Monthly Best Of on 03/28/2011




A pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-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

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[The Y2K bug [Le bug de l'an 2000]]
[Do you believe that Real Numbers exist for a computer and that floating point computations are safe?]
[Please, visit A Virtual Space-Time Travel Machine, the place where you can find thousands of pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 03/28/2011 and last updated on 06/30/2018 14:04:46 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures:



Tridimensional representation of a hexadimensional Calabi-Yau manifold
1-175 reference(s)
From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
2-160 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
3-131 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
4-107 reference(s)
Quark and gluon structure of a nucleon
5-104 reference(s)
The Lorenz attractor
6-94 reference(s)
The random walk of photons escaping the Sun
7-89 reference(s)
Zoom in on the von Koch curve
8-78 reference(s)
Quark and gluon structure of a nucleon
9-77 reference(s)
The random walk of photons escaping the Sun
10-76 reference(s)
Foggy Babel Tower -a tribute to Brueghel the Elder-
11-71 reference(s)
The random walk of photons escaping the Sun
12-70 reference(s)
The Möbius strip
13-70 reference(s)
A tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
14-70 reference(s)
Welcome aboard a Virtual Space-Time Travel Machine
15-69 reference(s)
Artistic view of the prime numbers
16-68 reference(s)
From the infinitely small to the infinitely big
17-64 reference(s)
LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
18-62 reference(s)
Hypercube
19-54 reference(s)
Autostereogram with an hidden volcano
20-50 reference(s)
Zoom in on a pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
21-45 reference(s)
Tridimensional visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-
22-44 reference(s)
Autostereogram with an hidden volcano and 64 self-portraits
23-44 reference(s)
Intertwining
24-43 reference(s)
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
25-43 reference(s)
The Scream -a Tribute to Edvard Munch-
26-42 reference(s)
Artistic view of the Big Bang
27-41 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
28-40 reference(s)
Quantum vacuum fluctuations
29-39 reference(s)
The Syracuse conjecture for U(0)={1,2,3,4,...,262144}
30-39 reference(s)
Jean-François Colonna
31-37 reference(s)
Paradoxal Monument Valley at sunset
32-36 reference(s)
Fractal synthesis of mountains with vegetation and stormy clouds
33-34 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
34-34 reference(s)
An intertwining animation
35-33 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
36-33 reference(s)
Along the border of the Mandelbrot set
37-32 reference(s)
Recursive intertwining
38-32 reference(s)
Autostereogram with an hidden volcano
39-32 reference(s)
Beautiful self-similarity
40-31 reference(s)
Autostereogram with an hidden ring and ghost bows
41-31 reference(s)
Recursive 5-star
42-31 reference(s)
2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
43-31 reference(s)
A shell (Jeener surface 1)in motion
44-31 reference(s)
Reconstruction of a 3D structure -a cubic lattice-
45-30 reference(s)
Fractal structure of a nucleon
46-30 reference(s)
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
47-30 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-
48-30 reference(s)
A tridimensional fractal structure
49-29 reference(s)
The generalized Ulam spiral
50-28 reference(s)
Happy new year 2000
51-28 reference(s)
The Birth of the Universe
52-27 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)
53-26 reference(s)
An arbitrary surface (Jeener surface 2)in motion
54-26 reference(s)
The Lorenz attractor
55-26 reference(s)
The Jeener's triple Klein bottle
56-26 reference(s)
Tridimensional visualization of the Verhulst dynamics
57-25 reference(s)
Texture animation by means of the generalized Fourier filtering process
58-25 reference(s)
Synthesis of bidimensional texture by means of Fourier filtering
59-25 reference(s)
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
60-24 reference(s)
Tridimensional visualization of the Verhulst dynamics
61-24 reference(s)
Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
62-24 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
63-24 reference(s)
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
64-23 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
65-23 reference(s)
