Monthly Best Of on 11/28/2022




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 11/28/2022 and last updated on 10/03/2024 17:04:35 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The random walk of photons escaping the Sun
1-106 reference(s)		Artistic view of the prime numbers
2-101 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
3-91 reference(s)		Coalescence of 40832 particles -black holes?- inside a tridimensional parallelepipedic billiard
4-84 reference(s)
Autostereogram of the CMAP
5-71 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
6-70 reference(s)		The 1.024 first decimals -base 10- of 'pi' on a Bidimensional Hilbert Curve -iteration 5-
7-68 reference(s)		Autostereogram with an hidden ring and ghost bows
8-66 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
9-66 reference(s)		The generalized Ulam spiral
10-65 reference(s)		Tridimensional representation of a hexadimensional Calabi-Yau manifold
11-65 reference(s)		The Universe at the heart of a Calabi-Yau manifold
12-64 reference(s)
The 512 first decimals -base 10- of 'pi' on a Tridimensional Hilbert Curve -iteration 3-
13-60 reference(s)		A blue Sponge-tree -a Tribute to Yves Klein-
14-59 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
15-57 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 5-
16-56 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
17-52 reference(s)		The Lorenz attractor
18-51 reference(s)		Tridimensional display of the particle density of a bidimensional snowflake-like billiard
19-50 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
20-50 reference(s)
Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
21-48 reference(s)		The Road to Chaos -06/19/2022-
22-48 reference(s)		Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
23-48 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
24-46 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-
25-46 reference(s)		Autostereogram with an hidden volcano
26-45 reference(s)		Autostereogram with an hidden volcano
27-45 reference(s)		The K-smooth integers on a Bidimensional Hilbert Curve -iteration 5-
28-45 reference(s)
The Menger Sponge -iteration 5-
29-45 reference(s)		The Sierpinski Carpet -iteration 4-
30-44 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
31-44 reference(s)		Happy new year 2000
32-44 reference(s)
Bidimensional display of 31 Rational Numbers by means of the Stern-Brocot Tree
33-43 reference(s)		The Ulam spiral
34-43 reference(s)		The Birth of the Universe
35-43 reference(s)		Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
36-43 reference(s)
Untitled 0599 -a Tribute to Robert & Sonia Delaunay-
37-43 reference(s)		Botticelli anomaly on the Moon
38-42 reference(s)		Mountains and light cloud dynamics -this sequence being periodical-
39-42 reference(s)		Quark and gluon structure of a nucleon
40-42 reference(s)
The Node, Rama Revealed -a Tribute to Arthur C. Clarke and Gentry Lee-
41-42 reference(s)		Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
42-42 reference(s)		The prime numbers among the 1024 first integer numbers on a Bidimensional Hilbert Curve -iteration 5-
43-41 reference(s)		The same bidimensional scalar field displayed with 4 different color palettes
44-41 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
45-41 reference(s)		Artistic view of the Big Bang
46-40 reference(s)		An aperiodic Penrose tiling of the Golden Decagon -a Tribute to Piet Mondrian and Roger Penrose-
47-40 reference(s)		The Eratosthene sieve displaying 100x100 numbers
48-40 reference(s)
The foggy Babel Tower -a Tribute to Brueghel the Elder-
49-40 reference(s)		Sixteen interlaced fractal torus
50-40 reference(s)		The Jeener hypocycloidal snail
51-40 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
52-40 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
53-40 reference(s)		Along the border of the Mandelbrot set
54-39 reference(s)		Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier-
55-39 reference(s)		The intersection of the Menger Sponge -iteration 5- and of a quadridimensional Calabi-Yau manifold -tridimensional representation-
56-39 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-
57-39 reference(s)		Rotation about the Y (vertical)axis of the CMAP logo that can also be viewed as a set of 4x3 stereograms
58-39 reference(s)		The 64 first lines of the Pascal's Triangle -modulo 7-
59-38 reference(s)		Bidimensional display of 255 Rational Numbers by means of the Stern-Brocot Tree
60-38 reference(s)
The Node, The Garden of Rama -a Tribute to Arthur C. Clarke and Gentry Lee-
61-38 reference(s)		From Pluto to the Sun (non linear scales)
62-38 reference(s)		A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -100.000 digits, -base 10- into 050330... -128.508 digits, base 6-
63-38 reference(s)		A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
64-38 reference(s)
Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms
