Fibonaccitiles

Fibonaccitiles refers to a visual representation of the Fibonacci sequence using squares. This tiling is constructed by starting with two small squares, each with a side length of one unit. These are placed adjacent to each other. Next to these two squares, a larger square with a side length of two units is added, aligning with the combined side of the first two. Following this, a square with a side length of three units is placed adjacent to the existing arrangement. The process continues by adding squares with side lengths corresponding to the subsequent Fibonacci numbers: five, eight, thirteen, and so on. Each new square's side length is the sum of the two preceding squares' side lengths.

The arrangement of these squares creates a spiral pattern within the tiling. If you draw quarter circles within each square, connecting opposite corners, these arcs form a smooth, outward-spiraling curve. This curve closely approximates the golden spiral, which is mathematically related to the Fibonacci sequence. The ratio of successive Fibonacci numbers approaches the golden ratio (phi, approximately 1.618). Fibonaccitiles are often used as an educational tool to illustrate the Fibonacci sequence and its connection to the golden ratio and natural patterns. They can be found in art, architecture, and design, reflecting the aesthetic appeal of this mathematical relationship.