Monthly Best Of on 10/28/2021




A pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-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 10/28/2021 and last updated on 11/14/2023 17:50:17 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



Artistic view of the prime numbers
1-732 reference(s)		 The generalized Ulam spiral
2-71 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
3-62 reference(s)		 Untitled 0004
4-57 reference(s)
The random walk of photons escaping the Sun
5-56 reference(s)		 Quaternionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-
6-53 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-10.0,+20.0]x[-15.0,+15.0] (bird's-eye view)
7-50 reference(s)		 Fractal diffusion front in a bidimensional medium obtained by means of a random walk process (zoom in on the first steps)
8-50 reference(s)
The Universe at the heart of a Calabi-Yau manifold
9-48 reference(s)		 The bidimensional John Conway's life game
10-46 reference(s)		 Autostereogram with an hidden volcano
11-44 reference(s)		 Tridimensional zoom in on the Mandelbrot set
12-44 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
13-42 reference(s)		 A bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle
14-42 reference(s)		 Tridimensional texture animation by means of the Generalized Product
15-42 reference(s)		 Monument Valley at sunrise with light cloud dynamics -this sequence being periodical-
16-42 reference(s)
From Mars to the Sun
17-42 reference(s)		 Bidimensional rectangular billiard with a central obstacle and an initial flow of rotating particles
18-41 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-
19-41 reference(s)		 Bidimensional zoom in on the Mandelbrot set with display of the arguments
20-41 reference(s)
Bidimensional geometrical texture animation
21-40 reference(s)		 Dynamics of the even distribution of 6 points on a sphere -an Octahedron- by means of simulated annealing
22-40 reference(s)		 Dynamics of the even distribution of 24 points on a sphere by means of simulated annealing
23-40 reference(s)		 Bidimensional texture animation by means of the Generalized Product
24-40 reference(s)
The Möbius strip
25-40 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)
26-40 reference(s)		 The Sierpinski carpet -iteration 1 to 5-
27-39 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-
28-39 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-
29-39 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-
30-39 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-
31-39 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-
32-39 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
33-39 reference(s)		 A 'crumpled' Klein bottle defined by means of three bidimensional fields
34-35 reference(s)		 Happy new year 2000
35-33 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
36-33 reference(s)
A surface between the Möbius strip and the Klein bottle defined by means of three bidimensional fields
37-32 reference(s)		 A fractal vegetal structure
38-31 reference(s)		 Visualization of the Newton's method when computing the roots of Z^8=1
39-31 reference(s)		 64 elementary bidimensional binary cellular automata with 1 white starting central point
40-31 reference(s)
The generalized Ulam spiral
41-30 reference(s)		 Tridimensional fractal cross -iteration 4-
42-30 reference(s)		 The Klein bottle defined by means of three bidimensional fields
43-29 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
44-29 reference(s)
An aperiodic Penrose tiling of the plane
45-28 reference(s)		 Autostereogram with an hidden volcano
46-28 reference(s)		 Black dots on a square lattice
47-28 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
48-28 reference(s)
The random walk of photons escaping the Sun
49-27 reference(s)		 Cantor's diagonal argument
50-27 reference(s)		 The random walk of photons escaping the Sun
51-26 reference(s)		 Autostereogram with an hidden ring and ghost bows
52-25 reference(s)
The generalized Ulam spiral displaying 100 numbers
53-25 reference(s)		 The Bonan-Jeener-Klein triple bottle
54-25 reference(s)		 An aperiodic Penrose tiling of the plane
55-24 reference(s)		 A tridimensional fractal manifold defined by means of three tridimensional fields
56-24 reference(s)
Quantum vacuum fluctuations
57-23 reference(s)		 Quantum vacuum fluctuations
58-23 reference(s)		 An Archimedes spiral displaying 1000 numbers
59-23 reference(s)		 The Lorenz attractor
60-23 reference(s)
The Goldbach conjecture -the Goldbach comet- for the even numbers from 6 to 6244
61-23 reference(s)		 The Eratosthene sieve displaying 100x100 numbers
62-22 reference(s)		 N-body problem integration (N=3)displaying two planets with symmetrical initial conditions on circular trajectories
63-22 reference(s)		 Jean-François COLONNA (on 11/17/1994)with its fractal mountains
64-22 reference(s)
A special Klein bottle
65-22 reference(s)		 A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
66-21 reference(s)		 The Syracuse conjecture for U(0)={5,6,7,8,...,68} -'pseudo-ramdom walk' display: 'The Syracuse Sun'-
67-21 reference(s)		 The Sierpinski carpet -iteration 3-
