Monthly Best Of on 12/28/2010




A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-

Jean-François COLONNA
www.lactamme.polytechnique.fr
jean-francois.colonna@polytechnique.edu
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France

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Contents of this page:


1-The 128 most referenced Pictures:



From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
1-194 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
2-164 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
3-128 reference(s)		 The Lorenz attractor
4-107 reference(s)
The random walk of photons escaping the Sun
5-105 reference(s)		 The random walk of photons escaping the Sun
6-100 reference(s)		 Welcome aboard a Virtual Space-Time Travel Machine
7-95 reference(s)		 Hypercube
8-89 reference(s)
Quark and gluon structure of a nucleon
9-88 reference(s)		 A quaternionic Julia set -tridimensional cross-section-
10-87 reference(s)		 Zoom in on the von Koch curve
11-85 reference(s)		 Quark and gluon structure of a nucleon
12-84 reference(s)
The random walk of photons escaping the Sun
13-79 reference(s)		 From the infinitely small to the infinitely big
14-79 reference(s)		 64 elementary bidimensional binary cellular automata with 1 white starting central point
15-68 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
16-66 reference(s)
Foggy Babel Tower -a tribute to Brueghel the Elder-
17-62 reference(s)		 Texture animation by means of the generalized Fourier filtering process
18-62 reference(s)		 Intertwining
19-61 reference(s)		 LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
20-57 reference(s)
Autostereogram with an hidden volcano
21-56 reference(s)		 Artistic view of the prime numbers
22-56 reference(s)		 The random walk of photons escaping the Sun
23-51 reference(s)		 The Scream -a Tribute to Edvard Munch-
24-50 reference(s)
Tridimensional display of the Riemann Zeta function inside (-10.0,+60.0)x(-35.0,+35.0) (bird's-eye view)
25-47 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
26-44 reference(s)		 Recursive intertwining
27-43 reference(s)		 Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
28-40 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
29-40 reference(s)		 Autostereogram with an hidden volcano
30-39 reference(s)		 Paradoxal Monument Valley at sunset
31-37 reference(s)		 The Möbius strip
32-37 reference(s)
Electron-positron scattering
33-37 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)
34-36 reference(s)		 Along the border of the Mandelbrot set
35-34 reference(s)		 The trajectories of bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity
36-34 reference(s)
Autostereogram of Monument Valley
37-34 reference(s)		 The generalized Ulam spiral
38-33 reference(s)		 From Pluto to the Sun (non linear scales)
39-33 reference(s)		 Jean-François Colonna
40-33 reference(s)
Rotation about the X axis of the Lorenz attractor (5000 iterations), computed simultaneously on two different computers
41-32 reference(s)		 Along the border of the Mandelbrot set
42-31 reference(s)		 Fractal synthesis of mountains with vegetation and stormy clouds
43-30 reference(s)		 A set of 4x3 stereograms of a tridimensional visualization of the Verhulst dynamics
44-30 reference(s)
A set of 4x3 stereograms of an interpolation between a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')and a tridimensional Verhulst dynamics -tridimensional cross-section-
45-30 reference(s)		 Autostereogram with an hidden volcano
46-29 reference(s)		 Reconstruction of a 3D structure -a cubic lattice-
47-28 reference(s)		 Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
48-28 reference(s)
Artistic view of the Big Bang
49-27 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
50-27 reference(s)		 The generalized Ulam spiral displaying 100 numbers
51-27 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
52-27 reference(s)
Tridimensional visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-
53-25 reference(s)		 A shell (Jeener surface 1)in motion
54-25 reference(s)		 Autostereogram with an hidden ring and ghost bows
55-24 reference(s)		 Mountains and light clouds
56-24 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
57-24 reference(s)		 La Génèse (1974)
58-24 reference(s)		 Alien
59-23 reference(s)		 A tridimensional fractal manifold defined by means of three tridimensional fields
60-23 reference(s)
Autostereogram with an hidden volcano
61-22 reference(s)		 Autostereogram with an hidden volcano
62-22 reference(s)		 A variable Archimedes spiral displaying 1000 numbers
63-22 reference(s)		 Animation of a sunrise on mountains
64-22 reference(s)
Rotation about the X axis of the Lorenz attractor
65-22 reference(s)		 2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
66-22 reference(s)		 The Birth of the Universe
67-22 reference(s)		 Autostereogram with an hidden volcano and 64 self-portraits
68-22 reference(s)
