Monthly Best Of on 05/28/2026




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 05/28/2026 and last updated on 05/28/2026 22:14:53 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-369 reference(s)		Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
2-232 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
3-205 reference(s)		A 4-cube -an hypercube-
4-168 reference(s)
A fractal Klein bottle
5-165 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
6-153 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
7-148 reference(s)		The random walk of photons escaping the Sun
8-146 reference(s)
A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives. More than 50 years of progress in computer science -hardware and software-
9-144 reference(s)		From Pluto to the Sun -extrapolation 2-
10-144 reference(s)		Random pseudo-periodical quadrangulation of a cube -8x8x8-
11-142 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
12-135 reference(s)
Autostereogram with an hidden volcano
13-131 reference(s)		Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
14-127 reference(s)		Artistic view of the prime numbers
15-124 reference(s)		A random tiling of a square domain using 'generalized dominoes' made of a random number of squares
16-124 reference(s)
The smooth integers: the prime factor product -the radical function- of the integer numbers
17-116 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
18-114 reference(s)		The first four iterations of the construction of the von Koch snowflake
19-112 reference(s)		The Lorenz attractor
20-111 reference(s)
Autostereogram of the CMAP
21-110 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [1.2x10^15,1.3x10^15]-
22-110 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
23-109 reference(s)		The generalized Ulam spiral displaying 100 numbers
24-107 reference(s)
The same bidimensional scalar field displayed with 4 different color palettes
25-107 reference(s)		The Menger Sponge -iteration 5-
26-102 reference(s)		The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
27-102 reference(s)		Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
28-101 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
29-100 reference(s)		The foggy Babel Tower -a Tribute to Brueghel the Elder-
30-100 reference(s)		Quark and gluon structure of a nucleon
31-100 reference(s)		Fractal Self-Portrait -a Tribute to René Magritte-
32-98 reference(s)
Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers-
33-97 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
34-97 reference(s)		Gravitation and space-time curvature
35-94 reference(s)		Botticelli anomaly on the Moon
36-94 reference(s)
Jean-François COLONNA
37-94 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-
38-93 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)
39-92 reference(s)		Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
40-92 reference(s)
Mountains and fog
41-91 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 5-
42-91 reference(s)		Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
43-90 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 64 first prime numbers-
44-90 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
45-89 reference(s)		The random walk of photons escaping the Sun
46-89 reference(s)		The Jeener-Klein triple bottle
47-89 reference(s)		Elliptical trajectory of a planet around a star with perihelion advance (very exaggerated)
48-89 reference(s)
Artistic view of the Big Bang
49-88 reference(s)		Visualization of the Proth-Gilbreath Conjecture process for G(Pi(1.0025x10^15))=806.
50-88 reference(s)		The execution of a very simple program on a Turing Machine
51-87 reference(s)		Coalescence of 40832 particles -black holes?- inside a tridimensional parallelepipedic billiard -a static, non relativistic and bounded universe- with display of the dynamics of the mass histogram, during 204.8 time units
52-87 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
53-87 reference(s)		Untitled 0320
54-86 reference(s)		Quark and gluon structure of a nucleon
55-86 reference(s)		N-body problem integration (N=2)displaying a perfect Keplerian orbit
56-86 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
57-86 reference(s)		Visualization of the Proth-Gilbreath Conjecture process for G(Pi(1.0025x10^15))=806.
