Monthly Best Of on 10/28/2014




Quaternionic butterfly with extended arithmetics

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:



The tridimensional Ising Model with 2-state spins, temperature=0.2, random initial conditions and an increasing number of iterations -from 100 to 4000-
1-699 reference(s)
Zoom in on the von Koch curve
2-527 reference(s)
A tridimensional fractal manifold defined by means of three tridimensional fields
3-526 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
4-475 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
5-466 reference(s)
Bidimensional Hilbert Curve -iteration 4-
6-358 reference(s)
Tridimensional Hilbert Curve -iteration 3-
7-304 reference(s)
The random walk of photons escaping the Sun
8-215 reference(s)
Autostereogram with an hidden volcano
9-177 reference(s)
Reconstruction of a 3D structure -a cubic lattice-
10-173 reference(s)
The random walk of photons escaping the Sun
11-172 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
12-170 reference(s)
A punched paper tape
13-149 reference(s)
Autostereogram with an hidden volcano
14-141 reference(s)
64 elementary bidimensional binary cellular automata with 1 white starting central point
15-139 reference(s)
Happy new year 2000
16-134 reference(s)
Artistic view of the prime numbers
17-132 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
18-132 reference(s)
Autostereogram with an hidden volcano
19-130 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
20-125 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
21-122 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
22-122 reference(s)
A Peano 'fractal plane' defined by means of three bidimensional fields
23-109 reference(s)
The 126.646 first digits -base 6- of 'pi' displayed as an 'absolute' tridimensional random walk
24-99 reference(s)
The complement of the Menger sponge -iteration 4-
25-81 reference(s)
True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-
26-73 reference(s)
Quantum vacuum fluctuations
27-72 reference(s)
Mystery mountain at sunrise
28-72 reference(s)
A fractal-fractal tree
29-71 reference(s)
The Bonan-Jeener's triple Klein bottle
30-70 reference(s)
An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
31-70 reference(s)
Cauliflowers, seaweeds, shells,... with fog
32-67 reference(s)
Chaotic trajectory: multiple reflexions between two parallel planes for 64 different initial conditions
33-67 reference(s)
The Lorenz attractor
34-66 reference(s)
An amazing cross-section inside the complement of the Menger sponge -iteration 4-
35-63 reference(s)
Particle diffusion inside the Hiroko Kitaoka model of the human pulmonary acinus with membrane permeability
36-63 reference(s)
4 evenly distributed points on a sphere -a Tetrahedron- by means of simulated annealing
37-62 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
38-61 reference(s)
Tridimensional display of the Riemann Zeta function inside (-50.0,+50.0)x(-50.0,+50.0) (bird's-eye view)
39-60 reference(s)
Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation)
40-59 reference(s)
An amazing cross-section inside the Menger sponge -iteration 4- with a 1/O conformal transformation in the Octonionic space -tridimensional cross-section-
41-58 reference(s)
Autostereogram with an hidden volcano and 64 self-portraits
42-57 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
43-56 reference(s)
Autostereogram with an hidden ring and ghost bows
44-55 reference(s)
A bidimensional field
45-54 reference(s)
An amazing cross-section inside the Menger sponge -iteration 4- with a OxO conformal transformation in the Octonionic space -tridimensional cross-section-
46-53 reference(s)
Intertwining
47-52 reference(s)
True colors autostereogram of a fractal landscape
48-52 reference(s)
Snowy day
49-51 reference(s)
The normal field of a shell (Jeener surface 1)
50-51 reference(s)
The bidimensional Ising Model after 1000 iterations, with 2-state spins, random initial conditions and for a temperature equal to the critical temperature
51-50 reference(s)
Autostereogram -using a periodical paradoxal structure as a desguise texture- with an hidden gaussian mountain
52-50 reference(s)
A bidimensional field
53-49 reference(s)
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
54-49 reference(s)
Tridimensional visualization of a bidimensional turbulent flow
55-49 reference(s)
The Scream -a Tribute to Edvard Munch-
56-48 reference(s)
Foggy Babel Tower -a tribute to Brueghel the Elder-
57-47 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
58-47 reference(s)
A fractal Klein bottle
59-47 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)
60-46 reference(s)
The tridimensional Ising Model with 2-state spins, temperature=0.4 and random initial conditions
61-46 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
62-46 reference(s)
