Monthly Best Of on 09/28/2021




An interpolation between a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')and a tridimensional Verhulst dynamics -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 09/28/2021 and last updated on 10/03/2024 17:04:20 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The first four iterations of the construction of the von Koch snowflake
1-80 reference(s)		Untitled 0004
2-59 reference(s)		Tridimensional display of the Riemann Zeta function inside [-10.0,+20.0]x[-15.0,+15.0] (bird's-eye view)
3-51 reference(s)		The random walk of photons escaping the Sun
4-43 reference(s)
Monument Valley at sunrise with light cloud dynamics -this sequence being periodical-
5-42 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
6-41 reference(s)		A bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle
7-41 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-
8-41 reference(s)
The bidimensional John Conway's life game
9-41 reference(s)		Bidimensional rectangular billiard with a central obstacle and an initial flow of rotating particles
10-40 reference(s)		From Mars to the Sun
11-40 reference(s)		Bidimensional zoom in on the Mandelbrot set with display of the arguments
12-40 reference(s)
The front of a forest fire -white- obtained by means of a bidimensional random walk process (bird's-eye view, zoom in on the first steps)
13-40 reference(s)		Artistic view of the prime numbers
14-40 reference(s)		Bidimensional quasi-symmetrical fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
15-39 reference(s)		Dynamics of the even distribution of 6 points on a sphere -an Octahedron- by means of simulated annealing
16-39 reference(s)
The Möbius strip
17-39 reference(s)		Quaternionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-
18-39 reference(s)		Bidimensional geometrical texture animation
19-38 reference(s)		The 'exponential' spreading of a tridimensional epidemic -the COVID-19 coronavirus?- without confinement -1430 particles-, with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-
20-38 reference(s)
The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with a zero death rate and with a 50% infection, starting with just one infected person -red particle on bottom left picture-
21-38 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-
22-38 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
23-38 reference(s)		Dynamics of the even distribution of 24 points on a sphere by means of simulated annealing
24-38 reference(s)
Bidimensional texture animation by means of the Generalized Product
25-38 reference(s)		Fractal diffusion front in a bidimensional medium obtained by means of a random walk process (zoom in on the first steps)
26-38 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 50% infection, starting with just one infected person -red particle on bottom left picture-
27-37 reference(s)		The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-
28-37 reference(s)
Tridimensional texture animation by means of the Generalized Product
29-37 reference(s)		Tridimensional zoom in on the Mandelbrot set
30-37 reference(s)		The Lorenz attractor
31-36 reference(s)		Rotation about the Y (vertical)axis of sixteen interlaced torus that can also be viewed as a set of 4x3 stereograms
32-32 reference(s)
The generalized Ulam spiral
33-30 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
34-30 reference(s)		Black dots on a square lattice
35-29 reference(s)		64 elementary bidimensional binary cellular automata with 1 white starting central point
36-29 reference(s)
The random walk of photons escaping the Sun
37-28 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
38-28 reference(s)		Autostereogram with an hidden volcano
39-27 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
40-27 reference(s)
Autostereogram with an hidden volcano
41-25 reference(s)		How to compute 'pi' with a gun
42-24 reference(s)		An interpolation between the quadruple Jeener bottle and the octuple Jeener bottle defined by means of three bidimensional fields
43-23 reference(s)		The Universe at the heart of a Calabi-Yau manifold
44-22 reference(s)
The Sierpinski Carpet -iteration 3-
45-21 reference(s)		A fractal vegetal structure
46-19 reference(s)		The Lorenz attractor
47-19 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
48-19 reference(s)
The configuration entropy of a set of n=64 particles
49-18 reference(s)		Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
50-17 reference(s)		The generalized Ulam spiral displaying 100 numbers
51-17 reference(s)		Happy new year 2000
52-17 reference(s)
An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
53-17 reference(s)		Quantum vacuum fluctuations
54-16 reference(s)		Autostereogram with an hidden ring and ghost bows
55-16 reference(s)		A tridimensional fractal manifold defined by means of three tridimensional fields
56-16 reference(s)
The Klein bottle
57-16 reference(s)		From Pluto to the Sun (non linear scales)
58-16 reference(s)		Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
59-16 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
60-16 reference(s)
The Sierpinski Carpet -iteration 1-
61-15 reference(s)		Foggy soft Archimedes mountains
62-15 reference(s)		Autostereogram with an hidden volcano
