The Beauty of Mathematics
Art and Mathematics
Mathematics, the Language of Nature (and Art?)






Jean-François COLONNA
[Contact me]

www.lactamme.polytechnique.fr

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

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[Please, visit A Virtual Machine for Exploring Space-Time and Beyond, the place where you can find thousands of pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 10/08/2023 and last updated on 01/01/2024 11:56:04 -CET-)



[en français/in french]



Pi Decimals and Brownian Motion :


The 126.646 first digits -base 6- of 'pi' displayed as an 'absolute' tridimensional random walk
.

Tridimensional brownian motion
.





From Elementary Iterations to Unexpected Behavior :


The Lorenz attractor
.

Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-
.





Iterations in the Complex Plane and Beyond :


A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments
.

A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-
.

Close-up on a foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-
.

Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
.

Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-
.

A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-
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A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-
.

A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) and with a 0 to pi rotation about the X axis -tridimensional cross-section-
.





The Menger Sponge, an Infinite Surface and Zero Volume :


The Menger Sponge -iteration 5-
.

An amazing cross-section inside the Menger Sponge -iteration 5-
.

The erosion of an amazing cross-section inside the Menger Sponge -iteration 5-
.

Untitled 0320
.

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-
.





Filling Knots :


A Ball described by means of an 'open' 3-foil torus knot -iteration 3-
.

A Ball described by means of an 'open' 3-foil torus knot -iteration 4-
.

A Tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-
.





Fractal Geometry and Natural Phenomena :


Monument Valley at sunrise
.

Botticelli anomaly on the Moon
.

Mountains and fog
.





Revisiting Geocentrism :


The journey of an Earth-like planet (green) in the Solar System -point of view of the virtual planet-
.





Journey to the Planck Scale (Mathematics, an Optical Instrument?) :


Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-
.

Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-
.





Art and Mathematics :


Fractal Self-Portrait -'Décalcomanie', a Tribute to René Magritte-
.

A tribute to Sandro Botticelli and Victor Vasarely-
.

Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-
.

Untitled 0155 -a Tribute to Yves Tanguy-
.

Dissonance chaude/Dissonance froide -a Tribute to Paul Sérusier-
.

Untitled 0305
.

The Mathematics are the key of the Multiverse
.




Copyright © Jean-François COLONNA, 2023-2024.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2023-2024.