Soft Archimedes mountains (bird's-eye view)
63-45 reference(s)
Quark and gluon structure of a nucleon
64-45 reference(s)
A bidimensional field
65-44 reference(s)
The generalized Ulam spiral
66-44 reference(s)
N-body problem integration (N=10)displaying the actual Solar System with its simultaneous 2.pi rotation, our Earth being at the origin of the coordinates
67-43 reference(s)
Autostereogram with an hidden volcano
68-42 reference(s)
Artistic view (bird's-eye view)of an hexagonal tiling of the hyperbolic Poincaré disk -iteration 4-
69-42 reference(s)
From Pluto to the Sun -extrapolation 2-
70-42 reference(s)
The Lorenz attractor
71-42 reference(s)
Tridimensional display of the Riemann Zeta function inside (+0.1,+0.9)x(0,+50)
72-41 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
73-40 reference(s)
Autostereogram of Monument Valley
74-40 reference(s)
Zoom in on mountains (with 3D clipping, bird's-eye view)
75-40 reference(s)
From Pluto to the Sun (non linear scales)
76-39 reference(s)
Tridimensional fractal structure
77-39 reference(s)
Autostereogram with an hidden volcano
78-38 reference(s)
Sixteen interlaced fractal torus
79-38 reference(s)
The complement of the Menger sponge -iteration 2-
80-37 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
81-37 reference(s)
Bidimensional crenellated billiard with 678 isotropic non interacting particles
82-35 reference(s)
Tridimensional display of the generalized Ulam spiral displaying 4096 numbers
83-35 reference(s)
A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.58...,+0.63...,0,0) with 10 iterations -tridimensional cross-section-
84-35 reference(s)
Tridimensional filamentous fractal structure
85-34 reference(s)
Erosion of a bidimensional random medium
86-34 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
87-34 reference(s)
A pseudo-periodical Penrose tiling of the Golden Decagon
88-33 reference(s)
A pseudo-periodical Penrose tiling of the plane
89-33 reference(s)
The simple case of a bidimensional scalar (fractal)field presented in four widely differing color palettes
90-33 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')with a 1/Z conformal transformation in the complex plane -tridimensional cross-section-
91-33 reference(s)
2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-
92-33 reference(s)
Bidimensional abstract texture with random anthropomorphic patterns
93-32 reference(s)
Bidimensional abstract texture with random anthropomorphic patterns
94-32 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -the Sun point of view-
95-32 reference(s)
Tridimensional fractal structure -the space-time foam?-
96-32 reference(s)
Clouds
97-31 reference(s)
A quaternionic Julia set -tridimensional cross-section-
98-31 reference(s)
Sixteen interlaced torus
99-31 reference(s)
The 126.646 first digits -base 6- of 'phi' -the golden ratio- displayed as an 'absolute' tridimensional random walk
100-30 reference(s)
Painted Desert
101-29 reference(s)
Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
102-29 reference(s)
A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(0.229292,-0.444326,0,0) -tridimensional cross-section-
103-29 reference(s)
Jean-François Colonna
104-29 reference(s)
No Title 0174
105-29 reference(s)
A fractal polyhedron
106-29 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
107-29 reference(s)
Artistic view of the Big Bang
108-28 reference(s)
The generalized Ulam spiral displaying 2025 numbers
109-28 reference(s)
The Goldbach conjecture -the Goldbach comet- for the even numbers from 6 to 411678
110-28 reference(s)
From the infinitely small to the infinitely big
111-28 reference(s)
The 64 first lines of the Pascal's Triangle
112-27 reference(s)
An Archimedes spiral displaying the 100.000 first digits -base 10- of 'pi'
113-27 reference(s)
Quark and gluon structure of the nucleon
114-27 reference(s)
Quark and gluon dynamics of the nucleon
115-26 reference(s)
The tridimensional field defining the three coordinates of a tridimensional manifold
116-26 reference(s)
An hexagonal tiling of the hyperbolic Poincaré disk -iteration 5-
117-26 reference(s)
Fractal synthesis of mountains and clouds
118-26 reference(s)
Fractal synthesis of mountains with vegetation and stormy clouds
119-26 reference(s)
Quark and gluon structure of a nucleon
120-26 reference(s)
Tridimensional visualization of a conformal mapping of the Verhulst dynamics
121-26 reference(s)
Hypercube
122-26 reference(s)
A fractal torus
123-26 reference(s)
Birds and fishes
124-26 reference(s)
The Jeener's triple Klein bottle
125-26 reference(s)
Tridimensional display of the Riemann Zeta function inside (-10.0,+20.0)x(-15.0,+15.0) (bird's-eye view)
126-25 reference(s)
Intertwining
127-25 reference(s)
The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-
128-25 reference(s)




2-The 128 most referenced Pages:



1-demo_14
651 reference(s)
2-help.
