Monthly Best Of on 12/28/2025




The K-smooth integers on a Bidimensional Hilbert Curve -iteration 5-

Jean-François COLONNA
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www.lactamme.polytechnique.fr

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France

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(CMAP28 WWW site: this page was created on 12/28/2025 and last updated on 12/28/2025 22:15:30 -CET-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



The eroded Menger Sponge -iteration 3-
1-280 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
2-186 reference(s)		The first four iterations of the construction of the von Koch snowflake
3-161 reference(s)		Autostereogram of a quaternionic Julia set -tridimensional cross-section-
4-156 reference(s)
Jean-François COLONNA (on 11/17/1994)with its fractal mountains
5-141 reference(s)		An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
6-124 reference(s)		Artistic view of the prime numbers
7-123 reference(s)		The Sierpinski Carpet -iteration 1 to 5-
8-110 reference(s)
The generalized Ulam spiral
9-107 reference(s)		The Lorenz attractor
10-107 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
11-107 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 256 prime numbers following 100000...-
12-105 reference(s)
Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
13-103 reference(s)		Fractal Self-Portrait -a Tribute to René Magritte-
14-103 reference(s)		Tridimensional display of 36 eigenstates of the Hydrogen atom (bidimensional computation)
15-102 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [4*10^14,5*1014]-
16-101 reference(s)
The random walk of photons escaping the Sun
17-100 reference(s)		The evolution of the sphere using the Lorenz attractor
18-98 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
19-97 reference(s)		Quark and gluon structure of a nucleon
20-94 reference(s)
The distance {Earth-Mars} -millions of kilometers- starting on 01/01/1950 AD and during seven marsian years
21-93 reference(s)		The Menger Sponge -iteration 5-
22-93 reference(s)		An amazing cross-section inside the Menger Sponge -iteration 5-
23-92 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 64 first prime numbers-
24-91 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
25-91 reference(s)		The Jeener-Klein triple bottle
26-91 reference(s)		A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives
27-90 reference(s)		Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-
28-88 reference(s)
N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite)computed with 2 slightly different sets of initial conditions (sensitivity to initial conditions)
29-88 reference(s)		Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
30-87 reference(s)		From Pluto to the Sun (non linear scales)
31-86 reference(s)		Rotation about the Y (vertical)axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms
32-86 reference(s)
Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
33-86 reference(s)		Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold
34-86 reference(s)		Tridimensional display of the 'EinStein' aperiodic 'Spectre' tiling
35-85 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
36-85 reference(s)
Tridimensional representation of a hexadimensional Calabi-Yau manifold
37-85 reference(s)		Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0]
38-84 reference(s)		The Ulam spiral displaying 2025 numbers
39-84 reference(s)		The journey of an Earth-like virtuel planet (green)from Pluto (grey) to the Sun (yellow) -point of view of the virtual planet-
40-84 reference(s)
The bidimensional Ising Model with 2-state spins, temperature=0.2 and random initial conditions
41-84 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 64 first prime numbers-
42-84 reference(s)		The Proth-Gilbreath Conjecture -display of the process for the 32 first prime numbers-
43-84 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [2*10^14,3*1014]-
44-84 reference(s)
Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
45-84 reference(s)		Mapping on a sphere family of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
46-83 reference(s)		A 4-cube -an hypercube-
47-83 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
48-82 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
49-82 reference(s)		Happy new year 2000
50-82 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
51-82 reference(s)		The Bonan-Jeener-Klein triple bottle
52-82 reference(s)
Untitled 0652
53-81 reference(s)		A fractal Klein bottle
54-81 reference(s)		LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
55-81 reference(s)		Mapping on a sphere of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
56-80 reference(s)
A close-up of the 'EinStein' aperiodic 'Spectre' tiling
57-80 reference(s)		Kasner billiard: Time-dependent billiard (from negative curvature to positive curvature)with one accelerated particle
58-80 reference(s)		The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 6-
59-80 reference(s)		N-body problem integration (N=4)with one yellow star and two planets (the red one being very heavy and the blue one and its white satellite being light) -blue body point of view-
60-80 reference(s)
Bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity
61-79 reference(s)		The journey of an Earth-like planet (green)in the Solar System -point of view of the virtual planet-
62-79 reference(s)		The journey of an Earth-like virtuel planet (green)in the Solar System -point of view of the virtual planet-
63-79 reference(s)		Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
64-79 reference(s)
Untitled 0668
65-79 reference(s)		The execution of a very simple program on a Turing Machine
66-78 reference(s)		An aperiodic Penrose tiling of the plane
67-78 reference(s)		Along the border of the Mandelbrot set
