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NUMBER THEORY (AND MORE...)

[Théorie des Nombres (et autres sujets...)]

Tridimensional display of the Riemann Zeta function inside (-10.0,20.0)x(-15.0,15.0)

Jean-François COLONNA

CMAP (Centre de Mathématiques APpliquées), Ecole Polytechnique, CNRS
91128 Palaiseau Cedex
France

tel = +33.(0)1.69.33.46.45
jean-francois.colonna@polytechnique.edu

http://www.lactamme.polytechnique.fr

http://www.cmap.polytechnique.fr/~colonna

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(this page was created on 03/15/2000)
(this page -belonging to the CMAP28 site- was last updated on 03/01/2010 20:13:56 -CET-)

Number Theory (and more...) [Théorie des Nombres (et autres sujets...)] :

Conway's Surreal Numbers [Les Nombres Surréels de Conway] :
Functions of a Complex Variable [Fonctions d'une Variable Complexe] :
Gamma Function [La Fonction Gamma] :
Riemann's Zeta Function [La Fonction Zêta de Riemann] :
Prime Numbers [Les Nombres Premiers] :
Arrangement of N Points on a Sphere [Placement de N Points sur une Sphère] :
Knots [Noeuds] :
Monodimensional Binary Cellular Automata [Automates Cellulaires Binaires Monodimensionnels] :
Monodimensional "Quasi-Continous" Cellular Automata [Automates Cellulaires "Quasi-Continus" Monodimensionnels] :
Bidimensional Cellular Automata [Automates Cellulaires Bidimensionnels] :
Voronoi Diagrams [Diagrammes de Voronoï] :
Conformal Transformations [Transformations Conformes] :

Number Theory (and more...) [Théorie des Nombres (et autres sujets...)] :

Conway's Surreal Numbers [Les Nombres Surréels de Conway] :

Generation of the 63 first Conway's surreal numbers

Generation of the 63x63 first Conway's surreal complex numbers

Generation of the 2x63-1 first Conway's surreal complex numbers

Generation of the 63x63 first Conway's surreal complex numbers

Functions of a Complex Variable [Fonctions d'une Variable Complexe] :

The relief -modulus- of the function exp(1/z)defined by means of three bidimensional fields

The relief -modulus- of the function exp(1/z)with argument mapping (bird's-eye view)

The relief -modulus- of the function exp(1/z)with argument mapping

The relief -modulus- of the function sin(z)defined by means of three bidimensional fields

The relief -modulus- of the function sin(z)with argument mapping

Gamma Function [La Fonction Gamma] :

Tridimensional display of the Gamma function inside (-20.0,20.0)x(-20.0,20.0) (bird's-eye view)

Tridimensional display of the Gamma function inside (-20.0,20.0)x(-20.0,20.0)

Bidimensional zoom in on the Z=Gamma(Z)iteration with display of the arguments

Tridimensional display of the Z=Gamma(Z)iteration inside (-20.0,20.0)x(-20.0,20.0) (bird's-eye view)

Tridimensional display of the Z=Gamma(Z)iteration inside (-20.0,20.0)x(-20.0,20.0)

Riemann's Zeta Function [La Fonction Zêta de Riemann] :

Tridimensional display of the Riemann Zeta function inside (-10.0,20.0)x(-15.0,15.0) (bird's-eye view)

Tridimensional display of the Riemann Zeta function inside (-10.0,20.0)x(-15.0,15.0)

Tridimensional display of the Riemann Zeta function inside (-10.0,60.0)x(-35.0,35.0) (bird's-eye view)

Tridimensional display of the Riemann Zeta function inside (-10.0,60.0)x(-35.0,35.0)

Tridimensional display of the Riemann Zeta function inside (-50.0,50.0)x(-50.0,50.0) (bird's-eye view)

Tridimensional display of the Riemann Zeta function inside (-50.0,50.0)x(-50.0,50.0)

Bidimensional zoom in on the Z=Zeta(Z)iteration with display of the arguments

Tridimensional display of the Z=Zeta(Z)iteration inside (-20.0,20.0)x(-20.0,20.0) (bird's-eye view)

Tridimensional display of the Z=Zeta(Z)iteration inside (-20.0,20.0)x(-20.0,20.0)

Artistic view of Ph(Zeta)

Prime Numbers [Les Nombres Premiers] :

The Liouville function displayed as a bidimensional random walk for the integer numbers from 2 to 1001

The Liouville function displayed as a bidimensional random walk for the integer numbers from 2 to 100001

The Liouville function displayed as a tridimensional random walk for the integer numbers from 2 to 150001

The special Liouville function displayed as a bidimensional random walk for the integer numbers from 2 to 200001 (Red), 2 to 400001 (Green) and 2 to 800001 (Blue)

