Ad Quadratum, the origin of the wave border pattern in Greek and Roman mosaics?

Previously I’ve shown how to plan out the Wave border pattern using offset circles, but what if there is another way, one much more rooted in geometry?
These photos show a possible formula that could have been used.
Ad quadratum is a pattern seen in the ancient world, there is a terracotta tablet from Mesopotamia incised with some geometrical diagrams which has been dated to 18th century BC and this has the circle within the square which forms the basis for this pattern. If you shade certain areas of this pattern you then get what is known as the Baravelle spiral, which looks remarkably similar to the wave border.


1. Ad quadratum, seen in examples of ancient geometry. A circle is drawn inside a square. Another square is then drawn inside this circle.
2. Continue this process .
3. Here you can see the squares and circles drawn out.
4. Block in (here using red) starting at the top right and just going one section of pattern at a time and you will naturally be drawn into the centre. This spiral, if you create another one opposite is known as The Baravelle spiral.


Here I’ve added a repeat of the pattern on either side and you can see the border being formed.


Here is a copy of a conventional wave border pattern and you can see the similarities. It would not be too difficult to mark a staff, adjusting the size of the curl to create the above from Ad quadratum.




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