384 reference(s)
3-An2000.01.Fra
373 reference(s)
4-Fractal.01
312 reference(s)
5-Galerie_Tributes.FV
306 reference(s)
6-Stereogrammes_AutoStereogrammes.01
304 reference(s)
7-FloatingPointNumbers.01.Fra
294 reference(s)
8-AVirtualSpaceTimeTravelMachine.Ang
286 reference(s)
9-GenieLogiciel_VisualisationScientifique.01.vv
258 reference(s)
10-AQuoiServentLesMathematiques.01
255 reference(s)
11-RealNumbers.01.Fra
240 reference(s)
12-mail.01.vv
232 reference(s)
13-AVirtualSpaceTimeTravelMachine.Fra
232 reference(s)
14-Galerie_DeterministicFractalGeometry.FV
227 reference(s)
15-Galerie_NewPictures.FV
223 reference(s)
16-FaireDeLaRecherche.01.vv
223 reference(s)
17-MathematiquesPhysiqueFractales.02
212 reference(s)
18-Galerie_NumberTheory.FV
209 reference(s)
19-MorePages.
208 reference(s)
20-AProposSite.01.Fra
202 reference(s)
21-SurfaceProjector.01.Fra
197 reference(s)
22-GoldenTriangle.01.Fra
197 reference(s)
23-ExpV_VirE.11
196 reference(s)
24-Galerie_ArtisticCreation.FV
193 reference(s)
25-DuModeleALImage.02.Fra
193 reference(s)
26-Galerie_NonDeterministicFractalGeometryNaturalPhenomenonSynthesis.FV
192 reference(s)
27-Galerie_ArtAndScience.FV
192 reference(s)
28-ImagesDuVirtuel.01.Fra.FV
191 reference(s)
29-NDimensionalDeterministicFractalSets.01.Fra
190 reference(s)
30-Galerie_GeneralitiesVisualization.FV
190 reference(s)
31-copyright.01.
188 reference(s)
32-UlamSpiral.01.Fra
188 reference(s)
33-NDimensionalDeterministicFractalSets.01.Ang
187 reference(s)
34-Galerie_CelestialMechanics.FV
187 reference(s)
35-DieuScience.01.Fra
187 reference(s)
36-SurfaceProjector.01.Ang
184 reference(s)
37-MathematiquesPhysiqueFractales.22
184 reference(s)
38-Galerie_BestOf.FV
178 reference(s)
39-Fractal.11
178 reference(s)
40-Fractal.03
178 reference(s)
41-De_L_EnseignementAssisteParOrdinateur_a_L_ExperimentationVirtuelle.01.Fra
177 reference(s)
42-EntrelacsIntertwinings.01.Ang
176 reference(s)
43-Autostereograms.01.
176 reference(s)
44-Kepler.02.
174 reference(s)
45-EnsembleDesGaleries.DIAPO.0001
174 reference(s)
46-MouvementsRelatifs_et_ObservationsAstronomiques.01.Fra
173 reference(s)
47-OrdinateursEtCalculs.01.Fra
171 reference(s)
48-Galerie_TextureSynthesis.FV
171 reference(s)
49-Galerie_Astrophysics.FV
170 reference(s)
50-EntrelacsIntertwinings.01.Fra
169 reference(s)
51-LOG_xiMc.11
168 reference(s)
52-ImpossibleStructures.01.Fra
168 reference(s)
53-FloatingPointNumbers.01.Ang
168 reference(s)
54-catalogue.11
167 reference(s)
55-GenieLogiciel.01.Fra
167 reference(s)
56-AnimFractal.01.
167 reference(s)
57-ImpossibleStructures.01.Ang
166 reference(s)
58-Galerie_QuantumMechanics.FV
166 reference(s)
59-MonodimensionalCellularAutomata.01.Fra
165 reference(s)
60-Galerie_ParticleSystems.FV
165 reference(s)
61-NatureDesMathematiques.01.vv.Fra
163 reference(s)
62-subject.01.
