNumbers.01.Ang
45 reference(s)		60-MathematiquesEtRepresentations.01.vv.Ang
45 reference(s)
61-Galerie_ParticleSystems.FV
45 reference(s)		62-RealNumbers.01.Fra
44 reference(s)
63-Pcatalogue.11
44 reference(s)		64-MonodimensionalCellularAutomata.01.Ang
44 reference(s)
65-Galerie_ArtAndScience.FV
44 reference(s)		66-DieuScience.01.Fra
44 reference(s)
67-Exposition_MairieCinquiemeArrondissementParis_202001_202002
43 reference(s)		68-DieuScience.01.Ang
43 reference(s)
69-Commentaires_DefinitionOctonions.01
43 reference(s)		70-MesExpositionsPassees.01
42 reference(s)
71-LesCourbesRemplissantes.02.Fra
42 reference(s)		72-Commentaires_ModeleIsingTriDimensionnel.01
42 reference(s)
73-BEST.20121228
42 reference(s)		74-VCcatalogue.11
41 reference(s)
75-NDimensionalDeterministicFractalSets.01.Ang
41 reference(s)		76-Informations_GoodNewsAndBadNews.01.Ang
41 reference(s)
77-MiseEnSceneDesNombres.01.vv.Ang
40 reference(s)		78-Galerie_CelestialMechanics.DIAPO.0001
40 reference(s)
79-Commentaires_EnsembleMandelbrotOctonion.01
40 reference(s)		80-infinity.01.vv
39 reference(s)
81-UlamSpiral.01.Ang
39 reference(s)		82-Multivers.01.Ang
39 reference(s)
83-LesCourbesRemplissantes.01.Fra
39 reference(s)		84-Kepler.02.
39 reference(s)
85-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.DIAPO.0001
39 reference(s)		86-FloatingPointNumbers.01.Ang
39 reference(s)
87-EnsembleDesGaleries.DIAPO.0795
39 reference(s)		88-Commentaires_DefinitionPseudoQuaternions.01
39 reference(s)
89-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_1
38 reference(s)		90-VAcatalogue.11
38 reference(s)
91-PerteDeLaDistributivite.01.DIS2
38 reference(s)		92-Informations_AboutPicturesAnimationsAndFiles.01.Ang
38 reference(s)
93-IAGenerativesImages.01.Ang
38 reference(s)		94-Galerie_RCMGalerie.FV
38 reference(s)
95-Galerie_PALETTES_A
38 reference(s)		96-Galerie_BestOf.FV
38 reference(s)
97-DecimalesPi_100000.vv
38 reference(s)		98-subject.01.
37 reference(s)
99-Galerie_Tributes.FV
37 reference(s)		100-DuModeleALImage.01.Fra
37 reference(s)
101-ArtScience.01
37 reference(s)		102-create.03.
36 reference(s)
103-avirtualspacetimetravelmachine.ang
36 reference(s)		104-OrdinateursEtCalculs.01.Fra
36 reference(s)
105-LesCourbesRemplissantes.01.Ang
36 reference(s)		106-LeParadoxeDeFermi.01.Fra
36 reference(s)
107-Galerie_ImagesEssentiellesDesMathematiques.FV
36 reference(s)		108-Galerie_ImagesDidactiques.FV
36 reference(s)
109-xiirv_____.nota.t.
35 reference(s)		110-RasoirDOccamEtMathematiques.01.vv.Ang
35 reference(s)
111-Notations_AppartientA.01
35 reference(s)		112-NatureDesMathematiques.01.vv.Fra
35 reference(s)
113-MonodimensionalCellularAutomata.01.Fra
35 reference(s)		114-MathematiquesPhysiqueFractales.12
35 reference(s)
115-LesCourbesRemplissantes.02.Ang
35 reference(s)		116-ImpossibleStructures.01.Fra
35 reference(s)
117-GenieLogiciel.01.Fra
35 reference(s)		118-Galerie_ArtisticCreation.FV
35 reference(s)
119-ExpV_VirE.Fra
35 reference(s)		120-Commentaires_Hyperboloide.02
35 reference(s)
121-Commentaires_FluideInstationnaireBiDimensionnelIdeal.01
35 reference(s)		122-Commentaires_EnsembleMandelbrotQuaternion.01
35 reference(s)
123-Bard.01.Fra
35 reference(s)		124-Bard.01.Ang
35 reference(s)
125-AnimFractal.01.
35 reference(s)		126-AVirtualSpaceTimeTravelMachine.Fra
35 reference(s)
127-AQuoiServentLesMathematiques.02
35 reference(s)		128-MathematiquesPhysiqueFractales.02.27
34 reference(s)

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




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