65-38 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
66-37 reference(s)		Fractal 'celestial body' based on a torus with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
67-37 reference(s)		A parallelepipedic extended Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
68-37 reference(s)
Fractal Self-Portrait -a Tribute to René Magritte-
69-37 reference(s)		Heterogeneous -tridimensional fractal field- random meshing of a cube
70-37 reference(s)		Untitled 0320
71-36 reference(s)		The Road to Chaos -06/19/2022-
72-36 reference(s)
The prime numbers among the 512 first integer numbers on a Tridimensional Hilbert Curve -iteration 3-
73-36 reference(s)		Untitled 0605
74-36 reference(s)		The digits {0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5} on a Bidimensional Hilbert Curve -iteration 2-
75-36 reference(s)		A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
76-36 reference(s)
Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
77-36 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
78-36 reference(s)		Untitled 0604 -a Tribute to Yves Klein-
79-35 reference(s)		The K-smooth integers on a generalized Ulam spiral
80-35 reference(s)
Bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity
81-34 reference(s)		Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
82-34 reference(s)		Mountains at sunrise
83-34 reference(s)		A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
84-34 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
85-34 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) and with a 0 to pi rotation about the X axis -tridimensional cross-section-
86-34 reference(s)		Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
87-34 reference(s)		An aperiodic Penrose tiling of the plane
88-33 reference(s)
The Sierpinski Carpet -iteration 2-
89-33 reference(s)		The construction process of the Sierpinski Carpet
90-33 reference(s)		A punched paper tape
91-33 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
92-33 reference(s)
A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-
93-33 reference(s)		Monument Valley at sunrise
94-33 reference(s)		Untitled 0155 -a Tribute to Yves Tanguy-
95-33 reference(s)		Quark and gluon structure of a nucleon
96-33 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)
97-33 reference(s)		An extended Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
98-33 reference(s)		Untitled 0597
99-33 reference(s)		Self-Portrait -'This is not an apple', a Tribute to René Magritte-
100-33 reference(s)
Black dots on a square lattice
101-33 reference(s)		Anaglyph -blue=right, red=left- of an hypercube
102-33 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
103-33 reference(s)		Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 1.083.984 galaxies)obtained by means of a non deterministic fractal process
104-33 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
105-33 reference(s)		Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
106-32 reference(s)		24 evenly distributed points on a sphere by means of simulated annealing
107-32 reference(s)		The generalized Ulam spiral displaying 1024 numbers
108-32 reference(s)
Sunny Monument Valley
109-32 reference(s)		The K-smooth integers on a Tridimensional Hilbert Curve -iteration 3-
110-32 reference(s)		The 2/3/5/7-smooth integers on a generalized Ulam spiral
111-32 reference(s)		The smooth integers
112-32 reference(s)
N-body problem integration (N=5)displaying four planets with symmetrical initial conditions on elliptic trajectories -'geocentric' point of view, green body-
113-32 reference(s)		A Tridimensional Tribute to Sandro Botticelli
114-32 reference(s)		Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
115-31 reference(s)		Quantum vacuum fluctuations
116-31 reference(s)
The Mathematics are the key of the Multiverse
117-31 reference(s)		The Sierpinski Carpet -iteration 3-
118-31 reference(s)		Fractal synthesis of mountains with vegetation and clouds
119-31 reference(s)		The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
120-31 reference(s)
Distorsion of the Bonan-Jeener-Klein triple bottle
121-31 reference(s)		The Jeener-Klein triple bottle
122-31 reference(s)		Color palette 'jaune'
123-30 reference(s)		The smooth integers: the prime factor product -the radical function- of the integer numbers
124-30 reference(s)
The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
125-30 reference(s)		display of the inclination of two elliptic trajectories
126-30 reference(s)		An amazing generalized cross-section inside the Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
127-30 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 2-
128-30 reference(s)




2-The 128 most referenced Pages (*):

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



1-ImagesEncadreesDisponibles.01
448 reference(s)		2-Vcatalogue.11
213 reference(s)
3-demo_14
149 reference(s)		4-An2000.01.Fra
137 reference(s)
5-AVirtualSpaceTimeTravelMachine.Ang
130 reference(s)		6-help.