68-21 reference(s)
A pay slip
69-21 reference(s)		 Recursive subdivision of four Golden Rectangles -a Tribute to Piet Mondrian-
70-21 reference(s)		 A surface between the Möbius strip and the Klein bottle defined by means of three bidimensional fields
71-21 reference(s)		 Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
72-21 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
73-21 reference(s)		 Rotation about the Y (vertical)axis of sixteen interlaced torus that can also be viewed as a set of 4x3 stereograms
74-20 reference(s)		 From Pluto to the Sun -extrapolation 2-
75-20 reference(s)		 From Pluto to the Sun (non linear scales)
76-20 reference(s)
Sixteen interlaced fractal torus
77-20 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
78-20 reference(s)		 The first four iterations of the construction of the von Koch snowflake
79-19 reference(s)		 Autostereogram with an hidden volcano
80-19 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)
81-19 reference(s)		 Tridimensional Hilbert Curve -iteration 3-
82-19 reference(s)		 A truncated quadrimensional Calabi-Yau manifold with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
83-19 reference(s)		 True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
84-18 reference(s)
The Sierpinski carpet -iteration 1-
85-18 reference(s)		 Artistic variation on the generalized Ulam spiral displaying 81 numbers
86-18 reference(s)		 Zoom in on a pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
87-18 reference(s)		 Hypercube
88-18 reference(s)
Isle of the Dead -a Tribute to Arnold Böcklin-
89-18 reference(s)		 Tridimensional visualization of a bidimensional turbulent flow
90-18 reference(s)		 Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
91-18 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
92-18 reference(s)
The Klein bottle
93-18 reference(s)		 One of the two subdivisions of the 'flat' Golden Triangle
94-17 reference(s)		 The Sierpinski carpet -iteration 5-
95-17 reference(s)		 The pseudo-quaternionic fractal set obtained when computing the roots of Q^3=1 using Newton's method with translation along the third axis of the pseudo-quaternionic space (a 'NewtonBulb') -tridimensional cross-section-
96-17 reference(s)
The generalized Ulam spiral displaying 1024 numbers
97-17 reference(s)		 Foggy soft Archimedes mountains
98-17 reference(s)		 Bidimensional zoom in on the Mandelbrot set
99-17 reference(s)		 A one sheet hyperboloid of revolution -negative curvature-
100-17 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
101-17 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
102-17 reference(s)		 The 'sharp' Golden Triangle
103-16 reference(s)		 One of the two subdivisions of the 'flat' Golden Triangle
104-16 reference(s)
A perfect tridimensional piston with following initial conditions: still piston, high temperature particles at left and low temperature particles at right, in a tridimensional box submitted to a vertical field of gravity
105-16 reference(s)		 Pseudo Olympic Rings
106-16 reference(s)		 A 'spiraling plane' defined by means of three bidimensional fields with depth of field effect
107-16 reference(s)		 Mountains and light cloud dynamics -this sequence being periodical-
108-16 reference(s)
Anaglyph -blue=right, red=left- of a tridimensional filamentous fractal structure
109-16 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
110-16 reference(s)		 The normal field of a tridimensional representation of a quadridimensional Calabi-Yau manifold
111-16 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
112-16 reference(s)
16 complex Julia sets along the border of the Mandelbrot set with display of the iteration numbers
113-15 reference(s)		 Along the border of the Mandelbrot set
114-15 reference(s)		 The Boy surface
115-15 reference(s)		 Tridimensional fractal aggregate with variable fractal dimension -increasing from front to back-
116-15 reference(s)
24 evenly distributed points on a sphere by means of simulated annealing
117-15 reference(s)		 Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle
118-15 reference(s)		 The Eratosthene sieve displaying 10x10 numbers
119-15 reference(s)		 Autostereogram with an hidden volcano and 64 self-portraits
120-15 reference(s)
Vibrating Tridimensional Hilbert Curve -iteration 3-
121-15 reference(s)		 Fractal 3-foil torus knot
122-15 reference(s)		 A fractal Möbius strip
123-15 reference(s)		 Synthesis of tridimensional textures by means of a fractal process
124-15 reference(s)
Fractal diffusion front in a bidimensional medium obtained by means of a random walk process
125-15 reference(s)		 A distorded -for the sake of display- 5-cube -an hyperhypercube-
126-15 reference(s)		 Heterogeneous -tridimensional fractal field- random meshing of a cube
127-15 reference(s)		 The Jeener-Klein triple bottle
128-15 reference(s)




2-The 128 most referenced Pages (*):

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



1-demo_14
432 reference(s)		 2-AVirtualSpaceTimeTravelMachine.Ang
425 reference(s)
3-An2000.01.Fra
338 reference(s)		 4-Galerie_NumberTheory.FV
292 reference(s)
5-help.
