Monthly Best Of on 02/28/2011




Tridimensional visualization of the Mandelbrot set

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

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[The Y2K Bug [Le bug de l'an 2000]]
[Real Numbers don't exist in Computers and Floating Point Computations aren't safe. [Les Nombres Réels n'existent dans les Ordinateurs et les Calculs Flottants ne sont pas sûrs.]]
[Please, visit A Virtual Machine for Exploring Space-Time and Beyond, the place where you can find thousands of pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 02/28/2011 and last updated on 11/14/2023 17:47:42 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
1-179 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
2-172 reference(s)		 Welcome aboard a Virtual Space-Time Travel Machine
3-110 reference(s)		 The Lorenz attractor
4-107 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
5-100 reference(s)		 The random walk of photons escaping the Sun
6-99 reference(s)		 The random walk of photons escaping the Sun
7-89 reference(s)		 Zoom in on a pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
8-89 reference(s)
Zoom in on the von Koch curve
9-80 reference(s)		 The random walk of photons escaping the Sun
10-80 reference(s)		 Hypercube
11-76 reference(s)		 Artistic view of the prime numbers
12-76 reference(s)
Quark and gluon structure of a nucleon
13-72 reference(s)		 The foggy Babel Tower -a Tribute to Brueghel the Elder-
14-66 reference(s)		 Electron-positron scattering
15-65 reference(s)		 Quark and gluon structure of a nucleon
16-64 reference(s)
From the infinitely small to the infinitely big
17-63 reference(s)		 Intertwining
18-54 reference(s)		 Autostereogram with an hidden volcano
19-54 reference(s)		 LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
20-54 reference(s)
The Scream -a Tribute to Edvard Munch-
21-52 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
22-51 reference(s)		 A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
23-50 reference(s)		 Fractal synthesis of mountains with vegetation and stormy clouds
24-49 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
25-48 reference(s)		 The Möbius strip
26-43 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-10.0,+60.0]x[-35.0,+35.0] (bird's-eye view)
27-42 reference(s)		 Jean-François COLONNA (on 11/17/1994)with its fractal mountains
28-42 reference(s)
Tridimensional visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
29-40 reference(s)		 Autostereogram with an hidden volcano
30-39 reference(s)		 Texture animation by means of the generalized Fourier filtering process
31-39 reference(s)		 Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
32-38 reference(s)
Quantum vacuum fluctuations
33-37 reference(s)		 Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
34-37 reference(s)		 Artistic view of the Big Bang
35-36 reference(s)		 Along the border of the Mandelbrot set
36-36 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
37-35 reference(s)		 The Jeener-Klein triple bottle
38-35 reference(s)		 Recursive 5-star
39-34 reference(s)		 Animation of a sunrise on mountains
40-34 reference(s)
Recursive intertwining
41-33 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
42-33 reference(s)		 64 elementary bidimensional binary cellular automata with 1 white starting central point
43-31 reference(s)		 Quark and gluon dynamics of the nucleon
44-30 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
45-29 reference(s)		 Autostereogram with an hidden volcano and 64 self-portraits
46-29 reference(s)		 A shell (Jeener surface 1)in motion
47-29 reference(s)		 The generalized Ulam spiral displaying 100 numbers
48-28 reference(s)
Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
49-28 reference(s)		 Rotation about the X axis of the Lorenz attractor
50-28 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)
51-27 reference(s)		 From Pluto to the Sun (non linear scales)
52-27 reference(s)
Tridimensional visualization of the Verhulst dynamics
53-27 reference(s)		 Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
54-26 reference(s)		 2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
55-26 reference(s)		 Along the border of the Mandelbrot set
56-25 reference(s)
Autostereogram with an hidden ring and ghost bows
57-25 reference(s)		 Reconstruction of a 3D structure -a cubic lattice-
58-24 reference(s)		 The Birth of the Universe
59-24 reference(s)		 Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
60-24 reference(s)
An arbitrary surface (Jeener surface 2)in motion
61-23 reference(s)		 Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
62-23 reference(s)		 Tridimensional zoom in on the Mandelbrot set with mapping of the arguments