122 reference(s)
7-mail.01.vv
95 reference(s)		8-Informations_AboutPicturesAnimationsAndFiles.01.Ang
91 reference(s)
9-copyright.01.
82 reference(s)		10-Stereogrammes_AutoStereogrammes.01
67 reference(s)
11-GenieLogiciel_VisualisationScientifique.01.vv
61 reference(s)		12-Galerie_ArtisticCreation.FV
59 reference(s)
13-Galerie_NewPictures.FV
57 reference(s)		14-xiirv_____.nota.t.
56 reference(s)
15-LOG_xiMc.11
55 reference(s)		16-Informations_GoodNewsAndBadNews.01.Fra
55 reference(s)
17-Fractal.01
55 reference(s)		18-FloatingPointNumbers.01.Fra
55 reference(s)
19-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
54 reference(s)		20-UlamSpiral.01.Fra
51 reference(s)
21-GoldenTriangle.01.Fra
50 reference(s)		22-Galerie_GeneralitiesVisualization.FV
50 reference(s)
23-Galerie_NumberTheory.FV
49 reference(s)		24-Galerie_CelestialMechanics.FV
49 reference(s)
25-Galerie_ArtAndScience.FV
49 reference(s)		26-xiirc_____.nota.t.
48 reference(s)
27-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
48 reference(s)		28-RealNumbers.01.Fra
46 reference(s)
29-Galerie_DeterministicFractalGeometry.FV
46 reference(s)		30-Fractal.11
46 reference(s)
31-VAcatalogue.11
45 reference(s)		32-AProposSite.01.Fra
45 reference(s)
33-MathematiquesPhysiqueFractales.12
44 reference(s)		34-Informations_GoodNewsAndBadNews.01.Ang
44 reference(s)
35-Galerie_ParticleSystems.FV
44 reference(s)		36-Galerie_ImagesDesMathematiques.FV
44 reference(s)
37-OrdinateursEtCalculs.01.Ang
43 reference(s)		38-Galerie_BestOf.FV
43 reference(s)
39-Fractal.21
43 reference(s)		40-AVirtualSpaceTimeTravelMachine.Fra
43 reference(s)
41-Web_Mail.01.vv
42 reference(s)		42-MathematiquesPhysiqueFractales.02
42 reference(s)
43-Fractal.03
42 reference(s)		44-FloatingPointNumbers.01.Ang
42 reference(s)
45-AnimFractal.01.
42 reference(s)		46-Galerie_TextureSynthesis.FV
41 reference(s)
47-SurfaceProjector.01.Ang
38 reference(s)		48-Galerie_QuantumMechanics.FV
38 reference(s)
49-Exposition_EcolePolytechnique_FeteDeLaScience_201910
37 reference(s)		50-DecimalesPi_1_100.vv
37 reference(s)
51-Autostereograms.01.
37 reference(s)		52-catalogue.11
36 reference(s)
53-SurfaceProjector.01.Fra
36 reference(s)		54-LeParadoxeDeFermi.01.Fra
36 reference(s)
55-FaireDeLaRecherche.01.vv
36 reference(s)		56-infinity.01.vv
35 reference(s)
57-UlamSpiral.01.Ang
35 reference(s)		58-OrdinateurMathematiquesArt.01.Fra
35 reference(s)
59-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
35 reference(s)		60-ExpV_VirE.Fra
35 reference(s)
61-DecimalesDePi.01.Fra
35 reference(s)		62-xiirs_____.nota.t.
34 reference(s)
63-subject.01.
