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

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-.	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.