63-23 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-
64-23 reference(s)
Happy new year 2000
65-23 reference(s)		 Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
66-23 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
67-23 reference(s)		 Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
68-22 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)
69-22 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)
70-21 reference(s)		 Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
71-21 reference(s)		 Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
72-21 reference(s)
Synthesis of bidimensional texture by means of Fourier filtering
73-21 reference(s)		 A tridimensional fractal structure
74-20 reference(s)		 Autostereogram with an hidden volcano
75-20 reference(s)		 Autostereogram with an hidden volcano
76-20 reference(s)
Cauliflowers, seaweeds, shells,... with fog
77-20 reference(s)		 Tridimensional visualization of the Verhulst dynamics
78-20 reference(s)		 Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
79-19 reference(s)		 Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
80-19 reference(s)
A recursive intertwining animation
81-19 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
82-19 reference(s)		 N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
83-19 reference(s)		 Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
84-19 reference(s)
The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
85-19 reference(s)		 Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
86-19 reference(s)		 Tridimensional representation of a quadridimensional Calabi-Yau manifold
87-19 reference(s)		 Evolution of a bidimensional binary cellular automaton with 1 white starting central point
88-19 reference(s)
Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view)
89-18 reference(s)		 The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
90-18 reference(s)		 Autostereogram with an hidden volcano
91-18 reference(s)		 Artistic view of a bidimensional texture obtained by means of the self-transformation of a fractal process
92-18 reference(s)
Autostereogram with an hidden volcano
93-17 reference(s)		 A pay slip
94-17 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
95-17 reference(s)		 Recursive pentagon
96-17 reference(s)
True colors autostereogram of a fractal landscape
97-17 reference(s)		 Close-up on a foggy 'MandelBox' -tridimensional cross-section-
98-17 reference(s)		 A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
99-17 reference(s)		 A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
100-17 reference(s)
A set of 4x3 stereograms of a tridimensional visualization of the Verhulst dynamics
101-17 reference(s)		 Tridimensional visualization of the Verhulst dynamics
102-17 reference(s)		 The Lorenz attractor
103-17 reference(s)		 A shell (Jeener surface 1)
104-17 reference(s)
True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
105-16 reference(s)		 Computation of the roots of Z^3=1 using Newton's method
106-16 reference(s)		 A tridimensional fractal manifold defined by means of three tridimensional fields
107-16 reference(s)		 The generalized Ulam spiral displaying 1024 numbers
108-16 reference(s)
Botticelli anomaly on the Moon
109-16 reference(s)		 A pseudo-quaternionic Mandelbrot set (a 'MandelBulb')-'the children round' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
110-16 reference(s)		 A quaternionic Julia set -tridimensional cross-section-
111-16 reference(s)		 The first two iterations of the construction of the von Koch curve
112-15 reference(s)
The generalized Ulam spiral
113-15 reference(s)		 Autostereogram of Monument Valley
114-15 reference(s)		 Mountains and light cloud dynamics -this sequence being periodical-
115-15 reference(s)		 Mountains and light clouds
116-15 reference(s)
From Pluto to the Sun -extrapolation 2- (non linear scales)
117-15 reference(s)		 A set of 4x3 stereograms of a tridimensional visualization of the Verhulst dynamics
118-15 reference(s)		 Rotation about the X axis of the Lorenz attractor (1000 iterations), computed simultaneously on two different computers
119-15 reference(s)		 The Bonan-Jeener-Klein triple bottle
120-15 reference(s)
A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
121-14 reference(s)		 Autostereogram of a quaternionic Julia set -tridimensional cross-section-
122-14 reference(s)		 Alien
123-14 reference(s)		 24 evenly distributed points on a sphere by means of simulated annealing
124-14 reference(s)
Earthquake
125-14 reference(s)		 Different modes of representation of a tridimensional cross-section of a Quaternionic Julia set
126-14 reference(s)		 An arbitrary surface (Jeener surface 2)
127-14 reference(s)		 Tridimensional zoom in on the Mandelbrot set
128-14 reference(s)




