Monthly Best Of on 12/28/2024




Tridimensional fractal structure

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 12/28/2024 and last updated on 12/28/2024 22:07:40 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The numerical reversibility of the bidimensional billiard -192 particles-
1-657 reference(s)		The eroded Menger Sponge -iteration 3-
2-624 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
3-468 reference(s)		Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
4-321 reference(s)
The Goldbach conjecture
5-268 reference(s)		Tridimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity
6-216 reference(s)		N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed with 2 slightly different sets of initial conditions (sensitivity to initial conditions)
7-191 reference(s)		The numerical irreversibility of the bidimensional billiard -768 particles-
8-176 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
9-145 reference(s)		The random walk of photons escaping the Sun
10-140 reference(s)		A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
11-135 reference(s)		Autostereogram with an hidden volcano
12-130 reference(s)
The self-similarity of the von Koch curve displayed by means of a zoom in with a ratio that is equal to 3
13-115 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
14-115 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-
15-101 reference(s)		The numerical irreversibility of the bidimensional billiard -336 particles-
16-98 reference(s)
The dynamics of the diffusion process in a bidimensional medium obtained by means of a random walk process
17-95 reference(s)		Isotropic random walk of 64 particles on a bidimensional square lattice
18-94 reference(s)		Bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity
19-91 reference(s)		The first four iterations of the construction of the von Koch snowflake
20-90 reference(s)
Bidimensional domino effect
21-89 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
22-86 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
23-85 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
24-81 reference(s)
The generalized Ulam spiral
25-80 reference(s)		Bidimensional zoom in on the Mandelbrot set
26-80 reference(s)		The random walk of photons escaping the Sun
27-79 reference(s)		Artistic view of the prime numbers
28-79 reference(s)
Tridimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity
29-78 reference(s)		Autostereogram of the CMAP
30-77 reference(s)		Bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to an attractive central field of gravity
31-77 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
32-75 reference(s)
Along the border of the Mandelbrot set
33-73 reference(s)		Erosion of a bidimensional random (with large scale correlations)island
34-73 reference(s)		The distances Sun-Earth-Jupiter-Saturn-Uranus-Neptune during one neptunian year
35-72 reference(s)		Iterations in the complex plane: the computation of the Mandelbrot set
36-72 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
37-72 reference(s)		Dynamics of the even distribution of 24 points on a sphere by means of simulated annealing
38-71 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 409.6 time units
39-70 reference(s)		Rotation about the Y (vertical)axis of a tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
40-70 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
41-70 reference(s)		A distorded -for the sake of display- 5-cube -an hyperhypercube-
42-68 reference(s)		The number of divisors of the 1.024 first integer numbers on a Bidimensional Hilbert Curve -iteration 5-
43-67 reference(s)		Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-
44-66 reference(s)
Rotation about the Y (vertical)axis of a tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation) that can also be viewed as a set of 4x3 stereograms
45-66 reference(s)		Fractal diffusion front in a bidimensional medium obtained by means of a random walk process
46-66 reference(s)		Rotation about the Y (vertical)axis of the CMAP logo that can also be viewed as a set of 4x3 stereograms
47-66 reference(s)		A Peano 'fractal plane' defined by means of three bidimensional fields
48-65 reference(s)
A regular 7-gon -an heptagon-
49-65 reference(s)		From Pluto to the Sun -extrapolation 2-
50-65 reference(s)		A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
51-65 reference(s)		Autostereogram with an hidden volcano
52-64 reference(s)
Bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
53-63 reference(s)		From Pluto to the Sun
54-63 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
55-63 reference(s)		The Lorenz attractor
56-62 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
57-62 reference(s)		Bidimensional geometrical texture animation
58-61 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-
59-61 reference(s)		Bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity
60-59 reference(s)
The ABC conjecture
61-59 reference(s)		Hypercube
62-58 reference(s)		About the length of the von Koch curve
63-57 reference(s)		The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- with partial confinement -201 particles-, with a zero death rate and a 100% infection, starting with just one infected person -red particle on bottom left picture-
64-57 reference(s)
The number of divisors of the 512 first integer numbers on a Tridimensional Hilbert Curve -iteration 1-
65-57 reference(s)		Waltzing Monument Valley
66-57 reference(s)		The bidimensional John Conway's life game
67-57 reference(s)		Isle of the Dead -a Tribute to Arnold Böcklin-
68-57 reference(s)
Rotation about the X axis of a tridimensional brownian motion
69-57 reference(s)		Bidimensional rectangular billiard with 64 isotropic particles and without collisions
70-56 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
71-56 reference(s)		The Many World Theory of Hugh Everett
72-55 reference(s)
Cauliflowers, seaweeds, shells,...
