In the fall of my freshman year in architecture school, we had a graphic design project to create a ‘tile’ that would look interesting on its own, and when it was repeated it would take on a different visual composition.
I’d heard about the Golden Section / Golden Ratio which is a proportion that was supposed to show up in many places in nature like the spiral of a nautilus shell, or the layout of seeds in a sunflower. The ancient Greeks used the Golden Ratio in the designs of their temples, and many designers since then have looked to the Golden Ratio to create compositions that were thought to be the most aesthetically ideal. (check out https://en.wikipedia.org/wiki/Golden_ratio for more)
So this seemed like a good place to start on my ‘tile’ design. After a few attempts shifting & overlapping Golden Ratio rectangles, I made arcs along the length of each side of a Golden rectangle. Then I rotated a second rectangle from the corner of the first and created a square with an empty corner. The arcs created a seed or flower pattern that diagonally pointed towards the open corner. When these tiles are repeated the arcs create interlocking circles with the same Golden Ration proportion.
This became my project solution with the addition of some color in the tiles, and I liked it so much, I committed to using it as a logo if I ever started my own architectural practice. And 17 years later it became the logo for Limitless Blue architecture & sustainable design!