Mapping on the Mobius strip of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3- ('Mapping' sur un ruban de Mobius d'un sous-ensemble fini d'un pavage periodique du plan utilisant 4 flocons de neige de type von Koch -iteration 3-) {a chapter of 'Mathematics - A Virtual Instrument For Exploring Space Time And Beyond'}

Mapping on the Möbius strip of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3- ['Mapping' sur un ruban de Möbius d'un sous-ensemble fini d'un pavage périodique du plan utilisant 4 flocons de neige de type von Koch -itération 3-].

See an artistic view:

Untitled 0657

Some few fractal shapes (like the von Koch snowflake) can be used to tile the plane using scaling and rotations:

A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

A periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-

4 snowflakes
3 iterations.

Artistic view of a tridimensional display of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

Artistic view of a tridimensional display of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

Artistic view of a tridimensional display of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-

4 snowflakes
3 iterations.

Mapping on a cylinder of a finite subset of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

Mapping on a cylinder of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

Mapping on a cylinder of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-

4 snowflakes
3 iterations.

Mapping on a sphere of a finite subset of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

Mapping on a sphere of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

Mapping on a sphere of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-

4 snowflakes
3 iterations.

Mapping on a torus of a finite subset of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

Mapping on a torus of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

Mapping on a torus of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-

4 snowflakes
3 iterations.

Mapping on the Möbius strip of a finite subset of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

Mapping on the Möbius strip of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

Mapping on the Möbius strip of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-

4 snowflakes
3 iterations.

Mapping on the Klein bottle of a finite subset of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

Mapping on the Klein bottle of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

Mapping on the Klein bottle of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-

4 snowflakes
3 iterations.

Bonan-Jeener double bottle

Mapping on the Bonan-Jeener double bottle of a finite subset of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

Mapping on the Bonan-Jeener double bottle of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

Mapping on the Bonan-Jeener double bottle of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-

4 snowflakes
3 iterations.

quadridimensional Calabi-Yau manifold

Mapping on a quadridimensional Calabi-Yau manifold of a finite subset of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

Mapping on a quadridimensional Calabi-Yau manifold of a finite subset of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

Mapping on a quadridimensional Calabi-Yau manifold of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-

4 snowflakes
3 iterations.

Some few fractal shapes (like the von Koch snowflake) can be used to tile the plane using scaling and rotations:

A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

A periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-

4 snowflakes
3 iterations.

Tridimensional display of a periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

Tridimensional display of a periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

Tridimensional display of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-

4 snowflakes
3 iterations.

A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

A periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-

4 snowflakes
3 iterations.

Some few fractal shapes (like the von Koch snowflake) can be used to tile the plane using scaling and rotations:

A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 2-

2 snowflakes
2 iterations.

A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 4-

2 snowflakes
4 iterations.

A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 5-

2 snowflakes
5 iterations.

A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 2-

2 snowflakes
2 iterations.

A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-

2 snowflakes
3 iterations.

A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 4-

2 snowflakes
4 iterations.

A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 5-

2 snowflakes
5 iterations.

Empty

Empty

Empty

A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 5-

2 snowflakes
5 iterations.

Some few fractal shapes (like the von Koch snowflake) can be used to tile the plane using scaling and rotations:

A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 2-

3 snowflakes
2 iterations.

A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 4-

3 snowflakes
4 iterations.

A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 5-

3 snowflakes
5 iterations.

A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 2-

3 snowflakes
2 iterations.

A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-

3 snowflakes
3 iterations.

A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 4-

3 snowflakes
4 iterations.

A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 5-

3 snowflakes
5 iterations.

Empty

Empty

Empty

A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 5-

3 snowflakes
5 iterations.

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