68-78 reference(s)
The bidimensional brownian motion of 891 particles
69-78 reference(s)		The numerical irreversibility of the bidimensional billiard -768 particles-
70-78 reference(s)		Mountains and light cloud dynamics -this sequence being periodical-
71-78 reference(s)		Tridimensional zoom in on the Mandelbrot set
72-78 reference(s)
Three hexagons and the twenty-eight first strictly positive integer numbers -nine of them being prime numbers-
73-78 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [5*10^14,6*1014]-
74-78 reference(s)		The numerical irreversibility of the bidimensional billiard -768 particles-
75-77 reference(s)		The construction of a tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
76-77 reference(s)
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) and with a 0 to pi rotation about the X axis -tridimensional cross-section-
77-77 reference(s)		Simultaneous visualization of the number of prime numbers and of the G(Pi(x)) function during the verification of the Proth-Gilbreath Conjecture
78-77 reference(s)		The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [3*10^14,4*1014]-
79-77 reference(s)		Sixteen interlaced fractal torus
80-77 reference(s)
Tridimensional representation of our familiar tridimensional space
81-77 reference(s)		Tridimensional representation of a quadridimensional Calabi-Yau manifold
82-77 reference(s)		The first four iterations of the construction of the von Koch snowflake
83-76 reference(s)		The Universe at the heart of a Calabi-Yau manifold
84-76 reference(s)
The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- with partial confinement -201 particles-, with a zero death rate and a 50% infection, starting with just one infected person -red particle on bottom left picture-
85-76 reference(s)		The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- with partial confinement -201 particles-, with a zero death rate and a 100% infection, starting with just one infected person -red particle on bottom left picture-
86-76 reference(s)		A computer room in the eighties -Courtesy of Philippe Lavialle-
87-76 reference(s)		The smooth integers: the prime factor product -the radical function- of the integer numbers
88-76 reference(s)
A 'conic' cross-section inside the Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
89-76 reference(s)		Erosion of a set of four bidimensional random (with small and large scale correlations)islands
90-76 reference(s)		Tridimensional display of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
91-75 reference(s)		A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 4-
92-75 reference(s)
A tridimensional field made of the Menger Sponge -iteration 5-
93-75 reference(s)		A tridimensional intertwining inside a 'tridimensional epicycloïdal' pseudo-torus
94-75 reference(s)		A tridimensional field
95-75 reference(s)		The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with cluster(s), with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-
96-75 reference(s)
The multiplicative persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-
97-75 reference(s)		The Goldbach Conjecture for the even numbers from 6 to 1564
98-75 reference(s)		Cantor's diagonal argument
99-75 reference(s)		Causal set obtained by means of an homogeneous random meshing of a cube
100-75 reference(s)
Tridimensional brownian motion
101-75 reference(s)		The Sierpinski Carpet -iteration 4-
102-74 reference(s)		The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-
103-74 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
104-74 reference(s)
A bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle and with display of velocity histograms
105-74 reference(s)		A Bidimensional Hilbert-like Curve defined with {X1(...),Y1(...)} related to a periodical impossible structure -iteration 4-
106-74 reference(s)		A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-
107-74 reference(s)		Fractal Self-Portrait -'Décalcomanie', a Tribute to René Magritte-
108-74 reference(s)
A fractal-fractal tree
109-74 reference(s)		From the infinitely small to the infinitely big
110-74 reference(s)		The abelian -commutative- group defined on elliptic curves
111-74 reference(s)		Free fall in the vacuum
112-74 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
113-74 reference(s)		Evolution of a tridimensional representation of a quadridimensional Calabi-Yau manifold
114-74 reference(s)		Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 637.312 galaxies)obtained by means of a non deterministic fractal process
115-74 reference(s)		Bidimensional brownian motion -the colors used (magenta,red,yellow,green,cyan)are an increasing function of the time- and its 'external border' -white-
116-74 reference(s)
A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 5-
117-73 reference(s)		Quantum vacuum fluctuations
118-73 reference(s)		Artistic view of the Big Bang
119-73 reference(s)		A tridimensional structure made of six Golden Decagons with aperiodic Penrose tilings
120-73 reference(s)
Bidimensional closed self-avoiding brownian motion on a torus
121-73 reference(s)		A tridimensional field
122-73 reference(s)		The Sierpinski Carpet -iteration 3- with colors -a Tribute to Karl Menger and Piet Mondrian-
123-73 reference(s)		Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier-
124-73 reference(s)
A random permutation of pixel blocks of an aperiodic Penrose tiling of the plane
125-73 reference(s)		A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} -iteration 3-
126-73 reference(s)		A sphere described by means of a Bidimensional Hilbert-like Curve -iteration 6-
127-73 reference(s)		The K-smooth integers on a Bidimensional Hilbert Curve -iteration 1-
128-73 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
3145 reference(s)		2-xiirv_____.nota.t.
