This is a picture of the Great Mosque in Kairouan, Tunsie showing the distinct pattern of pillars. arches and dome imprints commonly seen in Historical architecture.
This is a picture of a Coliseum in eternal Rome. This Coliseum shows the constant repetitions in Arch shaped windows around the exterior of the building. The immense self supporting dome on this building are actually perfect hemispheres with the cylinders below them being the same diameter.
This image is the El Castillo in Chichen Itza. This is an ancient Mayan Temple following a strict pattern of rectangles and squares moving up from the base to the top. This also represents dilation in the scaling down of each base as it reaches to the top.
This is an example of Islamic architecture which is a specific type of geometrical patterns in architecture. These carvings and painting are located on the main dome in the Selimiye Mosque. The invasion and conquer of the Persian empire lead to the most famous style in architecture the horseshoe arch and many murals consisting of octagonal patterns.
The Sally Port of Sheikh Lot Allah Mosque is a private mosque built for a royal family. This is an exact example of the octagonal patterns in Islamic architecture. The actual octagon shapes that Muslims are so fascinated by actually represent their way of life. Religion is very important to Muslims and represent it in their 4 design schemes in buildings.