243 reference(s)		 6-Galerie_ArtisticCreation.FV
243 reference(s)
7-Galerie_GeneralitiesVisualization.FV
222 reference(s)		 8-Galerie_DeterministicFractalGeometry.FV
213 reference(s)
9-Galerie_ArtAndScience.FV
211 reference(s)		 10-Vcatalogue.11
202 reference(s)
11-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
196 reference(s)		 12-RealNumbers.01.Fra
194 reference(s)
13-mail.01.vv
190 reference(s)		 14-Galerie_ParticleSystems.FV
188 reference(s)
15-copyright.01.
187 reference(s)		 16-Stereogrammes_AutoStereogrammes.01
181 reference(s)
17-demo
172 reference(s)		 18-realnumbers
170 reference(s)
19-logiciel
170 reference(s)		 20-demo14
170 reference(s)
21-demo.14
170 reference(s)		 22-nombresreels
168 reference(s)
23-an2000
168 reference(s)		 24-genielogiciel
166 reference(s)
25-ImagesDuVirtuel.01.Fra.FV
163 reference(s)		 26-OrdinateursEtCalculs.01.Ang
157 reference(s)
27-Web_Mail.01.vv
156 reference(s)		 28-Galerie_CelestialMechanics.FV
156 reference(s)
29-Fractal.01
155 reference(s)		 30-FloatingPointNumbers.01.Fra
155 reference(s)
31-FloatingPointNumbers.01.Ang
155 reference(s)		 32-Fractal.11
154 reference(s)
33-Galerie_TextureSynthesis.FV
152 reference(s)		 34-SurfaceProjector.01.Fra
151 reference(s)
35-LOG_xiMc.11
149 reference(s)		 36-MathematiquesPhysiqueFractales.02
148 reference(s)
37-EntrelacsIntertwinings.01.Ang
145 reference(s)		 38-Galerie_Tributes.FV
144 reference(s)
39-Galerie_ImagesDidactiques.FV
144 reference(s)		 40-Informations_GoodNewsAndBadNews.01.Fra
143 reference(s)
41-Galerie_ImagesDesMathematiques.FV
143 reference(s)		 42-SurfaceProjector.01.Ang
142 reference(s)
43-Informations_AboutPicturesAnimationsAndFiles.01.Ang
142 reference(s)		 44-ImpossibleStructures.01.Fra
142 reference(s)
45-AProposSite.01.Fra
141 reference(s)		 46-GoldenTriangle.01.Fra
140 reference(s)
47-subject.01.
139 reference(s)		 48-VirtualChaos.01.Fra
138 reference(s)
49-NDimensionalDeterministicFractalSets.01.Ang
138 reference(s)		 50-Galerie_NewPictures.FV
138 reference(s)
51-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
138 reference(s)		 52-NDimensionalDeterministicFractalSets.01.Fra
136 reference(s)
53-Galerie_QuantumMechanics.FV
136 reference(s)		 54-AnimFractal.01.
136 reference(s)
55-UlamSpiral.01.Fra
135 reference(s)		 56-MorePages.
135 reference(s)
57-GenieLogiciel.01.Fra
135 reference(s)		 58-Galerie_Astrophysics.FV
135 reference(s)
59-MonodimensionalCellularAutomata.01.Ang
134 reference(s)		 60-Galerie_AnthropomorphicPatterns.FV
134 reference(s)
61-ArtEtMathematiques.01
134 reference(s)		 62-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
133 reference(s)
63-ImagesDuVirtuel.01.Fra
133 reference(s)		 64-Kepler.02.