2-The 128 most referenced Pages (*):

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



1-demo_14
984 reference(s)		 2-AVirtualSpaceTimeTravelMachine.Ang
573 reference(s)
3-An2000.01.Fra
420 reference(s)		 4-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
358 reference(s)
5-NDimensionalDeterministicFractalSets.01.Ang
357 reference(s)		 6-Fractal.01
357 reference(s)
7-GenieLogiciel_VisualisationScientifique.01.vv
296 reference(s)		 8-Galerie_DeterministicFractalGeometry.FV
296 reference(s)
9-Galerie_ArtisticCreation.FV
295 reference(s)		 10-help.
290 reference(s)
11-SurfaceProjector.01.Ang
288 reference(s)		 12-FloatingPointNumbers.01.Fra
285 reference(s)
13-Vcatalogue.11
283 reference(s)		 14-SurfaceProjector.01.Fra
255 reference(s)
15-ImagesDuVirtuel.01.Fra.FV
248 reference(s)		 16-Galerie_GeneralitiesVisualization.FV
247 reference(s)
17-MathematiquesPhysiqueFractales.02
238 reference(s)		 18-NDimensionalDeterministicFractalSets.01.Fra
236 reference(s)
19-FloatingPointNumbers.01.Ang
232 reference(s)		 20-Galerie_ArtAndScience.DIAPO.0159
223 reference(s)
21-Galerie_ArtAndScience.DIAPO.0161
219 reference(s)		 22-Galerie_ArtAndScience.DIAPO.0160
219 reference(s)
23-AQuoiServentLesMathematiques.01
219 reference(s)		 24-Galerie_DeterministicFractalGeometry.DIAPO.0041
218 reference(s)
25-Galerie_ArtAndScience.DIAPO.0157
218 reference(s)		 26-Galerie_DeterministicFractalGeometry.DIAPO.0042
217 reference(s)
27-Galerie_ArtAndScience.DIAPO.0163
217 reference(s)		 28-Galerie_ArtAndScience.DIAPO.0158
217 reference(s)
29-Galerie_ArtAndScience.DIAPO.0156
217 reference(s)		 30-Autostereograms.01.
217 reference(s)
31-copyright.01.
216 reference(s)		 32-Informations_AboutPicturesAnimationsAndFiles.01.Ang
216 reference(s)
33-Galerie_DeterministicFractalGeometry.DIAPO.0045
216 reference(s)		 34-Galerie_ArtAndScience.DIAPO.0162
216 reference(s)
35-Galerie_ParticleSystems.FV
215 reference(s)		 36-Galerie_DeterministicFractalGeometry.DIAPO.0044
215 reference(s)
37-Galerie_DeterministicFractalGeometry.DIAPO.0039
215 reference(s)		 38-GenieLogiciel.01.Fra
214 reference(s)
39-Galerie_DeterministicFractalGeometry.DIAPO.0043
214 reference(s)		 40-Galerie_DeterministicFractalGeometry.DIAPO.0040
214 reference(s)
41-infinity.01.vv
213 reference(s)		 42-Galerie_DeterministicFractalGeometry.DIAPO.0055
213 reference(s)
43-Galerie_ArtisticCreation.DIAPO.0191
213 reference(s)		 44-Galerie_ArtAndScience.DIAPO.0150
213 reference(s)
45-Galerie_DeterministicFractalGeometry.DIAPO.0052
212 reference(s)		 46-Galerie_DeterministicFractalGeometry.DIAPO.0037
212 reference(s)
47-Galerie_ArtAndScience.DIAPO.0149
212 reference(s)		 48-Galerie_ArtAndScience.DIAPO.0148
212 reference(s)
49-Galerie_DeterministicFractalGeometry.DIAPO.0038
211 reference(s)		 50-Galerie_ArtisticCreation.DIAPO.0188
211 reference(s)
51-Galerie_DeterministicFractalGeometry.DIAPO.0046
210 reference(s)		 52-Galerie_DeterministicFractalGeometry.DIAPO.0036
210 reference(s)
53-Galerie_ArtisticCreation.DIAPO.0189
210 reference(s)		 54-Galerie_ArtisticCreation.DIAPO.0187
210 reference(s)
55-Galerie_ArtAndScience.DIAPO.0164
210 reference(s)		 56-Galerie_ArtAndScience.DIAPO.0155
210 reference(s)
57-Galerie_ArtAndScience.DIAPO.0152
210 reference(s)		 58-infinity.02.vv
209 reference(s)
59-Galerie_DeterministicFractalGeometry.DIAPO.0050
209 reference(s)		 60-Galerie_DeterministicFractalGeometry.DIAPO.0047
209 reference(s)
61-Galerie_ArtisticCreation.DIAPO.0190
208 reference(s)		 62-Galerie_ArtAndScience.DIAPO.0154
208 reference(s)
63-Galerie_ArtAndScience.DIAPO.0147
208 reference(s)		 64-Galerie_DeterministicFractalGeometry.DIAPO.0053
207 reference(s)
65-Galerie_DeterministicFractalGeometry.DIAPO.0051
207 reference(s)		 66-Galerie_DeterministicFractalGeometry.DIAPO.0048
207 reference(s)