464 reference(s)
3-catalogue.11
356 reference(s)		4-Vcatalogue.11
278 reference(s)
5-xiirf_____.nota.t.
276 reference(s)		6-xiirc_____.nota.t.
209 reference(s)
7-Web_Mail.01.vv
196 reference(s)		8-demo_14
195 reference(s)
9-xiirs_____.nota.t.
185 reference(s)		10-xiirC_____.nota.t.
150 reference(s)
11-ChatGPT.11.Fra
150 reference(s)		12-UlamSpiral.01.Fra
148 reference(s)
13-Stereogrammes_AutoStereogrammes.01
138 reference(s)		14-An2000.01.Fra
136 reference(s)
15-EnsembleDesGaleries.DIAPO.0041
134 reference(s)		16-EnsembleDesGaleries.DIAPO.0138
133 reference(s)
17-Fractal.01
132 reference(s)		18-EnsembleDesGaleries.DIAPO.0146
132 reference(s)
19-EnsembleDesGaleries.DIAPO.0145
131 reference(s)		20-NDimensionalDeterministicFractalSets.01.Ang
130 reference(s)
21-EnsembleDesGaleries.DIAPO.0154
130 reference(s)		22-EnsembleDesGaleries.DIAPO.0144
130 reference(s)
23-EnsembleDesGaleries.DIAPO.0141
130 reference(s)		24-ChatGPT.11.Ang
130 reference(s)
25-EnsembleDesGaleries.DIAPO.0148
129 reference(s)		26-EnsembleDesGaleries.DIAPO.0147
129 reference(s)
27-EnsembleDesGaleries.DIAPO.0135
129 reference(s)		28-EnsembleDesGaleries.DIAPO.0516
127 reference(s)
29-EnsembleDesGaleries.DIAPO.0237
127 reference(s)		30-EnsembleDesGaleries.DIAPO.0142
127 reference(s)
31-EnsembleDesGaleries.DIAPO.0053
127 reference(s)		32-EnsembleDesGaleries.DIAPO.0052
127 reference(s)
33-EnsembleDesGaleries.DIAPO.0517
126 reference(s)		34-EnsembleDesGaleries.DIAPO.0512
126 reference(s)
35-EnsembleDesGaleries.DIAPO.0514
125 reference(s)		36-EnsembleDesGaleries.DIAPO.0139
125 reference(s)
37-EnsembleDesGaleries.DIAPO.0137
125 reference(s)		38-EnsembleDesGaleries.DIAPO.0054
125 reference(s)
39-EnsembleDesGaleries.DIAPO.0042
125 reference(s)		40-EnsembleDesGaleries.DIAPO.0044
124 reference(s)
41-EnsembleDesGaleries.DIAPO.0040
124 reference(s)		42-LOG_xiMc.11
123 reference(s)
43-EnsembleDesGaleries.DIAPO.0513
123 reference(s)		44-EnsembleDesGaleries.DIAPO.0236
123 reference(s)
45-EnsembleDesGaleries.DIAPO.0153
123 reference(s)		46-EnsembleDesGaleries.DIAPO.0140
123 reference(s)
47-EnsembleDesGaleries.DIAPO.0108
123 reference(s)		48-EnsembleDesGaleries.DIAPO.0515
122 reference(s)
49-EnsembleDesGaleries.DIAPO.0238
122 reference(s)		50-EnsembleDesGaleries.DIAPO.0231
122 reference(s)
51-EnsembleDesGaleries.DIAPO.0155
122 reference(s)		52-EnsembleDesGaleries.DIAPO.0143
122 reference(s)
53-EnsembleDesGaleries.DIAPO.0136
122 reference(s)		54-EnsembleDesGaleries.DIAPO.0133
122 reference(s)
55-EnsembleDesGaleries.DIAPO.0043
122 reference(s)		56-EnsembleDesGaleries.DIAPO.0022
122 reference(s)
57-EnsembleDesGaleries.DIAPO.0511
121 reference(s)		58-EnsembleDesGaleries.DIAPO.0509
121 reference(s)
59-EnsembleDesGaleries.DIAPO.0129
121 reference(s)		60-EnsembleDesGaleries.DIAPO.0126
121 reference(s)
61-EnsembleDesGaleries.DIAPO.0038
121 reference(s)		62-ChatGPT.01.Fra
121 reference(s)
63-Galerie_DeterministicFractalGeometry.FV
120 reference(s)		64-EnsembleDesGaleries.DIAPO.0506
120 reference(s)
65-EnsembleDesGaleries.DIAPO.0233
120 reference(s)		66-EnsembleDesGaleries.DIAPO.0226
120 reference(s)
67-EnsembleDesGaleries.DIAPO.0212
120 reference(s)		68-EnsembleDesGaleries.DIAPO.0156
120 reference(s)
69-EnsembleDesGaleries.DIAPO.0127
