Monthly Best Of on 07/28/2026




A fractal surface defined by means of three bidimensional fields

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 07/28/2026 and last updated on 07/28/2026 22:08:07 -CEST-)




Contents of this page:


1-The 128 most referenced Pictures (*):

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



A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of an arbitrary random number (190496...)-base 10- with 33.333 time steps
1-666 reference(s)
The eroded Menger Sponge -iteration 3-
2-219 reference(s)
Visualization of the Proth-Gilbreath Conjecture process
3-156 reference(s)
Artistic view of the prime numbers
4-142 reference(s)
Autostereogram of a quaternionic Julia set -tridimensional cross-section-
5-136 reference(s)
A type 'B6-XYZ' pseudo-random walk defined by means of the 48 first 'decimals' of the transcendental Champernowne number -using all base 4 integer numbers-: 0.{1 2 3 4 5 1 0 1 1 1 2 1 3 1 4 1 5 2 0 2 1 2 2 2 3 2 4 2 5 3 0 3 1 3 2 3 3 3 4 3 5 4 0 4 1 4 2 4}
6-128 reference(s)
A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of 'pi' (141592...)with 492 more digits defining a helix -base 10- with 33.497 time steps
7-120 reference(s)
The Sierpinski Carpet -iteration 1 to 5-
8-115 reference(s)
Bidimensional brownian motion with a gaussian distribution law regarding the radial coordinate
9-114 reference(s)
N-body problem integration (N=10)displaying the actual Solar System during one plutonian year -Earth point of view-
10-108 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-
11-107 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
12-104 reference(s)
Fractal piano keyboard
13-99 reference(s)
Auguste Detœuf Room at the Ecole Polytechnique -09/15/2005-
14-99 reference(s)
An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-
15-97 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 100215...-
16-93 reference(s)
The random walk of photons escaping the Sun
17-92 reference(s)
The Lorenz attractor
18-90 reference(s)
The tiling of a 6x10 rectangle by means of the 12 different pentominos
19-89 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [1.2x10^15,1.3x10^15]-
20-89 reference(s)
A type 'B4-XY' pseudo-random walk defined by means of the 48 first 'decimals' of the transcendental Champernowne number -using all base 4 integer numbers-: 0.{1 2 3 1 0 1 1 1 2 1 3 2 0 2 1 2 2 2 3 3 0 3 1 3 2 3 3 1 0 0 1 0 1 1 0 2 1 0 3 1 1 0 1 1 1 1 1 2}
21-88 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
22-86 reference(s)
The execution of a very simple program on a Turing Machine
23-85 reference(s)
Mountains and fog
24-84 reference(s)
A tridimensional pseudo-random walk -spherical coordinates- defined by means of the 999 first decimals of the Champernowne number (1 2 3 4 5 6 7 8 9 10 11 12...)-base 10- with 333 time steps
25-79 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 64 first prime numbers-
26-79 reference(s)
Real windows of Paris buildings with random points
27-76 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [6*10^14,7*10^14]-
28-73 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
29-73 reference(s)
Untitled 0649
30-72 reference(s)
A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of 'pi' (141592...)-base 10- with 33.333 time steps
31-72 reference(s)
The quaternionic Julia set computed with A=(0,1,0,0)-tridimensional cross-section-
32-72 reference(s)
Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
33-72 reference(s)
Tridimensional representation of a quadridimensional Calabi-Yau manifold
34-72 reference(s)
A double spherical cross-section inside the Menger Sponge -iteration 5-
35-70 reference(s)
The Menger Sponge -iteration 5-
36-70 reference(s)
Untitled 0645
37-69 reference(s)
Tridimensional display of the particle trajectories of bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity
38-69 reference(s)
Botticelli anomaly on the Moon
39-69 reference(s)
Visualization of the Proth-Gilbreath Conjecture process for G(Pi(1.0025x10^15))=806.
40-69 reference(s)
A type 'B10-TP' pseudo-random walk defined by means of the 48 first decimals of the transcendental Champernowne number -using all base 10 integer numbers-: 0.{1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 2...}
41-68 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [1*10^14,2*10^14]-
42-68 reference(s)
N-body problem integration (N=2)displaying a perfect Keplerian orbit
43-67 reference(s)
An amazing cross-section inside the Menger Sponge -iteration 5-
44-67 reference(s)
Hypercube
45-67 reference(s)
Elliptical trajectory of a planet around a star with perihelion advance (very exaggerated)
46-67 reference(s)
Untitled 0662
47-66 reference(s)
A type 'B10-T' pseudo-random walk defined by means of the 48 first decimals of the transcendental Champernowne number -using all base 10 integer numbers-: 0.{1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 2...}
48-66 reference(s)
A half-random extended Menger Sponge -iteration 5-
49-66 reference(s)
A 1972 Télémécanique T1600 computer with a 32 KB central memory and two 512 KB disk drives. More than 50 years of progress in computer science -hardware and software-
50-65 reference(s)
From Pluto to the Sun (non linear scales)
51-65 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 121288...-
52-65 reference(s)
Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
53-65 reference(s)
LE BUG DE L'AN 2000 (comprendre l'informatique jusqu'à ses défaillances)
54-65 reference(s)
The Jeener-Klein triple bottle
55-65 reference(s)
A tridimensional intertwining made of the Menger Sponge -iteration 5- inside a sphere
56-64 reference(s)
The Sierpinski Carpet -iteration 4-
57-64 reference(s)
The generalized Ulam spiral displaying 100 numbers
58-64 reference(s)
Monument Valley at sunrise
59-64 reference(s)
The same bidimensional scalar field displayed with 4 different color palettes
