Do these patterns share some common mathematical rules, like the "golden ratio" from Euclidian geometry?

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The whole process of creating a handmade rug, from the initial design to the actual production, follows mathematical rules. In some styles of rug design, artists use the golden ratio. I sometimes apply this rule in my work, depending on what I want to create. I'm not sure if I've shared that here, but you can definitely check the #Pegahrug hashtag.