16 complex Julia sets along the border of the Mandelbrot set with display of the iteration numbers
69-21 reference(s)		 Tridimensional visualization of the Verhulst dynamics
70-21 reference(s)		 Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
71-20 reference(s)		 Tridimensional display of the Riemann Zeta function inside (-50.0,+50.0)x(-50.0,+50.0) (bird's-eye view)
72-19 reference(s)
The self-similarity of the von Koch curve
73-19 reference(s)		 Fractal natural form
74-19 reference(s)		 Botticelli anomaly on the Moon
75-19 reference(s)		 Different modes of representation of a tridimensional cross-section of a Quaternionic Julia set
76-19 reference(s)
Tridimensional artistic view of the Verhulst dynamics
77-19 reference(s)		 Artistic view of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0) -a Tribute to José Hernández- -tridimensional cross-section-
78-19 reference(s)		 The construction process of the von Koch curve
79-18 reference(s)		 Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
80-18 reference(s)
True colors autostereogram of a fractal landscape
81-18 reference(s)		 A set of 4x3 stereograms of a close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
82-18 reference(s)		 Close-up on a foggy 'MandelBox' -tridimensional cross-section-
83-18 reference(s)		 Tridimensional visualization of the Verhulst dynamics
84-18 reference(s)
Double impossible staircase
85-18 reference(s)		 High temperature particles in a bidimensional box submitted to a vertical field of gravity
86-17 reference(s)		 24 evenly distributed points on a sphere by means of simulated annealing
87-17 reference(s)		 The generalized Ulam spiral displaying 1024 numbers
88-17 reference(s)
A set of 4x3 stereograms of a tridimensional visualization of the Verhulst dynamics
89-17 reference(s)		 The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
90-17 reference(s)		 Tridimensional fractal structure
91-17 reference(s)		 Snowy Rocky Mountains
92-17 reference(s)
Generation of the 63 first Conway's surreal numbers
93-16 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
94-16 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
95-16 reference(s)		 A pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-'the children round' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
96-16 reference(s)
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
97-16 reference(s)		 Happy new year 2000
98-16 reference(s)		 Tridimensional visualization of a bidimensional turbulent flow
99-16 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
100-15 reference(s)
A perfect bidimensional piston with following initial conditions: still piston, high temperature particles at left and low temperature particles at right, in a bidimensional box submitted to a vertical field of gravity
101-15 reference(s)		 N-body problem integration (N=2)displaying a perfect Keplerian orbit
102-15 reference(s)		 An arbitrary surface (Jeener surface 2)in motion
103-15 reference(s)		 Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
104-15 reference(s)
Electron diffraction
105-15 reference(s)		 The Jeener's triple Klein bottle
106-15 reference(s)		 The first two iterations of the construction of the von Koch curve
107-14 reference(s)		 Intertwining based on the geometry of the Bonan-Jeener's triple Klein bottle
108-14 reference(s)
True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
109-14 reference(s)		 The normal field of a fractal surface defined by means of three bidimensional fields
110-14 reference(s)		 The same bidimensional scalar field displayed with 4 different color palettes
111-14 reference(s)		 N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors)
112-14 reference(s)
Tridimensional visualization of the Verhulst dynamics
113-14 reference(s)		 A set of 4x3 stereograms of a tridimensional visualization of the Verhulst dynamics
114-14 reference(s)		 Integration of 128 tridimensional cross-sections of a quaternionic Julia set computed along its fourth axis
115-14 reference(s)		 A tridimensional interpolation between a fractal structure and a cubic mesh
116-14 reference(s)
Tridimensional fractal structure
117-14 reference(s)		 Quantum vacuum fluctuations
118-13 reference(s)		 A recursive intertwining animation
119-13 reference(s)		 The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
120-13 reference(s)
Quark and gluon dynamics of the nucleon
121-13 reference(s)		 No Title 0094
122-13 reference(s)		 From Pluto to the Sun -extrapolation 2- (non linear scales)
123-13 reference(s)		 A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
124-13 reference(s)
A quaternionic Julia set -tridimensional cross-section-
125-13 reference(s)		 Fractal diffusion front in a bidimensional medium obtained by means of a random walk process
126-13 reference(s)		 A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 500 KB disk drives
127-12 reference(s)		 Animation of a natural form
128-12 reference(s)