73-55 reference(s)		A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of the square root of 2 (414213...)-base 10- with 33.333 time steps
74-55 reference(s)		Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
75-55 reference(s)		A fractal Möbius strip
76-55 reference(s)
The Piet Mondrian quadridimensional Calabi-Yau manifold -2D, 3D or 4D?-
77-55 reference(s)		LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
78-55 reference(s)		The Syracuse conjecture for U(0)={1,2,3,4,...,128} -monodimensional display-
79-54 reference(s)		Tridimensional billiard with 12 -initially- still particles submitted to an attractive central field of gravity
80-54 reference(s)
Bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
81-54 reference(s)		24 evenly distributed points on a sphere by means of simulated annealing
82-54 reference(s)		A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
83-54 reference(s)		The Mandelbrot set computed for 1 to 16 iterations with display of the arguments
84-54 reference(s)
A set of 4x3 stereograms of a fractal Klein bottle
85-54 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
86-54 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
87-54 reference(s)		The seven first bifurcation levels (over fifteen)of the human lung tree
88-54 reference(s)
Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
89-53 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
90-53 reference(s)		Simple random triangulation of the surface of a torus -18x18-
91-53 reference(s)		Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
92-53 reference(s)
Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
93-52 reference(s)		A Lissajous surface
94-52 reference(s)		Bidimensional Sierpinski billiard with 326 isotropic particles submitted to a strong vertical field of gravity
95-52 reference(s)		From 'geocentrism' to 'heliocentrism'
96-52 reference(s)
A random Menger Sponge -iteration 5-
97-52 reference(s)		Regular quadrangulation of the surface of a cylinder -18x18-
98-52 reference(s)		Happy new year 2000
99-52 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
100-52 reference(s)
Cantor's diagonal argument
101-52 reference(s)		The ABC conjecture
102-52 reference(s)		The Universe at the heart of a Calabi-Yau manifold
103-51 reference(s)		A fractal vegetal structure -'the Knowledge Tree'-
104-51 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
105-51 reference(s)		The numerical irreversibility of the bidimensional billiard -1376 particles-
106-51 reference(s)		Quark and gluon structure of a nucleon
107-51 reference(s)		N-body problem integration (N=3)with one yellow star and two planets (the red one being very heavy and the blue one being light)
108-51 reference(s)
Tridimensional visualizations of the Verhulst dynamics
109-51 reference(s)		Rotation about the Y (vertical)axis of the 5-foil torus knot on its torus, that can also be viewed as a set of 4x3 stereograms
110-51 reference(s)		A blue Sponge-tree -a Tribute to Yves Klein-
111-51 reference(s)		Black dots on a square lattice
112-51 reference(s)
Tridimensional Hilbert Curve -iteration 4-
113-51 reference(s)		Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
114-51 reference(s)		The Klein bottle
115-51 reference(s)		Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
116-50 reference(s)
The Syracuse conjecture for U(0)={3,6,9,12,...,786432}
117-50 reference(s)		Autostereogram with an hidden volcano
118-50 reference(s)		Rotation about the Y (vertical)axis of a tridimensional fractal aggregate that can also be viewed as a set of 4x3 pseudo-stereograms
119-50 reference(s)		Computation of the roots of Z^3=1 using Newton's method
120-50 reference(s)
An interpolation between two sets of interlaced torus -four and sixteen respectively- defined by means of three sets of bidimensional fields
121-50 reference(s)		Monument Valley at sunrise with light cloud dynamics -this sequence being periodical-
122-50 reference(s)		The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
123-50 reference(s)		From Pluto to the Sun (linear scales)
124-50 reference(s)
From Mars to the Sun
125-50 reference(s)		Double random triangulation of the volume of a sphere -8x8x8-
126-50 reference(s)		2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-
127-50 reference(s)		The Continuum Hypothesis (CH)
128-50 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
2230 reference(s)		2-Web_Mail.01.vv
247 reference(s)
3-Stereogrammes_AutoStereogrammes.01
158 reference(s)		4-Galerie_Animations.FV
137 reference(s)
5-demo_14
105 reference(s)		6-Vcatalogue.11
103 reference(s)
7-mail.01.vv
93 reference(s)		8-An2000.01.Fra
92 reference(s)
9-help.