The generalized Ulam spiral displaying 100 numbers
66-22 reference(s)
Botticelli anomaly on the Moon
67-22 reference(s)
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
68-22 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
69-22 reference(s)
Along the border of the Mandelbrot set
70-21 reference(s)
Artistic view of a bidimensional texture obtained by means of the self-transformation of a fractal process
71-21 reference(s)
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
72-21 reference(s)
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
73-21 reference(s)
A shell (Jeener surface 1)
74-21 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
75-21 reference(s)
Quark and gluon dynamics of the nucleon
76-20 reference(s)
The erection of the Babel Tower
77-20 reference(s)
The Lorenz attractor
78-20 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
79-20 reference(s)
Tridimensional display of the Riemann Zeta function inside (-50.0,+50.0)x(-50.0,+50.0)
80-19 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
81-19 reference(s)
Autostereogram with an hidden volcano
82-19 reference(s)
Recursive pentagon
83-19 reference(s)
24 evenly distributed points on a sphere by means of simulated annealing
84-19 reference(s)
A tridimensional fractal manifold defined by means of three tridimensional fields
85-19 reference(s)
Binomial multiplicative cascade with ponderations equal to 0.4 -left- and 1-0.4=0.6 -right-
86-19 reference(s)
Autostereogram with an hidden volcano
87-18 reference(s)
Alien
88-18 reference(s)
The generalized Ulam spiral displaying 1024 numbers
89-18 reference(s)
From the infinitely small to the infinitely big
90-18 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
91-18 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
92-17 reference(s)
Different modes of representation of a tridimensional cross-section of a Quaternionic Julia set
93-17 reference(s)
Double impossible staircase
94-17 reference(s)
Binomial multiplicative cascade with ponderations equal to 0.3 -left- and 1-0.3=0.7 -right-
95-17 reference(s)
The first two iterations of the construction of the von Koch curve
96-16 reference(s)
True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
97-16 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
98-16 reference(s)
Animation of the artistic view of a bidimensional texture obtained by means of the self-transformation of a fractal process
99-16 reference(s)
Mountains and light cloud dynamics -this sequence being periodical-
100-16 reference(s)
From Pluto to the Sun (non linear scales)
101-16 reference(s)
The Bonan-Jeener's triple Klein bottle
102-16 reference(s)
Tridimensional display of the Riemann Zeta function inside (-10.0,+60.0)x(-35.0,+35.0) (bird's-eye view)
103-15 reference(s)
Computation of the roots of Z^3=1 using Newton's method
104-15 reference(s)
An arbitrary surface (Jeener surface 2)
105-15 reference(s)
Cloudy Mandelbrot set
106-15 reference(s)
Tridimensional visualization of the Mandelbrot set with mapping of the arguments
107-15 reference(s)
Tridimensional visualization of the Verhulst dynamics
108-15 reference(s)
A set of 4x3 stereograms of a tridimensional visualization of the Verhulst dynamics
109-15 reference(s)
A quaternionic Julia set -tridimensional cross-section-
110-15 reference(s)
A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 500 KB disk drives
111-14 reference(s)
No Title 0031
112-14 reference(s)
Fractal natural form
113-14 reference(s)
'There is a war' -a Tribute to Leonard Cohen-
114-14 reference(s)
The normal field of a fractal surface defined by means of three bidimensional fields
115-14 reference(s)
Autostereogram of Monument Valley
116-14 reference(s)
Mountains at sunrise
117-14 reference(s)
The Möbius strip
118-14 reference(s)
The monsters of the lily pond
119-14 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
120-14 reference(s)
Tridimensional fractal structure in a tridimensional torus
121-14 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
122-14 reference(s)
Tridimensional display of the Riemann Zeta function inside (-50.0,+50.0)x(-50.0,+50.0) (bird's-eye view)
123-13 reference(s)
The random walk of photons escaping the Sun
124-13 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
125-13 reference(s)
Three pendulums -the Red one, the Green one and the Blue one- and three magnets -white-
126-13 reference(s)
Tridimensional zoom in on the Mandelbrot set with mapping of the arguments
127-13 reference(s)
Computation of the Lorenz attractor on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors)
128-13 reference(s)