2-The 128 most referenced Pages:



1-demo_14
930 reference(s)		 2-Vcatalogue.11
862 reference(s)
3-AVirtualSpaceTimeTravelMachine.Ang
465 reference(s)		 4-An2000.01.Fra
427 reference(s)
5-Fractal.01
417 reference(s)		 6-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
416 reference(s)
7-Galerie_ArtisticCreation.FV
387 reference(s)		 8-MathematiquesPhysiqueFractales.02
341 reference(s)
9-SurfaceProjector.01.Ang
334 reference(s)		 10-NDimensionalDeterministicFractalSets.01.Fra
316 reference(s)
11-Galerie_GeneralitiesVisualization.FV
314 reference(s)		 12-Galerie_DeterministicFractalGeometry.FV
311 reference(s)
13-SurfaceProjector.01.Fra
290 reference(s)		 14-Galerie_ParticleSystems.FV
282 reference(s)
15-NDimensionalDeterministicFractalSets.01.Ang
251 reference(s)		 16-Galerie_ArtAndScience.FV
249 reference(s)
17-GenieLogiciel_VisualisationScientifique.01.vv
244 reference(s)		 18-FloatingPointNumbers.01.Fra
238 reference(s)
19-AQuoiServentLesMathematiques.01
238 reference(s)		 20-help.
232 reference(s)
21-EntrelacsIntertwinings.01.Fra
232 reference(s)		 22-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
229 reference(s)
23-Galerie_CelestialMechanics.FV
224 reference(s)		 24-Galerie_DeterministicFractalGeometry.DIAPO.0047
222 reference(s)
25-Galerie_DeterministicFractalGeometry.DIAPO.0046
222 reference(s)		 26-Galerie_DeterministicFractalGeometry.DIAPO.0045
221 reference(s)
27-Galerie_DeterministicFractalGeometry.DIAPO.0044
221 reference(s)		 28-Galerie_DeterministicFractalGeometry.DIAPO.0043
221 reference(s)
29-Galerie_DeterministicFractalGeometry.DIAPO.0039
221 reference(s)		 30-Galerie_DeterministicFractalGeometry.DIAPO.0050
219 reference(s)
31-Galerie_DeterministicFractalGeometry.DIAPO.0042
219 reference(s)		 32-Galerie_DeterministicFractalGeometry.DIAPO.0041
219 reference(s)
33-EntrelacsIntertwinings.01.Ang.DIAPO.0473
218 reference(s)		 34-EntrelacsIntertwinings.01.Ang
218 reference(s)
35-Galerie_DeterministicFractalGeometry.DIAPO.0040
217 reference(s)		 36-AProposSite.01.Fra
217 reference(s)
37-EntrelacsIntertwinings.01.Ang.DIAPO.0468
216 reference(s)		 38-AnimFractal.01.
215 reference(s)
39-Galerie_DeterministicFractalGeometry.DIAPO.0049
214 reference(s)		 40-EntrelacsIntertwinings.01.Ang.DIAPO.0471
214 reference(s)
41-Stereogrammes_AutoStereogrammes.01
213 reference(s)		 42-EntrelacsIntertwinings.01.Ang.DIAPO.0467
213 reference(s)
43-EntrelacsIntertwinings.01.Ang.DIAPO.0466
213 reference(s)		 44-MathematiquesPhysiqueFractales.01
212 reference(s)
45-Galerie_TextureSynthesis.FV
212 reference(s)		 46-Galerie_DeterministicFractalGeometry.DIAPO.0048
212 reference(s)
47-EntrelacsIntertwinings.01.Ang.DIAPO.0469
212 reference(s)		 48-EntrelacsIntertwinings.01.Ang.DIAPO.0465
212 reference(s)
49-EnsembleDesGaleries.DIAPO.0034
212 reference(s)		 50-EntrelacsIntertwinings.01.Ang.DIAPO.0470
211 reference(s)
51-EnsembleDesGaleries.DIAPO.0033
211 reference(s)		 52-NDimensionalDeterministicFractalSets.01.Ang.DIAPO.0371
210 reference(s)
53-NDimensionalDeterministicFractalSets.01.Ang.DIAPO.0369
210 reference(s)		 54-infinity.02.vv.DIAPO.0021
209 reference(s)
55-NDimensionalDeterministicFractalSets.01.Ang.DIAPO.0370
209 reference(s)		 56-EntrelacsIntertwinings.01.Ang.DIAPO.0464
209 reference(s)
57-Galerie_NewPictures.FV
208 reference(s)		 58-EntrelacsIntertwinings.01.Ang.DIAPO.0472
208 reference(s)
59-EnsembleDesGaleries.DIAPO.0035
208 reference(s)		 60-AVirtualSpaceTimeTravelMachine.Fra
208 reference(s)
61-MonodimensionalCellularAutomata.01.Fra
207 reference(s)		 62-Galerie_DeterministicFractalGeometry.DIAPO.0038
207 reference(s)
63-Galerie_DeterministicFractalGeometry.DIAPO.0037
