Monthly Best Of on 03/28/2013




Tridimensional visualization of the Mandelbrot set

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 03/28/2013 and last updated on 06/30/2018 14:05:40 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures:



Monument Valley à la David Hockney
1-419 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
2-348 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
3-190 reference(s)
The random walk of photons escaping the Sun
4-160 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
5-149 reference(s)
The random walk of photons escaping the Sun
6-126 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
7-117 reference(s)
The generalized Ulam spiral
8-116 reference(s)
Autostereogram with an hidden volcano
9-113 reference(s)
A tridimensional fractal manifold defined by means of three tridimensional fields
10-113 reference(s)
Autostereogram with an hidden volcano and 64 self-portraits
11-104 reference(s)
Artistic view of the prime numbers
12-100 reference(s)
Autostereogram with an hidden volcano
13-99 reference(s)
Happy new year 2000
14-97 reference(s)
Zoom in on the von Koch curve
15-90 reference(s)
Autostereogram with an hidden volcano
16-89 reference(s)
From low to high galaxy density in the local universe (the depth is displayed by means of the luminance)
17-85 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
18-83 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
19-75 reference(s)
Autostereogram with an hidden volcano
20-66 reference(s)
The Lorenz attractor
21-65 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
22-65 reference(s)
From Pluto to the Sun (non linear scales)
23-57 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
24-56 reference(s)
Along the border of the Mandelbrot set
25-55 reference(s)
Quark and gluon structure of a nucleon
26-54 reference(s)
Autostereogram with an hidden volcano
27-53 reference(s)
Foggy Babel Tower -a tribute to Brueghel the Elder-
28-51 reference(s)
Hypercube
29-51 reference(s)
A tridimensional cubic mesh defined by means of three tridimensional fields and transformed using the tridimensional life game
30-50 reference(s)
Sixteen interlaced torus
31-49 reference(s)
A pseudo-periodical Penrose tiling of the Golden Decagon
32-48 reference(s)
Two multiplexed autostereograms by means of a pi/2 rotation
33-48 reference(s)
The Jeener's triple Klein bottle
34-48 reference(s)
Autostereogram with an hidden ring and ghost bows
35-47 reference(s)
Tridimensional display of the inflationary Universe
36-46 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
37-46 reference(s)
The Scream -a Tribute to Edvard Munch-
38-45 reference(s)
Tridimensional display of the generalized Ulam spiral displaying 4096 numbers
39-45 reference(s)
Tridimensional visualization of the Mandelbrot set with mapping of the arguments -the Mont Saint Michel-
40-45 reference(s)
Tridimensional display of the Riemann Zeta function inside (-50.0,+50.0)x(-50.0,+50.0) (bird's-eye view)
41-44 reference(s)
The generalized Ulam spiral displaying 100 numbers
42-44 reference(s)
Reconstruction of a 3D structure -a cubic lattice-
43-43 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
44-43 reference(s)
From the infinitely small to the infinitely big
45-43 reference(s)
Autostereogram of Monument Valley
46-41 reference(s)
Quark and gluon structure of a nucleon
47-41 reference(s)
Sixteen interlaced fractal torus
48-39 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
49-38 reference(s)
The random walk of photons escaping the Sun
50-38 reference(s)
Quark and gluon dynamics of the nucleon
51-37 reference(s)
Fractal synthesis of mountains with vegetation and stormy clouds
52-37 reference(s)
A shell (Jeener surface 1)in motion
53-37 reference(s)
A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 500 KB disk drives
54-36 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
55-36 reference(s)
A 'fractal plane' with overhangings defined by means of three bidimensional fields
56-35 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
57-35 reference(s)
Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers-
58-35 reference(s)
Quantum vacuum fluctuations
59-34 reference(s)
Diffusion between two boxes (initial conditions: the left one is empty, the right one contains 256 particles), with collisions and display of the gravity center -white particle-
60-34 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
61-34 reference(s)
A demonstration of the Pythagoras' theorem
62-33 reference(s)
The same bidimensional scalar field displayed with 4 different color palettes
63-33 reference(s)
Tridimensional Hilbert Curve -iteration 3-
64-33 reference(s)
Paradoxal Monument Valley at sunset