132 reference(s)
65-GenieLogiciel_VisualisationScientifique.01.vv
132 reference(s)		 66-Galerie_DeterministicChaos.FV
130 reference(s)
67-Fractal.21
130 reference(s)		 68-DecimalesPi_1_100.vv
129 reference(s)
69-ImagesEncadreesDisponibles.01
128 reference(s)		 70-Galerie_SensitivityToRoundingOffErrors.FV
128 reference(s)
71-present.01.
127 reference(s)		 72-NatureDesMathematiques.01.vv.Fra
127 reference(s)
73-MonodimensionalCellularAutomata.01.Fra
127 reference(s)		 74-Commentaires_NKleinBottle.01
127 reference(s)
75-ImpossibleStructures.01.Ang
126 reference(s)		 76-AVirtualSpaceTimeTravelMachine.Fra
126 reference(s)
77-MathematiquesPhysiqueFractales.12
125 reference(s)		 78-create.03.
124 reference(s)
79-LeParadoxeDeFermi.01.Fra
124 reference(s)		 80-Galerie_SalonDAutomne.FV
124 reference(s)
81-DieuScience.01.Fra
124 reference(s)		 82-infinity.01.vv
123 reference(s)
83-Informations_GoodNewsAndBadNews.01.Ang
123 reference(s)		 84-Galerie_SignalProcessing.FV
123 reference(s)
85-FaireDeLaRecherche.01.vv
123 reference(s)		 86-Exposition_EcolePolytechnique_FeteDeLaScience_201910
123 reference(s)
87-UlamSpiral.01.Ang
122 reference(s)		 88-PerteDeLAssociativite.01
122 reference(s)
89-AQuoiServentLesMathematiques.01
122 reference(s)		 90-MOSA.LYAP.33.10000.20031207
121 reference(s)
91-ExpV_VirE.11
121 reference(s)		 92-ExpV_VirE.Ang
120 reference(s)
93-DecimalesPi_100000.vv
120 reference(s)		 94-SourceExemple_____xrq_____hydrogene.61.K.
119 reference(s)
95-LeParadoxeDeFermi.01.Ang
119 reference(s)		 96-HommageBenoitMandelbrot.11
119 reference(s)
97-Galerie_FluidMechanics.FV
119 reference(s)		 98-Autostereograms.01.
118 reference(s)
99-xDarchivesG__CMS5__sources__CMS5_____SIS_CMS5_12
117 reference(s)		 100-DieuScience.01.Ang
117 reference(s)
101-Commentaires_EnsembleJuliaOctonion.01
117 reference(s)		 102-OrdinateurMathematiquesArt.01.Fra
116 reference(s)
103-HommageBenoitMandelbrot.21
116 reference(s)		 104-GoldenTriangle.01.Ang
116 reference(s)
105-EntrelacsIntertwinings.01.Fra
116 reference(s)		 106-BEST.20010925
116 reference(s)
107-Galerie_NewPictures
115 reference(s)		 108-Commentaires_DefinitionQuaternions.01
115 reference(s)
109-NombresPremiers_10000.vv
114 reference(s)		 110-ManyChaos.01.Ang
114 reference(s)
111-Galerie_NumberTheory
114 reference(s)		 112-VirtualChaos.01.Ang
113 reference(s)
113-Galerie_BestOf.FV
113 reference(s)		 114-PatrimoineHumanite.02.Fra
112 reference(s)
115-IllusionConnaissance.02
112 reference(s)		 116-Fractal.03
112 reference(s)
117-ExpV_VirE.Fra
112 reference(s)		 118-ConjectureDeSyracuse_0256.vv
112 reference(s)
119-Polynomials_RationalNumbers.01.Fra
111 reference(s)		 120-Pcatalogue.11
111 reference(s)
121-OrdinateursEtCalculs.01.Fra
111 reference(s)		 122-MathematiquesPhysiqueFractales.22
111 reference(s)
123-Galerie_SignalProcessing
111 reference(s)		 124-Fractal.02
111 reference(s)
125-Exposition_MairieCinquiemeArrondissementParis_202001_202002
111 reference(s)		 126-Ariane501.01.Fra
111 reference(s)
127-catalogue.11
110 reference(s)		 128-Notations_AppartientA.01
110 reference(s)

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Copyright © Jean-François COLONNA, 2021-2023.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2021-2023.