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Le blog de la section Math Euro Anglais du Lycée Baudelaire

Sierpinski’s triangle: Cosmati mosaics in the cathedral of Anagni

The cathedral of Santa Maria is located in the centre of Italy, in Anagni near Rome. It was built in the end of 11th century; it was commissioned by Bishop St. Peter of Salerno. The construction lasted 34 Years. It’s a mix between two styles of churches: the facade is Romanesque and the inside is Gothic.

Actually, in this cathedral older than 8 centuries, we can see patterns in the floor using the Sierpinski’s triangle. This floor was made in 1104

The pattern on this picture is the floor mosaic in the cathedral of Anagni. The most important of these functions is that they create self-similar structures, structures with parts that have the same form as the entire structure. On the picture, you see that the biggest triangles contain the next biggest triangles, surrounded by three triangles of the same kind, containing the next biggest triangle, etc. This process can be infinitely repeated.

Indeed, we know that the Sierpinski’s triangle was introduced in 1915 by Wadaw Sierpinski but in reality similar patterns appeared in the cosmati mosaics of this cathedral first. And it’s possibly the oldest handmade fractal mosaic.

Cathedral of Anagni

Cathedral of Anagni

The floor mosaic of Anagni

The floor mosaic of Anagni

The interior of the cathedral

The interior of the cathedral

Sierpinski triangle

Sierpinski triangle

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