65-32 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)
66-32 reference(s)
A tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
67-32 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
68-32 reference(s)
Quantum vacuum fluctuations
69-30 reference(s)
Autostereogram of 8 color-multiplexed quaternionic Julia sets -tridimensional cross-sections-
70-30 reference(s)
Botticelli anomaly on the Moon
71-30 reference(s)
Autostereogram -using a periodical paradoxal structure as a desguise texture- with an hidden gaussian mountain
72-30 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
73-29 reference(s)
Quaternionic butterfly with extended arithmetics -a tribute to Laurent Schwartz-
74-28 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
75-28 reference(s)
A quaternionic Julia set -tridimensional cross-section-
76-28 reference(s)
Artistic view of the Big Bang
77-27 reference(s)
The generalized Ulam spiral displaying 1024 numbers
78-27 reference(s)
Close-up on a foggy 'MandelBox' -tridimensional cross-section-
79-27 reference(s)
A fractal hypercube
80-27 reference(s)
Autostereogram -using periodical light clouds as desguise texture- with a hidden gaussian mountain
81-26 reference(s)
Universe or Multiverse -The fractal Universe-?
82-25 reference(s)
The Syracuse conjecture for U(0)={5,6,7,8,...,20} -polar coordinates display-
83-25 reference(s)
True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
84-25 reference(s)
The Möbius strip
85-25 reference(s)
LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
86-25 reference(s)
An interpolation between a 'double sphere' and a cylinder
87-24 reference(s)
The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-
88-24 reference(s)
Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability
89-24 reference(s)
A pseudo-periodical Penrose tiling of the plane
90-23 reference(s)
Intertwining
91-23 reference(s)
7-foil torus knot on its torus
92-23 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-
93-23 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
94-22 reference(s)
Monument Valley à la David Hockney
95-22 reference(s)
The Birth of the Universe
96-22 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
97-22 reference(s)
The Solar System with a green virtual planet -virtual planet point of view-
98-21 reference(s)
Bidimensional visualization of the Verhulst dynamics -(grey,orange,red)display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-
99-21 reference(s)
Rotation about the X axis of the Lorenz attractor
100-21 reference(s)
Jean-François Colonna
101-21 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
102-21 reference(s)
The tower -a tribute to Vladimir Tatline-
103-21 reference(s)
Tridimensional display of the Riemann Zeta function inside (-10.0,+60.0)x(-35.0,+35.0) (bird's-eye view)
104-20 reference(s)
Tridimensional display of the Riemann Zeta function inside (-10.0,+20.0)x(-15.0,+15.0) (bird's-eye view)
105-20 reference(s)
Along the border of the Mandelbrot set
106-20 reference(s)
The Syracuse conjecture for U(0)={1,2,3,4,...,128} -monodimensional display-
107-20 reference(s)
Recursive intertwining
108-20 reference(s)
Fractal natural form
109-20 reference(s)
2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
110-20 reference(s)
The tridimensional Ising Model with 2-state spins, temperature=0.2, random initial conditions and an increasing number of iterations -from 100 to 4000-
111-20 reference(s)
A fractal Möbius strip
112-20 reference(s)
Electron-positron scattering
113-20 reference(s)
Tridimensional display of the Riemann Zeta function inside (-50.0,+50.0)x(-50.0,+50.0)
114-19 reference(s)
Bidimensional display of the rounding-off errors when computing the Verhulst dynamics
115-19 reference(s)
No Title 0154
116-19 reference(s)
The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
117-19 reference(s)
The quaternionic fractal set obtained when computing the roots of Q^3=1 using Newton's method with translation along the third axis of the quaternionic space -tridimensional cross-section-
118-19 reference(s)
A demonstration of the Pythagoras' theorem
119-19 reference(s)
24 evenly distributed points on a sphere by means of simulated annealing
120-19 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)
121-19 reference(s)
Tridimensional Hilbert Curve -iteration 4-
122-19 reference(s)
Fractal 7-foil torus knot
123-19 reference(s)
A fractal sphere
124-19 reference(s)
A shell (Jeener surface 1)
125-19 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
126-19 reference(s)
Rotation about the Y (vertical)axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms
127-19 reference(s)
The construction process of the von Koch curve
128-18 reference(s)