2-The 128 most referenced Pages:



1-demo_14
1046 reference(s)
2-AVirtualSpaceTimeTravelMachine.Ang
536 reference(s)
3-NDimensionalDeterministicFractalSets.01.Ang
445 reference(s)
4-An2000.01.Fra
402 reference(s)
5-Fractal.01
323 reference(s)
6-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
294 reference(s)
7-Galerie_ArtisticCreation.FV
288 reference(s)
8-Galerie_DeterministicFractalGeometry.FV
282 reference(s)
9-help.
273 reference(s)
10-SurfaceProjector.01.Ang
273 reference(s)
11-Vcatalogue.11
266 reference(s)
12-GenieLogiciel_VisualisationScientifique.01.vv
264 reference(s)
13-SurfaceProjector.01.Fra
260 reference(s)
14-FloatingPointNumbers.01.Fra
253 reference(s)
15-MathematiquesPhysiqueFractales.02
243 reference(s)
16-AQuoiServentLesMathematiques.01
228 reference(s)
17-mail.01.vv
227 reference(s)
18-FloatingPointNumbers.01.Ang
219 reference(s)
19-AVirtualSpaceTimeTravelMachine.Fra
218 reference(s)
20-Autostereograms.01.
217 reference(s)
21-Galerie_GeneralitiesVisualization.FV
216 reference(s)
22-Informations_AboutPicturesAnimationsAndFiles.01.Ang
215 reference(s)
23-present.01.
211 reference(s)
24-copyright.01.
208 reference(s)
25-infinity.01.vv
206 reference(s)
26-Galerie_ParticleSystems.FV
206 reference(s)
27-Galerie_ArtAndScience.FV
203 reference(s)
28-Stereogrammes_AutoStereogrammes.01
201 reference(s)
29-NDimensionalDeterministicFractalSets.01.Fra
201 reference(s)
30-Galerie_DeterministicFractalGeometry.DIAPO.0061
200 reference(s)
31-Galerie_DeterministicFractalGeometry.DIAPO.0050
200 reference(s)
32-Galerie_DeterministicFractalGeometry.DIAPO.0052
198 reference(s)
33-Galerie_DeterministicFractalGeometry.DIAPO.0042
198 reference(s)
34-Galerie_DeterministicFractalGeometry.DIAPO.0057
197 reference(s)
35-Galerie_DeterministicFractalGeometry.DIAPO.0056
197 reference(s)
36-Galerie_DeterministicFractalGeometry.DIAPO.0055
197 reference(s)
37-Galerie_DeterministicFractalGeometry.DIAPO.0046
197 reference(s)
38-Galerie_DeterministicFractalGeometry.DIAPO.0041
197 reference(s)
39-AProposSite.01.Fra
197 reference(s)
40-ImagesDuVirtuel.01.Fra
196 reference(s)
41-Galerie_DeterministicFractalGeometry.DIAPO.0054
196 reference(s)
42-Galerie_DeterministicFractalGeometry.DIAPO.0053
196 reference(s)
43-Galerie_DeterministicFractalGeometry.DIAPO.0051
196 reference(s)
44-Galerie_DeterministicFractalGeometry.DIAPO.0049
196 reference(s)
45-Galerie_DeterministicFractalGeometry.DIAPO.0043
196 reference(s)
46-Galerie_ArtAndScience.DIAPO.0160
196 reference(s)
47-Galerie_ArtAndScience.DIAPO.0159
196 reference(s)
48-Galerie_QuantumMechanics.FV
195 reference(s)
49-Galerie_DeterministicFractalGeometry.DIAPO.0048
195 reference(s)
50-Galerie_ArtAndScience.DIAPO.0166
195 reference(s)
51-Galerie_ArtAndScience.DIAPO.0164
195 reference(s)
52-Galerie_ArtAndScience.DIAPO.0162
195 reference(s)
53-ExpV_VirE.01.Fra
195 reference(s)
54-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
194 reference(s)
55-MonodimensionalCellularAutomata.01.Fra
194 reference(s)
56-Galerie_DeterministicFractalGeometry.DIAPO.0060
194 reference(s)
57-Galerie_DeterministicFractalGeometry.DIAPO.0059
194 reference(s)
58-Galerie_DeterministicFractalGeometry.DIAPO.0058
194 reference(s)
59-Galerie_DeterministicFractalGeometry.DIAPO.0047
194 reference(s)
60-Galerie_DeterministicFractalGeometry.DIAPO.0045
194 reference(s)
61-Galerie_ArtAndScience.DIAPO.0165
194 reference(s)
62-Galerie_ArtAndScience.DIAPO.0163
194 reference(s)
63-Galerie_ArtAndScience.DIAPO.0158
194 reference(s)
64-Galerie_ArtAndScience.DIAPO.0156
194 reference(s)
65-Galerie_ArtAndScience.DIAPO.0152
194 reference(s)