207 reference(s)		 64-FaireDeLaRecherche.01.vv
207 reference(s)
65-NDimensionalDeterministicFractalSets.01.Ang.DIAPO.0368
206 reference(s)		 66-Galerie_DeterministicFractalGeometry.DIAPO.0035
206 reference(s)
67-Galerie_DeterministicFractalGeometry.DIAPO.0027
206 reference(s)		 68-Galerie_DeterministicFractalGeometry.DIAPO.0026
206 reference(s)
69-EnsembleDesGaleries.DIAPO.0020
206 reference(s)		 70-infinity.02.vv.DIAPO.0020
205 reference(s)
71-NatureDesMathematiques.01.vv.Fra
205 reference(s)		 72-Galerie_DeterministicFractalGeometry.DIAPO.0029
205 reference(s)
73-Galerie_DeterministicFractalGeometry.DIAPO.0028
205 reference(s)		 74-EntrelacsIntertwinings.01.Ang.DIAPO.0463
205 reference(s)
75-EnsembleDesGaleries.DIAPO.0038
205 reference(s)		 76-EnsembleDesGaleries.DIAPO.0037
205 reference(s)
77-Commentaires_DefinitionTransformeeDeFourier.01
205 reference(s)		 78-Galerie_BestOf.FV
204 reference(s)
79-EnsembleDesGaleries.DIAPO.0036
204 reference(s)		 80-EnsembleDesGaleries.DIAPO.0022
204 reference(s)
81-EnsembleDesGaleries.DIAPO.0021
204 reference(s)		 82-EnsembleDesGaleries.DIAPO.0001
204 reference(s)
83-present.01.
203 reference(s)		 84-infinity.02.vv.DIAPO.0022
203 reference(s)
85-GenieLogiciel.01.Fra
203 reference(s)		 86-Galerie_NumberTheory.FV
203 reference(s)
87-Galerie_BestOf.DIAPO.0023
203 reference(s)		 88-ExpV_VirE.11
203 reference(s)
89-infinity.02.vv
202 reference(s)		 90-NDimensionalDeterministicFractalSets.01.Ang.DIAPO.0367
202 reference(s)
91-Galerie_DeterministicFractalGeometry.DIAPO.0036
202 reference(s)		 92-Galerie_DeterministicFractalGeometry.DIAPO.0025
202 reference(s)
93-FloatingPointNumbers.01.Ang
202 reference(s)		 94-ExpV_VirE.Fra
202 reference(s)
95-EnsembleDesGaleries.DIAPO.0019
202 reference(s)		 96-infinity.02.vv.DIAPO.0019
201 reference(s)
97-infinity.01.vv
201 reference(s)		 98-RealNumbers.01.Fra
201 reference(s)
99-Informations_AboutPicturesAnimationsAndFiles.01.Ang
201 reference(s)		 100-Galerie_DeterministicChaos.FV
201 reference(s)
101-EntrelacsIntertwinings.01.Ang.DIAPO.0460
201 reference(s)		 102-EnsembleDesGaleries.DIAPO.0039
201 reference(s)
103-EntrelacsIntertwinings.01.Ang.DIAPO.0462
200 reference(s)		 104-EntrelacsIntertwinings.01.Ang.DIAPO.0461
200 reference(s)
105-EnsembleDesGaleries.DIAPO.0040
200 reference(s)		 106-EnsembleDesGaleries.DIAPO.0032
200 reference(s)
107-EnsembleDesGaleries.DIAPO.0018
200 reference(s)		 108-Autostereograms.01.
200 reference(s)
109-infinity.02.vv.DIAPO.0023
199 reference(s)		 110-Galerie_NewPictures.DIAPO.0025
199 reference(s)
111-Galerie_NewPictures.DIAPO.0022
199 reference(s)		 112-Galerie_DeterministicFractalGeometry.DIAPO.0030
199 reference(s)
113-Galerie_BestOf.DIAPO.0026
199 reference(s)		 114-ExpV_VirE.01.Fra
199 reference(s)
115-infinity.02.vv.DIAPO.0018
198 reference(s)		 116-copyright.01.
198 reference(s)
117-catalogue.11
198 reference(s)		 118-Galerie_QuantumMechanics.FV
198 reference(s)
119-Galerie_BestOf.DIAPO.0025
198 reference(s)		 120-Galerie_BestOf.DIAPO.0024
198 reference(s)
121-Galerie_BestOf.DIAPO.0022
198 reference(s)		 122-mail.01.vv
197 reference(s)
123-Galerie_NewPictures.DIAPO.0027
197 reference(s)		 124-Galerie_DeterministicFractalGeometry.DIAPO.0034
197 reference(s)
125-Galerie_DeterministicFractalGeometry.DIAPO.0032
197 reference(s)		 126-Galerie_DeterministicFractalGeometry.DIAPO.0024
197 reference(s)
127-infinity.02.vv.DIAPO.0024
196 reference(s)		 128-infinity.02.vv.DIAPO.0017
196 reference(s)

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Copyright (c) Jean-François Colonna, 2010-2018.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2010-2018.