60-64 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)
61-64 reference(s)
Jean-François Colonna (on 11/17/1994)with its fractal mountains
62-64 reference(s)
La Génèse (1974)
63-64 reference(s)
A type 'B10-RP' pseudo-random walk defined by means of the 48 first decimals of the transcendental Champernowne number -using all base 10 integer numbers-: 0.{1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 2...}
64-63 reference(s)
A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
65-63 reference(s)
Mountains at sunrise
66-63 reference(s)
The Menger Sponge -iteration 5-
67-63 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 256 prime numbers following 100000...-
68-63 reference(s)
The Jeener-Klein bottle loop 1
69-63 reference(s)
Tridimensional display of the Riemann Zeta function inside [-10.0,+60.0]x[-35.0,+35.0] (bird's-eye view)
70-62 reference(s)
Mapping on a torus of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
71-62 reference(s)
The generalized Ulam spiral displaying 1024 numbers
72-62 reference(s)
Quark and gluon structure of a nucleon
73-62 reference(s)
Quark and gluon structure of a nucleon
74-62 reference(s)
A Douady rabbit -a complex Julia set computed with A=(-0.13,+0.77)- with display of the arguments
75-62 reference(s)
The Klein bottle described by means of a Bidimensional Hilbert Curve -iteration 7-
76-62 reference(s)
Untitled 0642
77-61 reference(s)
Where is the Universe?
78-61 reference(s)
The execution of a very simple program on a Turing Machine
79-61 reference(s)
A tridimensional intertwining inside a Jeener intertwining
80-61 reference(s)
A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of 'phi' -the golden ratio- (618033...)-base 10- with 33.333 time steps
81-61 reference(s)
Untitled 0671
82-61 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [9*10^14,10^15]-
83-61 reference(s)
The Universe at the heart of a Calabi-Yau manifold
84-60 reference(s)
Artistic view of the Big Bang
85-60 reference(s)
A punched paper tape
86-60 reference(s)
A regular 3-gon -an equilateral triangle-
87-60 reference(s)
The Menger Sponge -iteration 2-
88-60 reference(s)
Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
89-60 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
90-60 reference(s)
The Lorenz attractor
91-60 reference(s)
Tridimensional display of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation)
92-60 reference(s)
The construction of the tridimensional Hilbert Curve -iteration 3-
93-60 reference(s)
An extended Menger Sponge -iteration 3- displaying the 10.665 first values of G(Pi(x)) modulo 2 of the Proth-Gilbreath conjecture
94-60 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [5*10^14,6*10^14]-
95-60 reference(s)
An amazing cross-section inside the Menger Sponge -iteration 5- with a tridimensional non linear transformation
96-59 reference(s)
An amazing cross-section inside the Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-
97-59 reference(s)
Rotation about the X axis of the Lorenz attractor (1000 iterations), computed simultaneously on two different computers
98-59 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 1024 prime numbers following 120662...-
99-59 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [1.3x10^15,1.4x10^15]-
100-59 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [7*10^14,8*10^14]-
101-59 reference(s)
Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 1.083.984 galaxies)obtained by means of a non deterministic fractal process
102-59 reference(s)
A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-
103-58 reference(s)
Autostereogram with an hidden volcano
104-58 reference(s)
An extended Menger Sponge -iteration 4-
105-58 reference(s)
A spherical cross-section inside the Menger Sponge -iteration 5-
106-58 reference(s)
The Menger Sponge -iteration 3-
107-58 reference(s)
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
108-58 reference(s)
Random pseudo-periodical quadrangulation of a cube -8x8x8-
109-58 reference(s)
A foggy pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb')computed with A=(-0.581514...,+0.635888...,0,0) and with a rotation about the Y axis -tridimensional cross-section-
110-58 reference(s)
Tridimensional display of 36 eigenstates of the Hydrogen atom (bidimensional computation)
111-58 reference(s)
Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known
112-58 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 256 prime numbers following 100000...-
113-58 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 256 prime numbers following 100000...-
114-58 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 32 first prime numbers-
115-58 reference(s)
The Proth-Gilbreath Conjecture -display of the G(Pi(x)) function for x E [8*10^14,9*10^14]-
116-58 reference(s)
Tridimensional fractal surface (bird's-eye view)
117-58 reference(s)
Artistic view of a tridimensional display of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-
118-57 reference(s)
Tridimensional display of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-
119-57 reference(s)
The first four iterations of the construction of the von Koch snowflake
120-57 reference(s)
Quantum vacuum fluctuations
121-57 reference(s)
A tridimensional field
122-57 reference(s)
A pseudo-octonionic Mandelbrot set (a 'MandelBulb')-tridimensional cross-section-
123-57 reference(s)
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb')-tridimensional cross-section-
124-57 reference(s)
The Lorenz attractor -sensitivity to initial conditions (displayed as the central point of each frame)-
125-57 reference(s)
Fractal Self-Portrait -'Décalcomanie', a Tribute to René Magritte-
126-57 reference(s)
A 'linear' Horner surface of the fourth degree
127-57 reference(s)
The Proth-Gilbreath Conjecture -display of the process for the 32 first prime numbers-
128-57 reference(s)