161 reference(s)
63-infinity.01.vv
161 reference(s)
64-IllusionConnaissance.02
161 reference(s)
65-Galerie_DeterministicChaos.FV
161 reference(s)
66-infinity.02.vv
160 reference(s)
67-Galerie_SignalProcessing.FV
159 reference(s)
68-GoldenTriangle.01.Ang
158 reference(s)
69-VisitesGaleriesEnfouies.01.Fra
156 reference(s)
70-UlamSpiral.01.Ang
155 reference(s)
71-NombresEtLumiere.01.vv.Fra
154 reference(s)
72-Galerie_SensitivityToRoundingOffErrors.FV
154 reference(s)
73-OrdinateurMathematiquesArt.01.Fra
153 reference(s)
74-MonodimensionalCellularAutomata.01.Ang
153 reference(s)
75-demo.14
152 reference(s)
76-create.03.
152 reference(s)
77-nombresreels
151 reference(s)
78-an2000
151 reference(s)
79-VirtualChaos.01.Fra
151 reference(s)
80-RemarquesCerveau.01
151 reference(s)
81-OrdinateursEtCalculs.01.Ang
151 reference(s)
82-EnsembleDesGaleriesFractales.DIAPO.0001
151 reference(s)
83-realnumbers
150 reference(s)
84-genielogiciel
150 reference(s)
85-ManyChaos.01.Fra
150 reference(s)
86-Galerie_FluidMechanics.FV
150 reference(s)
87-ExpV_VirE.Ang
150 reference(s)
88-demo
149 reference(s)
89-logiciel
148 reference(s)
90-demo14
148 reference(s)
91-VisitesGaleriesEnfouies.01.Ang
148 reference(s)
92-AvantPropos.01.Fra
146 reference(s)
93-QuelquesQuestionsSurLaRecherche.01.Fra
145 reference(s)
94-MathematiquesEtCinematographe.01.vv
144 reference(s)
95-ManyChaos.01.Ang
144 reference(s)
96-LesApprentisDieux.01
144 reference(s)
97-AvantPropos.01.Ang
144 reference(s)
98-VirtualChaos.01.Ang
142 reference(s)
99-Fractal.02
142 reference(s)
100-fractal.01
141 reference(s)
101-Spheres.01
139 reference(s)
102-PerteDeLAssociativite.01
139 reference(s)
103-PatrimoineHumanite.02.Fra
138 reference(s)
104-MathematiquesEtRepresentations.01.vv.Ang
138 reference(s)
105-Informations_AboutPicturesAnimationsAndFiles.01.Ang
134 reference(s)
106-MathematiquesModeleOutilArtiste.02.Ang
133 reference(s)
107-ExpV_VirE.21
132 reference(s)
108-present.01.
127 reference(s)
109-Galerie_ImagesDesMathematiques.FV
125 reference(s)
110-ExpV_VirE.01.Fra
124 reference(s)
111-Informations_AboutPicturesAnimationsAndFiles.01.Fra
123 reference(s)
112-Commentaires_NKleinBottle.01
122 reference(s)
113-Informations_GoodNewsAndBadNews.01.Fra
121 reference(s)
114-ImagesDuVirtuel.01.Fra
121 reference(s)
115-MathematiquesPhysiqueFractales.01
120 reference(s)
116-Vcatalogue.11
119 reference(s)
117-demo_14.FV
117 reference(s)
118-Commentaires_FluideInstationnaireBiDimensionnelIdeal.01
117 reference(s)
119-Galerie_NumbersAndLight.FV
116 reference(s)
120-EnsembleDesGaleries.DIAPO.0002
116 reference(s)
121-ArtScience.11.Fra
116 reference(s)
122-MonumentValley.01.Ang
115 reference(s)
123-Galeries.01.vv
115 reference(s)
124-Galerie_GeneralitiesVisualization.DIAPO.0094
115 reference(s)
125-ArtEtMathematiques.01
115 reference(s)
126-Ariane501.01.Fra
115 reference(s)
127-ExpV_VirE.Fra
114 reference(s)
128-PerteDeLAssociativite.01.MUL3
113 reference(s)

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Copyright (c) Jean-François Colonna, 2014-2018.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2014-2018.