120 reference(s)		70-EnsembleDesGaleries.DIAPO.0047
120 reference(s)
71-EnsembleDesGaleries.DIAPO.0045
120 reference(s)		72-EnsembleDesGaleries.DIAPO.0035
120 reference(s)
73-EnsembleDesGaleries.DIAPO.0234
119 reference(s)		74-EnsembleDesGaleries.DIAPO.0157
119 reference(s)
75-EnsembleDesGaleries.DIAPO.0132
119 reference(s)		76-EnsembleDesGaleries.DIAPO.0131
119 reference(s)
77-EnsembleDesGaleries.DIAPO.0119
119 reference(s)		78-EnsembleDesGaleries.DIAPO.0106
119 reference(s)
79-EnsembleDesGaleries.DIAPO.0102
119 reference(s)		80-EnsembleDesGaleries.DIAPO.0039
119 reference(s)
81-Fractal.21
118 reference(s)		82-EnsembleDesGaleries.DIAPO.0518
118 reference(s)
83-EnsembleDesGaleries.DIAPO.0510
118 reference(s)		84-EnsembleDesGaleries.DIAPO.0504
118 reference(s)
85-EnsembleDesGaleries.DIAPO.0503
118 reference(s)		86-EnsembleDesGaleries.DIAPO.0242
118 reference(s)
87-EnsembleDesGaleries.DIAPO.0235
118 reference(s)		88-EnsembleDesGaleries.DIAPO.0151
118 reference(s)
89-EnsembleDesGaleries.DIAPO.0149
118 reference(s)		90-EnsembleDesGaleries.DIAPO.0134
118 reference(s)
91-EnsembleDesGaleries.DIAPO.0125
118 reference(s)		92-EnsembleDesGaleries.DIAPO.0122
118 reference(s)
93-EnsembleDesGaleries.DIAPO.0107
118 reference(s)		94-EnsembleDesGaleries.DIAPO.0099
118 reference(s)
95-EnsembleDesGaleries.DIAPO.0097
118 reference(s)		96-EnsembleDesGaleries.DIAPO.0072
118 reference(s)
97-EnsembleDesGaleries.DIAPO.0060
118 reference(s)		98-EnsembleDesGaleries.DIAPO.0034
118 reference(s)
99-EnsembleDesGaleries.DIAPO.0023
118 reference(s)		100-EnsembleDesGaleries.DIAPO.0158
117 reference(s)
101-EnsembleDesGaleries.DIAPO.0150
117 reference(s)		102-EnsembleDesGaleries.DIAPO.0130
117 reference(s)
103-EnsembleDesGaleries.DIAPO.0128
117 reference(s)		104-EnsembleDesGaleries.DIAPO.0109
117 reference(s)
105-EnsembleDesGaleries.DIAPO.0104
117 reference(s)		106-EnsembleDesGaleries.DIAPO.0103
117 reference(s)
107-EnsembleDesGaleries.DIAPO.0096
117 reference(s)		108-EnsembleDesGaleries.DIAPO.0090
117 reference(s)
109-EnsembleDesGaleries.DIAPO.0051
117 reference(s)		110-EnsembleDesGaleries.DIAPO.0036
117 reference(s)
111-EnsembleDesGaleries.DIAPO.0033
117 reference(s)		112-EnsembleDesGaleries.DIAPO.0507
116 reference(s)
113-EnsembleDesGaleries.DIAPO.0502
116 reference(s)		114-EnsembleDesGaleries.DIAPO.0232
116 reference(s)
115-EnsembleDesGaleries.DIAPO.0110
116 reference(s)		116-EnsembleDesGaleries.DIAPO.0105
116 reference(s)
117-EnsembleDesGaleries.DIAPO.0100
116 reference(s)		118-EnsembleDesGaleries.DIAPO.0098
116 reference(s)
119-EnsembleDesGaleries.DIAPO.0091
116 reference(s)		120-EnsembleDesGaleries.DIAPO.0037
116 reference(s)
121-Galerie_GeneralitiesVisualization.FV
115 reference(s)		122-EnsembleDesGaleries.DIAPO.0627
115 reference(s)
123-EnsembleDesGaleries.DIAPO.0593
115 reference(s)		124-EnsembleDesGaleries.DIAPO.0520
115 reference(s)
125-EnsembleDesGaleries.DIAPO.0152
115 reference(s)		126-EnsembleDesGaleries.DIAPO.0124
115 reference(s)
127-EnsembleDesGaleries.DIAPO.0121
115 reference(s)		128-EnsembleDesGaleries.DIAPO.0120
115 reference(s)

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Copyright © Jean-François COLONNA, -2025.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, -2025.