2-The 128 most referenced Pages:



1-demo_14
645 reference(s)
2-An2000.01.Fra
449 reference(s)
3-help.
387 reference(s)
4-Fractal.01
382 reference(s)
5-AQuoiServentLesMathematiques.01
376 reference(s)
6-FloatingPointNumbers.01.Fra
334 reference(s)
7-AVirtualSpaceTimeTravelMachine.Ang
328 reference(s)
8-aquoiserventlesmathematiques.01
325 reference(s)
9-Stereogrammes_AutoStereogrammes.01
318 reference(s)
10-FaireDeLaRecherche.01.vv
300 reference(s)
11-fractal.01
274 reference(s)
12-MathematiquesPhysiqueFractales.02
274 reference(s)
13-RealNumbers.01.Fra
269 reference(s)
14-GenieLogiciel_VisualisationScientifique.01.vv
248 reference(s)
15-MonodimensionalCellularAutomata.01.Fra
228 reference(s)
16-ExpV_VirE.11
227 reference(s)
17-Galerie_NumberTheory.FV
223 reference(s)
18-fairedelarecherche.01.vv
222 reference(s)
19-catalogue.11
220 reference(s)
20-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
220 reference(s)
21-Galerie_ArtisticCreation.FV
213 reference(s)
22-Galerie_DeterministicFractalGeometry.FV
211 reference(s)
23-AVirtualSpaceTimeTravelMachine.Fra
203 reference(s)
24-Galerie_GeneralitiesVisualization.FV
202 reference(s)
25-Galerie_ArtAndScience.FV
202 reference(s)
26-NatureDesMathematiques.01.vv.Fra
199 reference(s)
27-FloatingPointNumbers.01.Ang
198 reference(s)
28-mail.01.vv
197 reference(s)
29-GenieLogiciel.01.Fra
194 reference(s)
30-copyright.01.
193 reference(s)
31-ImagesDuVirtuel.01.Fra.FV
193 reference(s)
32-Galerie_NewPictures.FV
193 reference(s)
33-Fractal.03
190 reference(s)
34-AProposSite.01.Fra
190 reference(s)
35-UlamSpiral.01.Fra
187 reference(s)
36-Galerie_DeterministicChaos.FV
187 reference(s)
37-GoldenTriangle.01.Fra
185 reference(s)
38-SurfaceProjector.01.Ang
184 reference(s)
39-SurfaceProjector.01.Fra
183 reference(s)
40-subject.01.
182 reference(s)
41-UlamSpiral.01.Ang
182 reference(s)
42-OrdinateursEtCalculs.01.Fra
182 reference(s)
43-NDimensionalDeterministicFractalSets.01.Ang
182 reference(s)
44-DieuScience.01.Fra
182 reference(s)
45-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
180 reference(s)
46-NDimensionalDeterministicFractalSets.01.Fra
179 reference(s)
47-Galerie_QuantumMechanics.FV
179 reference(s)
48-ExpV_VirE.21
179 reference(s)
49-OrdinateurMathematiquesArt.01.Fra
178 reference(s)
50-Galerie_CelestialMechanics.FV
178 reference(s)
51-Fractal.11
177 reference(s)
52-Autostereograms.01.
176 reference(s)
53-AnimFractal.01.
176 reference(s)
54-Informations_AboutPicturesAnimationsAndFiles.01.Ang
174 reference(s)
55-EntrelacsIntertwinings.01.Fra
174 reference(s)
56-EnsembleDesGaleries.DIAPO.0001
173 reference(s)
57-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
173 reference(s)
58-infinity.01.vv
169 reference(s)
59-MorePages.
169 reference(s)
60-Kepler.02.
169 reference(s)
61-VirtualChaos.01.Fra
168 reference(s)
62-Galerie_BestOf.FV
168 reference(s)
63-Galerie_Astrophysics.FV
167 reference(s)
64-MonodimensionalCellularAutomata.01.Ang
166 reference(s)
65-IllusionConnaissance.02
166 reference(s)
66-infinity.02.vv
165 reference(s)
67-NombresEtLumiere.01.vv.Fra
