The Alhambra and The Alcazar (Spain)

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The Palaces

The Alhambra and Reales Alcázeres are palaces in Spain dating to the 14th century. The rulers who had these building constructed were Moors and hence Moslims. Their art consists to a large degree of geometric designs.

The Reales Alcázeres is also known as Alcázar of Seville. This royal palace was built in the 1360s. The Alcazar is listed as a Unesco World heritage Site.

The Alhambra dates from the same time period. Like the Alcazar, the Alhambra was also originally built as a fortress, and later used as a palace. The Alhambra is also listed as a Unesco World heritage Site.

The Alhambra is one of the sites visited by MC Escher during his younger years. Escher sketched some of the patterns he saw at the Alhambra, and further sketches of his from Cordoba are also well-known.

The Alhambra is a large palace and one can visit the gardens as well as the palace grounds.

Palace1.jpg Palace2.jpg

The designs throughout the Alhambra are very symmetric in nature. Below we see a window with a view of the palace gardens. The outline and the decoration above the window show reflectional symmetry. Around the doorway - show in the middle picture - we see examples of border patterns. More borders are visible just above the tiling that makes up the bottom of the wall. Also note the intricate designs above the pillars in the right hand picture.

Palace3.jpg Palace-crop.jpg Palace5.jpg

La Mezquita in Córdoba, Spain is a mosque converted to a catholic Cathedral. Escher visited this site as well and sketched the pillared halls.

La-mezquita-cordoba.jpg Mosque-of-Cordoba.jpg

The design of the Mezquita is very symmetric in nature. The photographs below clearly show the reflectional symmetry in the layout of the building.

Mezquita-Cordoba1.jpg Mezquita-Cordoba2.jpg


There are many examples of rozettes. Sometimes the rosette shows up as a seperate tile. Other times we can lift a patetrn from a larger border or tiling. The most common rozettes in these palaces are ones with no reflectional symmetry. Quite a few of the rozette are created with ribbons showing under- and over-crossings. Any ribbon work like that usually leads to what we call a purely cyclic pattern. The only symmetries present are rotational symmetries. Rozette-Spain1.jpg

Some of the panels on a wall may be decorated with one pattern. Such larger panels often have just 2 fold rotational symmetry, even though smaller components may have more symmetry than that.

Rozette1.jpg Rozette-wall.jpg Wall-part.jpg

In close-up we see some of the individual smaller rozettes. The most common rotational symmetries are of degree 4 and 8. An ocassional design with no symmetries is possible.

Rozette3.jpg Rozette4.jpg Rozette2.jpg Rozette-Spain2.jpg
Rosette-Spain5.jpg Rozette-Spain6.jpg Rozette-Spain7.jpg Rozette-Spain8.jpg

Border Patterns

Border patterns are quite interesting, and they appear as borders to the larger tilings, but they also appear on some of the benches as decoration. Note for instance the borders decorating the back and the bottom part of this seating area:


This bench - outside on the grounds - shows a tiling across the front of the seat:


This bench shows three different border patterns on the back of the seat and the pattern on the front also appears as a full tessellation on some walls.


Below are several more examples of border patterns. Some of these appear - quite literally - as the border of other tilings. While some of the borders are used to frame doorways and passages. The borders can appear both horizontally and vertically, but have been mainly shown here horizontally.

Alhambra-border1.jpg Alhambra-border2.jpg Alhambra-border3.jpg
Border-Spain1.jpg Border-Alcazar.jpg Border-Spain2.jpg

The underside of some of the arches also show border patterns. Some of these patterns are quite intricately carved.

Alcazararch1.jpg AlcazarArch2.jpg

Wallpaper Patterns

There are many different types of tilings and the easiest way to show some differences is to look at the orders of rotation. In general we can have no rotation, 2-fold rotation, 3-fold rotation,4-fold rotation, or 6-fold rotation.

No Rotation

This tessellation has no symmetries besides translations. We can choose any part of the tiling and note that nearby we will find copies of that specific pattern which repeats itself.


There is almost reflectional symmetry, but the under and over crossings prevent there from being true mirror lines. Note the simple border pattern just above the tiling.

2-Fold Rotations

AlhambraWall2.jpg Tiling-side-bench.jpg


3-Fold Rotations

4-Fold Rotations

AlhambraWall1.jpg Alcazar2.jpg

6-Fold Rotations

Alcazar3.jpg Alcazar4.jpg

Andalucia dag 12 036.jpg