88 reference(s)		10-ChatGPT.01.Fra
79 reference(s)
11-copyright.01.
75 reference(s)		12-avirtualspacetimetravelmachine.ang
73 reference(s)
13-Galerie_ParticleSystems.FV
72 reference(s)		14-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
72 reference(s)
15-ChatGPT.11.Fra
72 reference(s)		16-Galerie_NewPictures.FV
70 reference(s)
17-FloatingPointNumbers.01.Ang
70 reference(s)		18-xiirs_____.nota.t.
66 reference(s)
19-Informations_AboutPicturesAnimationsAndFiles.01.Ang
66 reference(s)		20-Fractal.01
62 reference(s)
21-LOG_xiMc.11
61 reference(s)		22-DecimalesDePi.01.Fra
61 reference(s)
23-AProposSite.01.Fra
61 reference(s)		24-IAGenerativesImages.01.Fra
59 reference(s)
25-Galerie_GeneralitiesVisualization.FV
59 reference(s)		26-xiirc_____.nota.t.
58 reference(s)
27-PerteDeLAssociativite.01.MUL3
58 reference(s)		28-stereogrammes_autostereogrammes.01
57 reference(s)
29-EntrelacsIntertwinings.01.Fra
57 reference(s)		30-subject.01.
56 reference(s)
31-UlamSpiral.01.Ang
56 reference(s)		32-Fractal.21
56 reference(s)
33-DecimalesPi_100000.vv
55 reference(s)		34-xtp_____AXmB.01.python.
54 reference(s)
35-UlamSpiral.01.Fra
54 reference(s)		36-Kepler.02.
54 reference(s)
37-catalogue.11
53 reference(s)		38-Informations_GoodNewsAndBadNews.01.Fra
53 reference(s)
39-Galerie_NumberTheory.FV
53 reference(s)		40-FloatingPointNumbers.01.Fra
53 reference(s)
41-DecimalesPi_1_100.vv
53 reference(s)		42-xiirk_____.nota.t.
52 reference(s)
43-An2000.03.Fra
51 reference(s)		44-xias_____.nota.t.
50 reference(s)
45-Exposition_EcolePolytechnique_CentenaireNaissanceBenoitMandelbrot_202410_202411_202412
50 reference(s)		46-SourceExemple_____xtc_____stereogra.01.c.
49 reference(s)
47-NombresEtLumiere.01.vv.Fra
49 reference(s)		48-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
49 reference(s)
49-Galerie_DeterministicFractalGeometry.FV
49 reference(s)		50-Galerie_ArtisticCreation.FV
49 reference(s)
51-Fractal.11
49 reference(s)		52-ChatGPT.01.Ang
49 reference(s)
53-MartiensEtMathematiques.01.Ang
48 reference(s)		54-LeParadoxeDeFermi.01.Fra
48 reference(s)
55-Bard.01.Ang
48 reference(s)		56-xiirv_____.nota.t.
47 reference(s)
57-Polynomials_RationalNumbers.01.Ang
47 reference(s)		58-PerteDeLAssociativite.01
47 reference(s)
59-MathematiquesPhysiqueFractales.02
47 reference(s)		60-LesCourbesRemplissantes.01.Ang
47 reference(s)
61-Informations_GoodNewsAndBadNews.01.Ang
47 reference(s)		62-Galerie_CollaborativeWorks..FV
47 reference(s)
63-Galerie_CelestialMechanics.FV
47 reference(s)		64-Galerie_ArtAndScience.FV
47 reference(s)
65-EntrelacsIntertwinings.01.Ang
47 reference(s)		66-AVirtualSpaceTimeTravelMachine.Fra
47 reference(s)
67-xiia_____.nota.t.
