The Devine Proportion, the Golden Rule, the Fibonacci Sequence. This isn't just a type of pattern, it's an intense mathematical problem of some sort that I can't even begin to wrap my head around. But all I know is that I like it. I know you'll like it too.
A Fibonacci number starts with zero (0) and one (1) added together. It goes like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... and continues by adding the last two numbers together for infinity. The Fibonacci sequence is a divinity of proportions, of sorts, and the most perfect representation of a Fibonacci sequence would be the florets of a Sunflower. Although Leonardo de Pisa (aka Fibonacci) introduced the sequence in his 1202 book Liber Abaci (Book of Arithmetic), the sequence has been described in earlier Indian Mathematics by Baudhayan in the c. 8th. BCE as Pythagorean triples (a2 + b2 = c2).
Sound familiar? 2-3-5 is the best way to determine if a wall is square. Basically, Fibonacci is easy to use in every aspect of our life. For all us kitchen & bath designers out there, try sequencing the cabinetry layout with 21" cabinets, 34" to finished countertop, 3" toekicks, wall cabinets 55" A.F.F., and make them stacked 21" each to 42" total. Just sayin' it's possible. What about a tile pattern? OH! How about the entire partition plan that is broken into a top view of the Fibonacci Spiral? Okay, I'm way to excited about this.