58-86 reference(s)		Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
59-86 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
60-86 reference(s)
Untitled 0649
61-85 reference(s)		A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 5-
62-85 reference(s)		Fractal piano keyboard
63-85 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
64-85 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
65-85 reference(s)		A dying Borg starship on Pluto
66-85 reference(s)		The generalized Ulam spiral
67-84 reference(s)		Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
68-84 reference(s)
A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
69-84 reference(s)		The tridimensional John Conway's life game with random initial conditions -1.0% of occupied cells-
70-84 reference(s)		2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
71-84 reference(s)		Tridimensional Hilbert Curve -iterations 1 to 3-
72-84 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [6*10^14,7*10^14]-
73-84 reference(s)		The execution of a very simple program on a Turing Machine
74-83 reference(s)		Bidimensional closed self-avoiding brownian motion on a torus
75-83 reference(s)		The Sierpinski Carpet -iteration 4-
76-83 reference(s)
The Sierpinski Carpet -iteration 5-
77-83 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-
78-83 reference(s)		A shell (Jeener surface 1)in motion
79-83 reference(s)		Untitled 0305
80-82 reference(s)
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-
81-82 reference(s)		The 256 first digits -base 10- of 'pi' on a Bidimensional Hilbert Curve -iteration 4- mapped on a sphere
82-82 reference(s)		Mountains and fog
83-82 reference(s)		An extended Menger Sponge -iteration 7- displaying the 211.210.335 first digits -base 2- of 'pi'
84-82 reference(s)
The tridimensional John Conway's life game with random initial conditions -25% of occupied cells-
85-82 reference(s)		Free fall in the vacuum
86-82 reference(s)		Tridimensional representation of a hexadimensional Calabi-Yau manifold
87-82 reference(s)		Untitled 0668
88-81 reference(s)
A punched card (actual size: 187x82 millimeters)
89-81 reference(s)		Bidimensional brownian motion -the colors used (magenta,red,yellow,green,cyan)are an increasing function of the time- and its 'external border' -white-
90-81 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
91-80 reference(s)		1-foil torus knot -obvious knot- on its torus and its asociated Möbius strip
92-80 reference(s)
The tridimensional John Conway's life game with random initial conditions -1.2% of occupied cells-
93-80 reference(s)		The tridimensional John Conway's life game with random initial conditions -24% of occupied cells-
94-80 reference(s)		The Birth of the Universe
95-80 reference(s)		Untitled 0671
96-80 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
97-80 reference(s)		Heterogeneous -tridimensional fractal field- random meshing of a cube
98-80 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 5-
99-79 reference(s)		The execution of a very simple program on a Turing Machine
100-79 reference(s)
Rotation about X and Y axes of the Boy surface
101-79 reference(s)		Mountains and light cloud dynamics -this sequence being periodical-
102-79 reference(s)		From Pluto to the Sun (non linear scales)
103-79 reference(s)		A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
104-79 reference(s)
The Klein bottle described by means of a Bidimensional Hilbert Curve -iteration 7-
105-79 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [3*10^14,4*10^14]-
106-79 reference(s)		Mapping on a sphere family of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
107-78 reference(s)		Along the border of the Mandelbrot set
108-78 reference(s)
Sunny Monument Valley
109-78 reference(s)		A full-random extended Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
110-78 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 2-
111-78 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [1.3x10^15,1.4x10^15]-
112-78 reference(s)
A distorded -for the sake of display- 5-cube -an hyperhypercube-
113-78 reference(s)		Mapping on the Bonan-Jeener double bottle of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
114-77 reference(s)		Mapping on a torus of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
115-77 reference(s)		The 64 first lines of the Pascal's Triangle
116-77 reference(s)
Fractal 'celestial body' based on a torus with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
117-77 reference(s)		Artistic view of gravitational waves
118-77 reference(s)		Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
119-77 reference(s)		Mapping on the Möbius strip of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
120-76 reference(s)
The Mathematics are the key of the Multiverse
121-76 reference(s)		Coalescence of 40832 particles -black holes?- inside a tridimensional parallelepipedic billiard -a static, non relativistic and bounded universe- during 409.6 time units
122-76 reference(s)		24 evenly distributed points on a sphere by means of simulated annealing
123-76 reference(s)		4 evenly distributed points on a sphere -a Tetrahedron- by means of simulated annealing
124-76 reference(s)
Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
125-76 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
126-76 reference(s)		Rotation about the Y (vertical)axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms
127-76 reference(s)		Untitled 0653
128-75 reference(s)




2-The 128 most referenced Pages (*):

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



1-artscience.11.ang.diapo.0019
22483 reference(s)		2-AVirtualSpaceTimeTravelMachine.Ang
2952 reference(s)
3-xiirv_____.nota.t.