63-14 reference(s)		Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
64-13 reference(s)
The 64 first lines of the Pascal's Triangle -modulo 5-
65-13 reference(s)		The 'sharp' Golden Triangle
66-13 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
67-13 reference(s)		The random walk of photons escaping the Sun
68-13 reference(s)
Pseudo Olympic Rings
69-13 reference(s)		An Archimedes spiral displaying 100000 numbers
70-13 reference(s)		The Goldbach conjecture -the Goldbach comet- for the even numbers from 6 to 6244
71-13 reference(s)		Sixteen interlaced fractal torus
72-13 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
73-13 reference(s)		Cantor's diagonal argument
74-13 reference(s)		Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
75-12 reference(s)		An aperiodic Penrose tiling of the plane
76-12 reference(s)
An aperiodic Penrose tiling of the plane
77-12 reference(s)		The Sierpinski Carpet -iteration 3- with colors -a Tribute to Karl Menger and Piet Mondrian-
78-12 reference(s)		A twisting rope
79-12 reference(s)		A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
80-12 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')with a 1/Z conformal transformation in the complex plane -tridimensional cross-section-
81-12 reference(s)		The Goldbach conjecture -the Goldbach comet or the Goldbach rainbow- for the even numbers from 6 to 41518
82-12 reference(s)		The CMAP logo
83-12 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
84-12 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
85-12 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
86-12 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
87-12 reference(s)		True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
88-11 reference(s)
The Sierpinski Carpet -iteration 5-
89-11 reference(s)		Bidimensional cross-sections of the Klein bottle
90-11 reference(s)		The set of bidimensional fields defining the 'Y' coordinate of an interpolation between the Möbius strip and a 'double sphere'
91-11 reference(s)		Artistic variation on the generalized Ulam spiral displaying 81 numbers
92-11 reference(s)
Bidimensional zoom in on the Mandelbrot set
93-11 reference(s)		A blue Sponge-tree -a Tribute to Yves Klein-
94-11 reference(s)		The bidimensional Ising Model with 2-state spins, a centred gaussian temperature field (minimum=0.035,maximum=0.6)and random initial conditions
95-11 reference(s)		Hypercube
96-11 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
97-11 reference(s)		Heterogeneous -tridimensional fractal field- random meshing of a cube
98-11 reference(s)		The Jeener-Klein triple bottle
99-11 reference(s)		A pay slip
100-10 reference(s)
Dynamics of the even distribution of 4 points on a sphere -a Tetrahedron- by means of simulated annealing
101-10 reference(s)		Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle
102-10 reference(s)		Color palette 'rouge'
103-10 reference(s)		Sixteen portraits (Lena)with an increasing size of the pixels -from 1 to 16-
104-10 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
105-10 reference(s)		From 'geocentrism' to 'heliocentrism'
106-10 reference(s)		Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
107-10 reference(s)		Rotation about the X axis of the Lorenz attractor (1000 iterations), computed simultaneously on two different computers
108-10 reference(s)
Jean-François COLONNA
109-10 reference(s)		Jean-François COLONNA (on 11/17/1994)with its fractal mountains
110-10 reference(s)		Anaglyph -blue=right, red=left- of an hypercube
111-10 reference(s)		Isle of the Dead -a Tribute to Arnold Böcklin-
112-10 reference(s)
A distorded -for the sake of display- 5-cube -an hyperhypercube-
113-10 reference(s)		The CMAP logo
114-10 reference(s)		Rotation about the Y (vertical)axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold
115-10 reference(s)		'Le bouquet tout fait' -a Tribute to René Magritte and Sandro Botticelli-
116-10 reference(s)
Rotation about the Y (vertical)axis of the Jeener-Klein triple bottle that can also be viewed as a set of 4x3 stereograms
117-10 reference(s)		A special Klein bottle
118-10 reference(s)		Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability
119-10 reference(s)		Quantum vacuum fluctuations
120-9 reference(s)
An aperiodic Penrose tiling of the plane
121-9 reference(s)		An aperiodic Penrose tiling of the plane
122-9 reference(s)		A pseudo-periodical triangular tiling of the plane
123-9 reference(s)		4 evenly distributed points on a sphere -a Tetrahedron- by means of simulated annealing
124-9 reference(s)
The Klein bottle defined by means of three bidimensional fields
125-9 reference(s)		The generalized Ulam spiral displaying 1024 numbers
126-9 reference(s)		An Archimedes spiral displaying 100 numbers
127-9 reference(s)		Color palette 'marron'
128-9 reference(s)




2-The 128 most referenced Pages (*):

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



1-demo_14
515 reference(s)		2-AVirtualSpaceTimeTravelMachine.Ang
411 reference(s)
3-An2000.01.Fra
281 reference(s)		4-Galerie_NumberTheory.FV
280 reference(s)
5-Galerie_ArtAndScience.FV
230 reference(s)		6-Galerie_GeneralitiesVisualization.FV
222 reference(s)
7-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
200 reference(s)		8-Stereogrammes_AutoStereogrammes.01
188 reference(s)
9-help.
