Fibonacci Word curve

See Wikipedia on the Fibonacci Word and the Fibonacci word fractal. Extract below.

A Fibonacci word is a specific sequence of binary digits (or symbols from any two-letter alphabet). The Fibonacci word is formed by repeated concatenation in the same way that the Fibonacci numbers are formed by repeated addition. It is a paradigmatic example of a Sturmian word and specifically, a morphic word. The name "Fibonacci word" has also been used to refer to the members of a formal language L consisting of strings of zeros and ones with no two repeated ones. Any prefix of the specific Fibonacci word belongs to L, but so do many other strings. L has a Fibonacci number of members of each possible length.

Definition Let $S_0$ be "0" and $S_1$ be "01". Now $S_{\mathrm{n}}$ (the concatenation of the previous sequence and the one before that). The infinite Fibonacci word is the limit $S_{\mathrm{\infty }}$ , that is, the (unique) infinite sequence that contains each $S_{\mathrm{n}}$ , for finite $n$ , as a prefix. Enumerating items from the above definition produces:

• $S_0$ 0
• $S_1$ 01
• $S_2$ 010
• $S_3$ 01001
• $S_4$ 01001010
• $S_5$ 0100101001001

Iteration: = bits / segments