1196 reference(s)		4-Vcatalogue.11
859 reference(s)
5-xiirf_____.nota.t.
660 reference(s)		6-xiirc_____.nota.t.
450 reference(s)
7-xiirs_____.nota.t.
342 reference(s)		8-Proth_Gilbreath_Conjecture.01.Ang
327 reference(s)
9-Galerie_PALETTES
296 reference(s)		10-xiirC_____.nota.t.
274 reference(s)
11-demo_14
207 reference(s)		12-help.
176 reference(s)
13-xiia_____.nota.t.
172 reference(s)		14-AVirtualSpaceTimeTravelMachine.VersionComplete.Ang
169 reference(s)
15-ChatGPT.11.Ang
161 reference(s)		16-xiak_____.nota.t.
157 reference(s)
17-ChatGPT.11.Fra
153 reference(s)		18-Galerie_NumberTheory.FV
152 reference(s)
19-xiirk_____.nota.t.
144 reference(s)		20-xiac_____.nota.t.
144 reference(s)
21-AVirtualSpaceTimeTravelMachine.VersionComplete.Fra
144 reference(s)		22-Galerie_DeterministicFractalGeometry.FV
138 reference(s)
23-An2000.01.Fra
138 reference(s)		24-ChatGPT.01.Fra
137 reference(s)
25-FloatingPointNumbers.01.Fra
135 reference(s)		26-mail.01.vv
134 reference(s)
27-Fractal.01
134 reference(s)		28-Stereogrammes_AutoStereogrammes.01
130 reference(s)
29-catalogue.11
128 reference(s)		30-xiaf_____.nota.t.
123 reference(s)
31-NDimensionalDeterministicFractalSets.01.Fra
119 reference(s)		32-xias_____.nota.t.
118 reference(s)
33-Fractal.11
117 reference(s)		34-present.01.
115 reference(s)
35-An2038.01.Fra
115 reference(s)		36-xiav_____.nota.t.
113 reference(s)
37-Proth_Gilbreath_Conjecture.01.Fra
110 reference(s)		38-IAGenerativesImages.01.Fra
110 reference(s)
39-Fractal.21
110 reference(s)		40-NatureDesMathematiques.01.vv.Fra
109 reference(s)
41-ExpV_VirE.11
108 reference(s)		42-MorePages.Ang.
107 reference(s)
43-copyright.01.
106 reference(s)		44-GenieLogiciel.01.Fra
106 reference(s)
45-Galerie_IdMCNRS.FV
106 reference(s)		46-Galerie_ArtisticCreation.FV
106 reference(s)
47-An2038.01.Ang
105 reference(s)		48-IAGenerativesImages.01.Ang
103 reference(s)
49-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
102 reference(s)		50-Galerie_ArtAndScience.FV
101 reference(s)
51-MathematiquesPhysiqueFractales.02
100 reference(s)		52-MonodimensionalCellularAutomata.01.Ang
99 reference(s)
53-GilbreathConjecture.01.Fra
99 reference(s)		54-DecimalesDePi.01.Fra
99 reference(s)
55-DEuclideAuGPS.01.Ang
99 reference(s)		56-Polynomials_RationalNumbers.01.Fra
98 reference(s)
57-NDimensionalDeterministicFractalSets.01.Ang
98 reference(s)		58-SurfaceProjector.01.Fra
97 reference(s)
59-Galerie_ImagesDesMathematiques.FV
97 reference(s)		60-FloatingPointNumbers.01.Ang
97 reference(s)
61-VAcatalogue.11
96 reference(s)		62-UlamSpiral.01.Fra
96 reference(s)
63-OrdinateursEtCalculs.01.Fra
96 reference(s)		64-NombresPremiers_10000.vv
96 reference(s)
65-LOG_xiMc.11
96 reference(s)		66-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
95 reference(s)
67-LesCourbesRemplissantes.02.Fra
94 reference(s)		68-Galerie_ParticleSystems.FV
94 reference(s)
69-Galerie_GeneralitiesVisualization.FV
94 reference(s)		70-DroitDeReponse.01.Fra
94 reference(s)
71-Galerie_NewPictures.FV
93 reference(s)		72-fractal.01
92 reference(s)
73-PerteDeLAssociativite.01
92 reference(s)		74-GoldenTriangle.01.Fra
92 reference(s)
75-MonodimensionalCellularAutomata.01.Fra
91 reference(s)		76-MathematiquesPhysiqueFractales.12
91 reference(s)
77-AnimFractal.01.