187 reference(s)		10-Galerie_ArtisticCreation.FV
185 reference(s)
11-RealNumbers.01.Fra
183 reference(s)		12-Galerie_DeterministicFractalGeometry.FV
182 reference(s)
13-Vcatalogue.11
180 reference(s)		14-Galerie_ParticleSystems.FV
180 reference(s)
15-copyright.01.
175 reference(s)		16-mail.01.vv
171 reference(s)
17-demo
166 reference(s)		18-demo.14
163 reference(s)
19-an2000
163 reference(s)		20-logiciel
162 reference(s)
21-demo14
161 reference(s)		22-realnumbers
160 reference(s)
23-genielogiciel
159 reference(s)		24-nombresreels
158 reference(s)
25-Fractal.01
153 reference(s)		26-ImagesDuVirtuel.01.Fra.FV
149 reference(s)
27-EntrelacsIntertwinings.01.Fra
149 reference(s)		28-MorePages.
147 reference(s)
29-MathematiquesPhysiqueFractales.02
147 reference(s)		30-Galerie_CelestialMechanics.FV
147 reference(s)
31-SurfaceProjector.01.Ang
145 reference(s)		32-Fractal.11
144 reference(s)
33-SurfaceProjector.01.Fra
143 reference(s)		34-LOG_xiMc.11
141 reference(s)
35-Galerie_ImagesDesMathematiques.FV
140 reference(s)		36-Web_Mail.01.vv
139 reference(s)
37-Informations_GoodNewsAndBadNews.01.Fra
139 reference(s)		38-FloatingPointNumbers.01.Fra
139 reference(s)
39-Galerie_QuantumMechanics.FV
137 reference(s)		40-AnimFractal.01.
137 reference(s)
41-UlamSpiral.01.Fra
135 reference(s)		42-Galerie_ImagesDidactiques.FV
134 reference(s)
43-Galerie_TextureSynthesis.FV
133 reference(s)		44-GoldenTriangle.01.Fra
132 reference(s)
45-AProposSite.01.Fra
132 reference(s)		46-NDimensionalDeterministicFractalSets.01.Ang
129 reference(s)
47-Informations_AboutPicturesAnimationsAndFiles.01.Ang
129 reference(s)		48-ImpossibleStructures.01.Fra
129 reference(s)
49-Galerie_Astrophysics.FV
129 reference(s)		50-MonodimensionalCellularAutomata.01.Fra
128 reference(s)
51-Galerie_Tributes.FV
128 reference(s)		52-MonodimensionalCellularAutomata.01.Ang
127 reference(s)
53-ImagesDuVirtuel.01.Fra
127 reference(s)		54-GenieLogiciel_VisualisationScientifique.01.vv
127 reference(s)
55-NDimensionalDeterministicFractalSets.01.Fra
125 reference(s)		56-Galerie_SensitivityToRoundingOffErrors.FV
125 reference(s)
57-Galerie_NumberTheory
125 reference(s)		58-Galerie_DeterministicChaos.FV
124 reference(s)
59-Galerie_NewPictures.FV
123 reference(s)		60-Galerie_AnthropomorphicPatterns.FV
123 reference(s)
61-PerteDeLAssociativite.01
122 reference(s)		62-AVirtualSpaceTimeTravelMachine.Fra
122 reference(s)
63-Kepler.02.