66-Galerie_DeterministicFractalGeometry.DIAPO.0040
193 reference(s)
67-Galerie_ArtAndScience.DIAPO.0157
193 reference(s)
68-Galerie_ArtAndScience.DIAPO.0155
193 reference(s)
69-Galerie_ArtAndScience.DIAPO.0154
193 reference(s)
70-Galerie_ArtAndScience.DIAPO.0153
193 reference(s)
71-Galerie_DeterministicFractalGeometry.DIAPO.0044
192 reference(s)
72-Galerie_DeterministicFractalGeometry.DIAPO.0039
192 reference(s)
73-Galerie_CollaborativeWorks..FV
192 reference(s)
74-Galerie_ArtAndScience.DIAPO.0161
192 reference(s)
75-Galerie_ArtAndScience.DIAPO.0149
192 reference(s)
76-AnimFractal.01.
192 reference(s)
77-GenieLogiciel.01.Fra
191 reference(s)
78-Galerie_DeterministicFractalGeometry.DIAPO.0037
191 reference(s)
79-Galerie_BestOf.FV
191 reference(s)
80-Galerie_ArtAndScience.DIAPO.0150
191 reference(s)
81-Galerie_ArtAndScience.DIAPO.0145
191 reference(s)
82-Galerie_ArtAndScience.DIAPO.0151
190 reference(s)
83-Galerie_ArtAndScience.DIAPO.0148
190 reference(s)
84-Galerie_ArtAndScience.DIAPO.0144
190 reference(s)
85-Galerie_ArtAndScience.DIAPO.0143
190 reference(s)
86-FaireDeLaRecherche.01.vv
190 reference(s)
87-Commentaires_DefinitionTransformeeDeFourier.01
190 reference(s)
88-infinity.02.vv
189 reference(s)
89-Galerie_DeterministicFractalGeometry.DIAPO.0038
189 reference(s)
90-Galerie_DeterministicFractalGeometry.DIAPO.0036
189 reference(s)
91-EnsembleDesGaleries.DIAPO.0001
189 reference(s)
92-catalogue.11
188 reference(s)
93-Galerie_NumberTheory.FV
188 reference(s)
94-Galerie_ArtisticCreation.DIAPO.0189
188 reference(s)
95-Galerie_ArtAndScience.DIAPO.0147
188 reference(s)
96-Galerie_ArtAndScience.DIAPO.0146
188 reference(s)
97-Galerie_ArtAndScience.DIAPO.0142
188 reference(s)
98-Informations_AboutPicturesAnimationsAndFiles.01.Fra
187 reference(s)
99-Galerie_DeterministicFractalGeometry.DIAPO.0035
187 reference(s)
100-Galerie_DeterministicFractalGeometry.DIAPO.0034
187 reference(s)
101-Galerie_ArtAndScience.DIAPO.0141
187 reference(s)
102-DieuScience.01.Fra
187 reference(s)
103-Galerie_ArtisticCreation.DIAPO.0184
186 reference(s)
104-Galerie_NewPictures.FV
185 reference(s)
105-Galerie_ArtisticCreation.DIAPO.0191
185 reference(s)
106-ExpV_VirE.Fra
185 reference(s)
107-Informations_GoodNewsAndBadNews.01.Fra
184 reference(s)
108-Galerie_ArtisticCreation.DIAPO.0190
184 reference(s)
109-NatureDesMathematiques.01.vv.Fra
183 reference(s)
110-ImagesDuVirtuel.01.Fra.FV
183 reference(s)
111-Galerie_BestOf.DIAPO.0023
183 reference(s)
112-Galerie_ArtAndScience.DIAPO.0140
183 reference(s)
113-ArtScience.11.Fra
183 reference(s)
114-Galerie_DeterministicFractalGeometry.DIAPO.0033
182 reference(s)
115-Galerie_ArtisticCreation.DIAPO.0186
182 reference(s)
116-Galerie_ArtisticCreation.DIAPO.0185
182 reference(s)
117-Galerie_TextureSynthesis.FV
181 reference(s)
118-Galerie_SalonDAutomne.FV
181 reference(s)
119-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.DIAPO.0142
181 reference(s)
120-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.DIAPO.0141
181 reference(s)
121-Galerie_CelestialMechanics.FV
181 reference(s)
122-Galerie_BestOf.DIAPO.0022
181 reference(s)
123-EntrelacsIntertwinings.01.Ang.DIAPO.0473
181 reference(s)
124-Commentaires_EspaceLyapunovComplexe.01
181 reference(s)
125-real.01.vv.
180 reference(s)
126-Galerie_QuantumMechanics.DIAPO.0005
180 reference(s)
127-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.DIAPO.0143
180 reference(s)
128-Commentaires_ProblemeDesNCorps.01
180 reference(s)

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




Copyright (c) Jean-François Colonna, 2011-2018.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2011-2018.