To render this figure, I placed the Fibonacci sequence into the spiral in the same way that natural numbers are placed into the Ulam spiral. I labeled the individual numbers in this spiral according to the rule: 0 = black square, 1 = white square (this process is illustrated in the animation below). The JavaScript scripting language was used to streamline this process.
What is a Fibonacci word?
A Fibonacci word is a specific sequence of binary digits (or, more generally, any two symbols). We obtain it similarly to the Fibonacci sequence, only instead of addition, we use concatenation of words. The first two terms are defined: S0 = 0, S1 = 01. The next term resulting from concatenation (i.e., adding the penultimate term to the last term) will be S2 = 010. The sequence of the first few digits of the Fibonacci words would therefore look like this: 0100101001001010010100100101001001…
What is the Ulam spiral?
The Ulam spiral
, also known as the prime spiral, is a diagram created by arranging natural numbers in a spiral and highlighting the prime numbers. It was discovered by mathematician Stanisław Ulam in 1963. Ulam wrote the natural numbers into a rectangular grid, placing the number 1 in the center and the other numbers spiraling outward.
Concept by: Vojta Maur
JavaScript code by: Pavel Burda