120 reference(s)		64-Fractal.21
120 reference(s)
65-EntrelacsIntertwinings.01.Ang
120 reference(s)		66-Informations_GoodNewsAndBadNews.01.Ang
119 reference(s)
67-VirtualChaos.01.Fra
118 reference(s)		68-OrdinateursEtCalculs.01.Ang
118 reference(s)
69-MOSA.LYAP.33.10000.20031207
118 reference(s)		70-Galerie_SignalProcessing.FV
117 reference(s)
71-Galerie_SalonDAutomne.FV
117 reference(s)		72-Fractal.03
117 reference(s)
73-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
116 reference(s)		74-FloatingPointNumbers.01.Ang
116 reference(s)
75-FaireDeLaRecherche.01.vv
116 reference(s)		76-Commentaires_EnsembleJuliaOctonion.01
116 reference(s)
77-ArtEtMathematiques.01
116 reference(s)		78-Galerie_NewPictures
115 reference(s)
79-ImpossibleStructures.01.Ang
114 reference(s)		80-ImagesEncadreesDisponibles.01
114 reference(s)
81-subject.01.
113 reference(s)		82-LeParadoxeDeFermi.01.Fra
113 reference(s)
83-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
113 reference(s)		84-present.01.
112 reference(s)
85-infinity.01.vv
112 reference(s)		86-UlamSpiral.01.Ang
112 reference(s)
87-NatureDesMathematiques.01.vv.Fra
112 reference(s)		88-IllusionConnaissance.02
112 reference(s)
89-GenieLogiciel.01.Fra
112 reference(s)		90-Exposition_MairieCinquiemeArrondissementParis_202001_202002
111 reference(s)
91-Galerie_DeterministicFractalGeometry
110 reference(s)		92-DieuScience.01.Fra
110 reference(s)
93-ExpV_VirE.11
109 reference(s)		94-VirtualChaos.01.Ang
108 reference(s)
95-SourceExemple_____xrq_____hydrogene.61.K.
108 reference(s)		96-Galerie_ArtisticCreation.DIAPO.0010
108 reference(s)
97-DecimalesPi_1_100.vv
108 reference(s)		98-Commentaires_NKleinBottle.01
108 reference(s)
99-AQuoiServentLesMathematiques.01
108 reference(s)		100-Informations_AboutPicturesAnimationsAndFiles.01.Fra
107 reference(s)
101-ExpV_VirE.Ang
107 reference(s)		102-Pcatalogue.11
106 reference(s)
103-Galerie_ParticleSystems
106 reference(s)		104-Exposition_EcolePolytechnique_FeteDeLaScience_201910
106 reference(s)
105-DuModeleALImage.02.Fra
106 reference(s)		106-Autostereograms.01.
106 reference(s)
107-HommageBenoitMandelbrot.11
105 reference(s)		108-Galerie_FluidMechanics.FV
105 reference(s)
109-Fractal.02
105 reference(s)		110-OrdinateursEtCalculs.01.Fra
104 reference(s)
111-Notations_AppartientA.01
104 reference(s)		112-ManyChaos.01.Ang
104 reference(s)
113-GoldenTriangle.01.Ang
104 reference(s)		114-Commentaires_DefinitionPseudoQuaternions.01
104 reference(s)
115-create.03.
103 reference(s)		116-NombresEtLumiere.01.vv.Fra
103 reference(s)
117-Multivers.01.Fra
103 reference(s)		118-MathematiquesPhysiqueFractales.12
103 reference(s)
119-LeParadoxeDeFermi.01.Ang
103 reference(s)		120-HommageBenoitMandelbrot.21
103 reference(s)
121-Galerie_BestOf.FV
103 reference(s)		122-ConjectureDeSyracuse_0128.Parity.vv
103 reference(s)
123-BEST.20180228
103 reference(s)		124-catalogue.11
102 reference(s)
125-OrdinateurMathematiquesArt.01.Fra
102 reference(s)		126-DecimalesPi_100000.vv
102 reference(s)
127-DecimalesDePi.01.Fra
102 reference(s)		128-NombresPremiers_10000.vv
101 reference(s)

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




Copyright © Jean-François COLONNA, 2021-2024.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2021-2024.