2-The 128 most referenced Pages (*):

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



1-AVirtualSpaceTimeTravelMachine.Ang
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2-ChatGPT.11.Fra
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3-Proth_Gilbreath_Conjecture.01.Ang
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4-Fractal.21
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5-Vcatalogue.11
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6-MorePages.Ang.
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7-xrC_____ObjetComplexe.C59__2.vv.t.
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10-VAcatalogue.11
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11-UlamSpiral.01.Ang
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12-Galerie_DeterministicFractalGeometry.FV
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13-xrC_____ObjetComplexe.Y1___2.vv.c.
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14-help.
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15-xiirv_____.PIPO.21.2..u.
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122-xrC_____images_1octet.01.vv.I.
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123-xrC_____ObjetComplexe.K1.vv.c.
95 reference(s)
124-xrC_____ObjetComplexe.I16__1.vv.c.
95 reference(s)
125-xrC_____ObjetComplexe.B4E__1.vv.c.
95 reference(s)
126-xrC_____ObjetComplexe.A12__2.vv.c.
95 reference(s)
127-xrC_____ObjetComplexe.A11__1.vv.t.
95 reference(s)
128-xrC_____OBJC.Y3d__1_______.11.DFractale.t.
95 reference(s)

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




Copyright © Jean-François Colonna, -2026.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, -2026.