67-Galerie_ArtAndScience.DIAPO.0151
207 reference(s)		 68-Galerie_ArtAndScience.DIAPO.0153
206 reference(s)
69-Galerie_ArtAndScience.DIAPO.0146
206 reference(s)		 70-Galerie_DeterministicFractalGeometry.DIAPO.0056
205 reference(s)
71-Galerie_DeterministicFractalGeometry.DIAPO.0054
205 reference(s)		 72-Galerie_DeterministicFractalGeometry.DIAPO.0035
205 reference(s)
73-Galerie_ArtAndScience.DIAPO.0145
205 reference(s)		 74-mail.01.vv
204 reference(s)
75-Galerie_DeterministicFractalGeometry.DIAPO.0049
204 reference(s)		 76-Galerie_ArtAndScience.DIAPO.0165
204 reference(s)
77-Stereogrammes_AutoStereogrammes.01
203 reference(s)		 78-Galerie_DeterministicFractalGeometry.DIAPO.0057
203 reference(s)
79-Galerie_ArtAndScience.DIAPO.0144
203 reference(s)		 80-Galerie_ArtAndScience.DIAPO.0141
203 reference(s)
81-DieuScience.01.Fra
203 reference(s)		 82-Galerie_QuantumMechanics.FV
202 reference(s)
83-Galerie_DeterministicFractalGeometry.DIAPO.0061
202 reference(s)		 84-Galerie_DeterministicFractalGeometry.DIAPO.0058
202 reference(s)
85-Galerie_ArtisticCreation.DIAPO.0186
202 reference(s)		 86-Galerie_ArtAndScience.DIAPO.0166
202 reference(s)
87-Galerie_ArtAndScience.DIAPO.0143
202 reference(s)		 88-Galerie_NewPictures.FV
201 reference(s)
89-Galerie_DeterministicFractalGeometry.DIAPO.0034
201 reference(s)		 90-Galerie_DeterministicFractalGeometry.DIAPO.0033
201 reference(s)
91-RealNumbers.01.Fra
200 reference(s)		 92-Galerie_DeterministicFractalGeometry.DIAPO.0059
199 reference(s)
93-AVirtualSpaceTimeTravelMachine.Fra
199 reference(s)		 94-Galerie_DeterministicFractalGeometry.DIAPO.0060
198 reference(s)
95-Galerie_BestOf.DIAPO.0020
198 reference(s)		 96-Galerie_ArtAndScience.DIAPO.0142
198 reference(s)
97-Galerie_DeterministicFractalGeometry.DIAPO.0032
197 reference(s)		 98-Informations_GoodNewsAndBadNews.01.Fra
196 reference(s)
99-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.DIAPO.0148
196 reference(s)		 100-Galerie_BestOf.DIAPO.0023
196 reference(s)
101-AProposSite.01.Fra
196 reference(s)		 102-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.DIAPO.0147
195 reference(s)
103-MonodimensionalCellularAutomata.01.Fra
194 reference(s)		 104-Galerie_ArtisticCreation.DIAPO.0184
194 reference(s)
105-Galerie_TextureSynthesis.DIAPO.0201
193 reference(s)		 106-Galerie_DeterministicFractalGeometry.DIAPO.0031
193 reference(s)
107-ExpV_VirE.Fra
193 reference(s)		 108-infinity.02.vv.DIAPO.0025
192 reference(s)
109-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.DIAPO.0146
192 reference(s)		 110-Galerie_GeneralitiesVisualization.DIAPO.0085
192 reference(s)
111-Galerie_ArtisticCreation.DIAPO.0183
192 reference(s)		 112-EntrelacsIntertwinings.01.Ang.DIAPO.0473
192 reference(s)
113-Galerie_DeterministicFractalGeometry.DIAPO.0029
191 reference(s)		 114-Galerie_BestOf.DIAPO.0022
191 reference(s)
115-Galerie_ArtAndScience.DIAPO.0140
191 reference(s)		 116-infinity.02.vv.DIAPO.0024
190 reference(s)
117-Informations_AboutPicturesAnimationsAndFiles.01.Fra
190 reference(s)		 118-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.DIAPO.0151
190 reference(s)
119-Galerie_BestOf.DIAPO.0024
190 reference(s)		 120-Galerie_ArtisticCreation.DIAPO.0185
190 reference(s)
121-ExpV_VirE.11
190 reference(s)		 122-present.01.
189 reference(s)
123-Galerie_DeterministicFractalGeometry.DIAPO.0030
189 reference(s)		 124-Galerie_DeterministicFractalGeometry.DIAPO.0028
189 reference(s)
125-Galerie_DeterministicChaos.DIAPO.0017
189 reference(s)		 126-Galerie_BestOf.DIAPO.0025
189 reference(s)
127-Galerie_BestOf.DIAPO.0019
189 reference(s)		 128-infinity.02.vv.DIAPO.0023
188 reference(s)

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




Copyright © Jean-François COLONNA, 2011-2023.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2011-2023.