34 reference(s)		64-PerteDeLAssociativite.01
34 reference(s)
65-Galerie_Tributes.FV
34 reference(s)		66-MonodimensionalCellularAutomata.01.Fra
33 reference(s)
67-Galerie_SignalProcessing.FV
33 reference(s)		68-Galerie_SelfPortraits.FV
33 reference(s)
69-EntrelacsIntertwinings.01.Fra
33 reference(s)		70-NatureDesMathematiques.01.vv.Fra
32 reference(s)
71-Kepler.02.
32 reference(s)		72-IllusionConnaissance.01
32 reference(s)
73-Galerie_Astrophysics.FV
32 reference(s)		74-EntrelacsIntertwinings.01.Ang
32 reference(s)
75-DecimalesPi_100000.vv
32 reference(s)		76-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_4
31 reference(s)
77-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_10
31 reference(s)		78-present.01.
31 reference(s)
79-infinity.02.vv
31 reference(s)		80-Pcatalogue.11
31 reference(s)
81-NombresPremiers_10000.vv
31 reference(s)		82-NDimensionalDeterministicFractalSets.01.Fra
31 reference(s)
83-Galerie_ImagesDidactiques.FV
31 reference(s)		84-Commentaires_NoeudTrefle.01
31 reference(s)
85-VirtualChaos.01.Ang
30 reference(s)		86-IllusionConnaissance.02
30 reference(s)
87-GenieLogiciel.01.Fra
30 reference(s)		88-Galerie_AnthropomorphicPatterns.FV
30 reference(s)
89-ConjectureDeSyracuse_0128.Parity.vv
30 reference(s)		90-NDimensionalDeterministicFractalSets.01.Ang
29 reference(s)
91-Multivers.01.Fra
29 reference(s)		92-LeNoeudInfini.01.Fra
29 reference(s)
93-ImagesDuVirtuel.01.Fra.FV
29 reference(s)		94-GoldenTriangle.01.Ang
29 reference(s)
95-Galerie_FluidMechanics.FV
29 reference(s)		96-Exposition_OperaDeMassy_201912_202001
29 reference(s)
97-EntrelacsIntertwinings.01.Ang.DIAPO.0247
29 reference(s)		98-DieuScience.01.Fra
29 reference(s)
99-Commentaires_DefinitionPseudoQuaternions.01
29 reference(s)		100-ArtEtMathematiques.01
29 reference(s)
101-NombresEtLumiere.01.vv.Fra
28 reference(s)		102-MorePages.Ang.
28 reference(s)
103-LeParadoxeDeFermi.01.Ang
28 reference(s)		104-HomeMade.01.vv
28 reference(s)
105-Galerie_SensitivityToRoundingOffErrors.FV
28 reference(s)		106-Galerie_DeterministicChaos.FV
28 reference(s)
107-EnsembleDesGaleriesFractales.DIAPO.0001
28 reference(s)		108-Downloading.01.vv
28 reference(s)
109-DieuScience.01.Ang
28 reference(s)		110-Commentaires_DefinitionPseudoOctonions.01
28 reference(s)
111-VisualisationRelief.01.vv.Fra
27 reference(s)		112-Polynomials_RationalNumbers.01.Fra
27 reference(s)
113-MathematiquesPhysiqueFractales.22
27 reference(s)		114-ManyChaos.01.Fra
27 reference(s)
115-ManyChaos.01.Ang
27 reference(s)		116-LesApprentisDieux.01
27 reference(s)
117-ImpossibleStructures.01.Fra
27 reference(s)		118-RasoirDOccamEtMathematiques.01.vv.Fra
26 reference(s)
119-OrdinateursEtCalculs.01.Fra
26 reference(s)		120-MonodimensionalCellularAutomata.01.Ang
26 reference(s)
121-MathematiquesEtRepresentations.01.vv.Ang
26 reference(s)		122-Exposition_EcolePolytechnique_AnneeMondialeDeLaPhysique_2005
26 reference(s)
123-ExpV_VirE.11
26 reference(s)		124-ConjectureDeSyracuse_0256.vv
26 reference(s)
125-AQuoiServentLesMathematiques.01
26 reference(s)		126-create.03.
25 reference(s)
127-VirtualChaos.01.Fra
25 reference(s)		128-VCcatalogue.11
25 reference(s)

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




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