Sketch 23: Pattern with squares and octagons

While exploring some areas around Isfahan I found a remote village Ashtarjan with a very old Ilkhanid mosque Jameh Mosque of Ashtarjan ( 1315–16 ). The mosque had some simple geometric decorations. Here is one of them.

Geometric pattern with squares and octagons.

In this short sketch we will analyse and reconstruct this pattern. This is very simple but very useful work.

First let see what mirror symmetries we have here. After drawing these lines we see that we have here a number of squares filled with pattern. It is enough to reconstruct one of these squares to get the whole design.

Step 1 – basic network

Start with a square and divide three of its angles into four equal parts. The fourth angle leave as it is.
Use the red points as centers of two arcs and the the large point for the radius of the arcs.

Step 3 – lines of the pattern

Draw the thick segments. This way we will get halves of two octagons and some space to create the remaining polygons.
This part is obvious. We get these two squares and quarter of another octagon.
After removing all construction lines and arcs we get the final template for the pattern. Now we can add colors and some extra decorations.

Step 4 – colors

Template with colors that are close to the original ceramic tiles on the mosque wall.

Step 5 – an extra decoration

Preparations for drawing a star inside the octagon.
Edges of the star
A small template of the pattern with decorations and colors for ceramic tiles.

Step 5 – final pattern

Below we have three instances of the pattern. The first one is just a larger template created from four copies of the template that we made in the previous step. NOTE – we use four instances of the small template by rotating them around the central white star. Below we have long frieze with four copies of the larger template. Further down we have a larger allover pattern with 16 copies of the larger template.

Pattern using four copies of the larger template.

Patterns like this one are often good starting point for some more complex designs. Try to think how to extend the white star into squares and octagons.

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