Didactical Pictures

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Jean-François COLONNA

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, 91120 Palaiseau, France

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(CMAP28 WWW site: this page was created on 05/03/2016 and last updated on 02/14/2023 13:16:36 -CET-)

- 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]
- Astrophysics and Cosmology [
*Astrophysique et Cosmologie*]: - Deterministic Chaos [
*Chaos Déterministe*]:
[More pictures about Deterministic Chaos]
- Miscellaneous [
*Divers*]:
[More pictures about Visualization]

The history of Mathematics. |

An equilateral triangle. | A right-angled triangle. |

A demonstration of the Pythagoras' theorem. | A demonstration of the Pythagoras' theorem. | A demonstration of the Pythagoras' theorem using a very poor picture. |

Two sets. |

A bijection. | A bijection. |

To count the members of a set. |

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'. |

How to compute 'pi' with a gun. |

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 point. |

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-. |

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-. |

A distorded -for the sake of display- 5-cube -an hyperhypercube-. |

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. |

Tridimensional representation of our familiar tridimensional space. |

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-. |

A bidimensional Hilbert-like curve defined with {X_{1}(...),Y_{1}(...)} -iteration 1-. |
A bidimensional Hilbert-like curve defined with {X_{2}(...),Y_{2}(...)} -iteration 2-. |

Tridimensional Hilbert Curve -iteration 1-. | Tridimensional Hilbert Curve -iteration 2-. | Tridimensional Hilbert Curve -iteration 3-. | Tridimensional Hilbert Curve -iteration 4-. |

The Mandelbrot set. | Bidimensional zoom in on 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)- with display of the arguments. | Iterations in the complex plane: the computation of a Julia set. |

Computation of the roots of Z^{3}=1 using Newton's method. |
Visualization of the Newton's method when computing the roots of Z^{3}=1. |

Along the border of the Mandelbrot set. |

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

A medium with percolation -top to bottom- using the 4-connexity. |
A medium with percolation -top to bottom- using the 8-connexity. |

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

The actual relative sizes of the Solar System bodies. |

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

Artistic view of gravitational waves. | Gravitation and space-time curvature. | Gravitation and space-time curvature. |

[More pictures about Statistical Mechanics]

[More pictures about Sensitivity to Rounding-Off Errors]

The Lorenz attractor. |

The configuration entropy of a set of n=64 particles. |

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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