164 reference(s)
68-ImpossibleStructures.01.Fra
164 reference(s)
69-Galerie_SignalProcessing.FV
164 reference(s)
70-Galerie_SensitivityToRoundingOffErrors.FV
164 reference(s)
71-EnsembleDesGaleriesFractales.DIAPO.0001
163 reference(s)
72-create.03.
162 reference(s)
73-Galerie_TextureSynthesis.FV
162 reference(s)
74-GoldenTriangle.01.Ang
161 reference(s)
75-EntrelacsIntertwinings.01.Ang
160 reference(s)
76-realnumbers
159 reference(s)
77-logiciel
158 reference(s)
78-genielogiciel
158 reference(s)
79-an2000
158 reference(s)
80-Galerie_ParticleSystems.FV
158 reference(s)
81-nombresreels
157 reference(s)
82-demo14
157 reference(s)
83-demo.14
157 reference(s)
84-demo
157 reference(s)
85-AvantPropos.01.Fra
157 reference(s)
86-present.01.
156 reference(s)
87-MathematiquesPhysiqueFractales.01
156 reference(s)
88-RemarquesCerveau.01
155 reference(s)
89-MathematiquesPhysiqueFractales.12
155 reference(s)
90-ExpV_VirE.Fra
155 reference(s)
91-Spheres.01
154 reference(s)
92-LOG_xiMc.11
154 reference(s)
93-VirtualChaos.01.Ang
152 reference(s)
94-ManyChaos.01.Fra
152 reference(s)
95-ExpV_VirE.01.Fra
152 reference(s)
96-VisitesGaleriesEnfouies.01.Fra
151 reference(s)
97-MathematiquesModeleOutilArtiste.02.Ang
151 reference(s)
98-ImpossibleStructures.01.Ang
151 reference(s)
99-ManyChaos.01.Ang
150 reference(s)
100-Fractal.02
148 reference(s)
101-AvantPropos.01.Ang
148 reference(s)
102-PerteDeLAssociativite.01
147 reference(s)
103-MathematiquesEtRepresentations.01.vv.Ang
147 reference(s)
104-MathematiquesEtCinematographe.01.vv
146 reference(s)
105-Commentaires_DefinitionComplexes.01
146 reference(s)
106-PatrimoineHumanite.02.Fra
144 reference(s)
107-OrdinateursEtCalculs.01.Ang
144 reference(s)
108-Commentaires_EnsembleMandelbrotComplexe.01
143 reference(s)
109-AQuoiServentLesMathematiques.03
143 reference(s)
110-Informations_AboutPicturesAnimationsAndFiles.01.Fra
142 reference(s)
111-VisitesGaleriesEnfouies.01.Ang
141 reference(s)
112-Commentaires_ModeleIsingBiDimensionnel.01
141 reference(s)
113-QuelquesQuestionsSurLaRecherche.01.Fra
140 reference(s)
114-Galerie_FluidMechanics.FV
140 reference(s)
115-ExpV_VirE.Ang
140 reference(s)
116-Commentaires_FluideInstationnaireBiDimensionnelIdeal.01
139 reference(s)
117-Commentaires_DefinitionQuaternions.01
139 reference(s)
118-Commentaires_DefinitionTransformeeDeFourier.01
137 reference(s)
119-Commentaires_VarieteHexaDimensionnelleCalabiYau.01
135 reference(s)
120-Commentaires_ModeleIsingTriDimensionnel.01
135 reference(s)
121-Commentaires_KleinBottle.02
135 reference(s)
122-PerteDeLAssociativite.01.ADD3
134 reference(s)
123-Commentaires_NKleinBottle.02
134 reference(s)
124-ExpV_VirE.01.Ang
133 reference(s)
125-LumiereVirtuelleParadoxale.01
132 reference(s)
126-HommageBenoitMandelbrot.21
132 reference(s)
127-PerteDeLAssociativite.01.MUL3
131 reference(s)
128-Commentaires_NKleinBottle.01
131 reference(s)

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




Copyright (c) Jean-François Colonna, 2013-2018.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2013-2018.