91 reference(s)		78-SurfaceProjector.01.Ang
90 reference(s)
79-Multivers.01.Fra
90 reference(s)		80-LeParadoxeDeFermi.01.Fra
89 reference(s)
81-WelcomeToMars.01.Ang
88 reference(s)		82-LesCourbesRemplissantes.01.Fra
88 reference(s)
83-Claude.11.AVirtualSpaceTimeTravelMachine.01.Fra
88 reference(s)		84-ChatGPT.11.AVirtualSpaceTimeTravelMachine.01.Fra
88 reference(s)
85-ChatGPT.01.Ang
88 reference(s)		86-WelcomeToMars.01.Fra
87 reference(s)
87-LesNombresTranscendants.01.Fra
87 reference(s)		88-GilbreathConjecture.01.Ang
87 reference(s)
89-Galerie_BestOf.FV
87 reference(s)		90-Exposition_EcolePolytechnique_FeteDeLaScience_202510
87 reference(s)
91-Galerie_HommageAPatriceJeener.FV
86 reference(s)		92-DieuScience.01.Fra
86 reference(s)
93-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
86 reference(s)		94-DEuclideAuGPS.01.Fra
86 reference(s)
95-ChatGPT.11.AVirtualSpaceTimeTravelMachine.01.Ang
86 reference(s)		96-AProposSite.01.Fra
85 reference(s)
97-RealNumbers.01.Fra
83 reference(s)		98-EntrelacsIntertwinings.01.Fra
83 reference(s)
99-DecimalesPi_1_100.vv
83 reference(s)		100-LeCinquantenaireDuCMAP.01.vv.Fra
82 reference(s)
101-LesCourbesRemplissantes.02.Ang
81 reference(s)		102-LeNoeudInfini.01.Fra
81 reference(s)
103-IrreversibiliteDuTempsNumerique.01.Ang
81 reference(s)		104-AVirtualSpaceTimeTravelMachine.Fra
81 reference(s)
105-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_1
80 reference(s)		106-create.03.
80 reference(s)
107-RemarquesCerveau.01
80 reference(s)		108-QuelquesQuestionsSurLaRecherche.01.Fra
80 reference(s)
109-Polynomials_RationalNumbers.01.Ang
80 reference(s)		110-MathematiquesPhysiqueFractales.22
80 reference(s)
111-MathematiquesPhysiqueFractales.02.1.12
80 reference(s)		112-HughEverettMultiverse.01.Fra
80 reference(s)
113-Galerie_SelfPortraits.FV
80 reference(s)		114-Galerie_Pi.FV
80 reference(s)
115-ExpV_VirE.Ang
80 reference(s)		116-EntrelacsIntertwinings.01.Ang
80 reference(s)
117-DecimalesPi_100000.vv
80 reference(s)		118-ImpossibleStructures.01.Fra
79 reference(s)
119-Galerie_RCMGalerie.FV
79 reference(s)		120-Galerie_NumbersAndLight.FV
79 reference(s)
121-BilletDHumeur_IntelligenceArtificielle.01.Fra
79 reference(s)		122-Bard.01.Fra
79 reference(s)
123-MathematiquesPhysiqueFractales.02.27
78 reference(s)		124-Informations_GoodNewsAndBadNews.01.Fra
78 reference(s)
125-MathematiquesPhysiqueFractales.02.11.3
77 reference(s)		126-Galerie_CelestialMechanics.FV
77 reference(s)
127-VirtualChaos.01.Fra
76 reference(s)		128-Le_Chat.01.Fra
76 reference(s)

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




Copyright © Jean-François COLONNA, -2026.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, -2026.