The Eratosthene sieve displaying 10x10 numbers

The Eratosthene sieve displaying 100x100 numbers

The generalized Ulam spiral displaying 100 numbers

The generalized Ulam spiral displaying 1024 numbers

The Archimedes spiral displaying 100 numbers

The Archimedes spiral displaying 1000 numbers

Artistic view of the prime numbers

Arrangement of N Points on a Sphere [Placement de N Points sur une Sphère] :

'Harmonious' arrangement of 4 points on a sphere -a Tetrahedron- by means of simulated annealing

'Harmonious' arrangement of 4 points on a sphere -a Tetrahedron- by means of simulated annealing

'Harmonious' arrangement of 6 points on a sphere -an Octahedron- by means of simulated annealing

'Harmonious' arrangement of 6 points on a sphere -an Octahedron- by means of simulated annealing

'Harmonious' arrangement of 8 points on a sphere by means of simulated annealing

'Harmonious' arrangement of 8 points on a sphere by means of simulated annealing

'Harmonious' arrangement of 12 points on a sphere -an Icosahedron- by means of simulated annealing

'Harmonious' arrangement of 12 points on a sphere -an Icosahedron- by means of simulated annealing

'Harmonious' arrangement of 24 points on a sphere by means of simulated annealing

'Harmonious' arrangement of 24 points on a sphere by means of simulated annealing

'Harmonious' arrangement of 26 points on a sphere by means of simulated annealing

Knots [Noeuds] :

3-foil torus knot on its torus

3-foil knot

5-foil torus knot on its torus

7-foil torus knot on its torus

Monodimensional Binary Cellular Automata [Automates Cellulaires Binaires Monodimensionnels ] :

An elementary monodimensional binary cellular automaton -86- with 1 white starting point -bottom middle-

An elementary monodimensional binary cellular automaton -86- with random white starting points -on the bottom line-

An elementary monodimensional binary cellular automaton -90- with 1 white starting point -bottom middle-

An elementary monodimensional binary cellular automaton -90- with 49 white starting points -on the bottom line-

An elementary monodimensional binary cellular automaton -106- with 1 white starting point -bottom middle-

An elementary monodimensional binary cellular automaton -106- with random white starting points -on the bottom line-

An elementary monodimensional binary cellular automaton -110- with 1 white starting point -bottom right-

An elementary monodimensional binary cellular automaton -110- with 49 white starting points -on the bottom line-

An elementary monodimensional binary cellular automaton -184- with 1 white starting point -bottom middle-

An elementary monodimensional binary cellular automaton -184- with random white starting points -on the bottom line-

Three successive elementary monodimensional binary cellular automata -106,90,86- with 1 yellow starting point -bottom middle-

Three successive elementary monodimensional binary cellular automata -106,90,86- with random yellow starting points -on the bottom line-

The alternative use of two elementary monodimensional binary cellular automata -168,165- with 1 white starting point -bottom middle-

The alternative use of two elementary monodimensional binary cellular automata -168,165- with periodical white starting points -on the bottom line-

The alternative use of two elementary monodimensional binary cellular automata -168,165- with random white starting points -on the bottom line-

256 elementary monodimensional binary cellular automata with 1 white starting point (bottom left is the automata number 0 when top right is the number 255)

256 elementary monodimensional binary cellular automata with 56% of white starting points (bottom left is the automata number 0 when top right is the number 255)

Monodimensional "Quasi-Continous" Cellular Automata [Automates Cellulaires "Quasi-Continus" Monodimensionnels] :

A monodimensional 'quasi-continuous' cellular automaton

A monodimensional 'quasi-continuous' cellular automaton

A monodimensional 'quasi-continuous' cellular automaton

A monodimensional 'quasi-continuous' cellular automaton

A monodimensional 'quasi-continuous' cellular automaton

A monodimensional 'quasi-continuous' cellular automaton

A monodimensional 'quasi-continuous' cellular automaton

Two alternative monodimensional 'quasi-continuous' cellular automata

Two alternative monodimensional 'quasi-continuous' cellular automata

A monodimensional 'quasi-continuous' cellular automaton with random perturbation of the rules

A monodimensional 'quasi-continuous' cellular automaton with random perturbation of the rules

Bidimensional Cellular Automata [Automates Cellulaires Bidimensionnels] :

The life game

64 elementary bidimensional binary cellular automata with 1 white starting central point

Tridimensional display of the evolution of a bidimensional binary cellular automaton with 1 white starting central point

Voronoi Diagrams [Diagrammes de Voronoï] :

Voronoi diagrams

Conformal Transformations [Transformations Conformes] :

1/Z conformal transformation of concentric circles

ZxZ conformal transformation of concentric circles

Copyright (c) Jean-François Colonna, 2000-2010.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) / Ecole Polytechnique, 2000-2010.