The Fibonacci word fractal is a fractal curve generated by the Fibonacci word. The picture shows the 23rd iteration of the curve. I used Binet's formula for the number of iterations (to reduce running time), and the Fibonacci formula for the digits (for the same reason). I had to use an abstract on the Fibonacci word fractal to find an exact algorithm that generates the fractal because there is no article on Wikipedia about the fractal. To find the paper on the fractal I used, copy and paste the following URL: http://hal.archives-ouvertes.fr/docs/00/36/79/72/PDF/The_Fibonacci_word_fractal.pdf On some browsers, you need Adobe Flash to open the abstract. There is an open question at the top of page 9... can you give a partial or complete answer to the question? I'd recommend Turbo Mode on the Flash Player.