Didactical Pictures

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Jean-François COLONNA

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France

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(CMAP28 WWW site: this page was created on 05/03/2016 and last updated on 12/08/2019 13:00:34 -CET-)

Mathematics [ Mathématiques]. |
Fractal Geometry [ Géométrie Fractale]. |
Celestial Mechanics [ Mécanique Céleste]. |
Deterministic Chaos [ Chaos Déterministe]. |
Miscellaneous [ Divers]. |

- Mathematics [
*Mathématiques*]:
[more pictures about Mathematics]
- Fractal Geometry [
*Géométrie Fractale*]:
[more pictures about Deterministic Fractal Geometry]
- Celestial Mechanics [
*Mécanique Céleste*]:
[more pictures about Celestial Mechanics]
- Deterministic Chaos [
*Chaos Déterministe*]:
[more pictures about Deterministic Chaos]
- Miscellaneous [
*Divers*]:
[more pictures about Visualization]

A demonstration of the Pythagoras' theorem. |

Two sets. |
A bijection. |

A bijection. |

A set 'E'. |
Two subsets 'SE1' and 'SE2' of a set 'E'. |
Two sets 'SE1' and 'SE2'. |
A set 'F' with two elements 'SE1' and 'SE2'. |

The four first power sets {P(E),P(P(E)),P(P(P(E))),P(P(P(P(E))))} of a one-element set E. |
The Continuum Hypothesis (CH). |
The Continuum Hypothesis (CH). |

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

The continuity. |
The differentiability. |
Definition of a tangent -orange- by means of a secant -red-. |

The continuity. |
The differentiability. |
Definition of a tangent -yellow- by means of a secant -orange-. |

The volume of a cube K -U being the unity cube-. |

A 0-cube -a point-. |
A 1-cube -a segment-. |
A 2-cube -a square-. |
A 3-cube -a cube-. |
A 4-cube -an hypercube-. |

The Golden Rectangle. |
Recursive subdivision of the Golden Rectangle by means of the Golden Ratio -phi-. |

The two subdivisions of the 'flat' Golden Triangle. |
The 'flat' Golden Triangle. |
One of the two subdivisions of the 'flat' Golden Triangle. |
One of the two subdivisions of the 'flat' Golden Triangle. |

A straigth line -a monodimensional manifold- or a cylinder -a bidimensional manifold- in the distance?. |
A cylinder -a bidimensional manifold-. |
A cylinder -a bidimensional manifold-. |

To add two numbers. |
To multiply two numbers. |

The abelian -commutative- group defined on elliptic curves. |

[more pictures about Non Deterministic Fractal Geometry]

The self-similarity of the von Koch curve. |
The self-similarity of the von Koch curve displayed by means of a zoom in with a ratio that is equal to 3. |

A perfect bidimensional fractal tree and the self-similarity. |
A perfect bidimensional fractal tree and the self-similarity. |
The self-similarity of a perfect bidimensional fractal tree. |

A random bidimensional fractal tree and the self-similarity. |
The self-similarity of a random bidimensional fractal tree. |

The Cantor triadic set -iterations 0 to 5-. |

The Sierpinski carpet -iteration 1-. |
The Sierpinski carpet -iteration 2-. |
The construction process of the Sierpinski carpet. |

The Menger sponge -iteration 1-. |
The Menger sponge -iteration 2-. |
The construction process of the Menger sponge. |

The Menger sponge -iteration 1-. |
The Menger sponge -iteration 2-. |
The construction process of the Menger sponge. |

The Mandelbrot set. |
Iterations in the complex plane. |
Iterations in the complex plane: the computation of the Mandelbrot set. |

A Douady rabbit -a complex Julia set computed with A=(-0.13,+0.77)-. |
Iterations in the complex plane: the computation of a Julia set. |

Along the border of the Mandelbrot set. |

The iterative process used to generate bidimensional fractal fields (large mesh). |

Fractal diffusion front in a bidimensional medium obtained by means of a random walk process. |

N-body problem integration (N=2) displaying a perfect Keplerian orbit. |
display of the inclination of two elliptic trajectories. |

From Pluto to the Sun. |
The journey of an Earth-like planet (green) in the Solar System -point of view of the virtual planet-. |

[more pictures about Statistical Mechanics]

[more pictures about Sensitivity to Rounding-Off Errors]

The Lorenz attractor. |

Free fall in the vacuum. |

The rain (or the snow) is falling. |

A childish Sun. |

A color palette with an increasing luminance. |
From cold to warm colors. |
From cold to warm colors. |
The same bidimensional scalar field displayed with 4 different color palettes. |

The RGB cube and the additive synthesis of colors. |
Anaglyphic glasses. |

The 'Tapestry' effect applied to a right-angled triangle. |
The 'CenterOf' effect applied to a right-angled triangle. |

Clockwise. |
Anticlockwise -trigonometric-. |

Simple chessboard. |
Simple chessboard. |
Simple chessboard. |
Simple chessboard. |

CMAP. |

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