The Cross-stitch curve is a similarity fractal. Set the Level slider to 0, click the green flag, and view the initiator. Set the Level slider to 1, click the green flag, and view the generator (see Notes and Credits for why knowing the initiator and generator is important).
The dimension of a similarity fractal is found by counting the number of equal-length line segments in the generator at level 1. Set the Level slider to 1, press the green flag, and view the generator. As you can see, it is composed of 5 equal line segments. In the Cross-stich, there are 5 equal-length segments. Call this N, and N = 5. Set the Level slider to 0,click the green flag, and view the initiator. As you can see, it takes three segments of the generator to make the initiator. Call this n, and n = 3. The fractal dimension is defined as log(N) ÷ log(n) From Mandelbrot, the fractal dimension = log(5) ÷ log(3) = 1.4649… Similarity fractals teach us that geometric curves exist that have fractional dimensions 'between' dimension 1 and dimension 2.