46 reference(s)		68-SurfaceProjector.01.Ang
46 reference(s)
69-NombresPremiers_10000.vv
46 reference(s)		70-NatureDesMathematiques.01.vv.Fra
46 reference(s)
71-NDimensionalDeterministicFractalSets.01.Ang
46 reference(s)		72-Galerie_DeterministicChaos.FV
46 reference(s)
73-Multivers.01.Fra
45 reference(s)		74-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis
45 reference(s)
75-Galerie_ImagesDesMathematiques.FV
45 reference(s)		76-Exposition_EcolePolytechnique_FeteDeLaScience_201910
45 reference(s)
77-ChatGPT.11.Ang
45 reference(s)		78-Pcatalogue.11
44 reference(s)
79-MathematiquesPhysiqueFractales.12
44 reference(s)		80-EnsembleDesGaleries.DIAPO.0795
44 reference(s)
81-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
44 reference(s)		82-Commentaires_DefinitionPseudoQuaternions.01
44 reference(s)
83-xiirf_____.nota.t.
43 reference(s)		84-MiseEnSceneDesNombres.01.vv.Ang
43 reference(s)
85-LesCourbesRemplissantes.02.Ang
43 reference(s)		86-Galerie_Pi.FV
43 reference(s)
87-Commentaires_DefinitionOctonions.01
43 reference(s)		88-AnimFractal.01.
43 reference(s)
89-xiaf_____.nota.t.
42 reference(s)		90-create.03.
42 reference(s)
91-MonodimensionalCellularAutomata.01.Ang
42 reference(s)		92-LesCourbesRemplissantes.01.Fra
42 reference(s)
93-LesApprentisDieux.01
42 reference(s)		94-Galerie_QuantumMechanics.FV
42 reference(s)
95-Exposition_OperaDeMassy_201912_202001
42 reference(s)		96-Commentaires_EnsembleMandelbrotOctonion.01
42 reference(s)
97-xiak_____.nota.t.
41 reference(s)		98-MesExpositionsPassees.01
41 reference(s)
99-GoldenTriangle.01.Fra
41 reference(s)		100-GoldenTriangle.01.Ang
41 reference(s)
101-Commentaires_EspaceLyapunovComplexe.01
41 reference(s)		102-BEST.20130728
41 reference(s)
103-xiav_____.nota.t.
40 reference(s)		104-MathematiquesPhysiqueFractales.22
40 reference(s)
105-Galerie_NumbersAndLight.FV
40 reference(s)		106-Galerie_ImagesDidactiques.FV
40 reference(s)
107-Galerie_Astrophysics.FV
40 reference(s)		108-ExpV_VirE.Ang
40 reference(s)
109-infinity.01.vv
39 reference(s)		110-VirtualChaos.01.Ang
39 reference(s)
111-SIlVousPlaitDessineMoiLInfini.01.Fra
39 reference(s)		112-Notations_AppartientA.01
39 reference(s)
113-Multivers.01.Ang
39 reference(s)		114-LesNombresTranscendants.01.Fra
39 reference(s)
115-LesCourbesRemplissantes.02.Fra
39 reference(s)		116-ImagesDuVirtuel.01.Fra.FV
39 reference(s)
117-Galerie_TextureSynthesis.FV
39 reference(s)		118-Fractal.03
39 reference(s)
119-xiirC_____.nota.t.
38 reference(s)		120-xiac_____.nota.t.
38 reference(s)
121-RemarquesCerveau.01
38 reference(s)		122-Informations_AboutPicturesAnimationsAndFiles.01.Fra
38 reference(s)
123-ExpositionsDiverses.01.Fra
38 reference(s)		124-Autostereograms.01.
38 reference(s)
125-An2000.06.Fra
38 reference(s)		126-RasoirDOccamEtMathematiques.01.vv.Ang
37 reference(s)
127-OrdinateurMathematiquesArt.01.Fra
37 reference(s)		128-NombresEtLumiere.02.vv.Ang
37 reference(s)

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




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