  Quasicrystals are fractal due to their self similar property. In this paper,
a new cycloidal fractal signature possessing the cardioid shape in the
Mandelbrot set is presented in the Fourier space of a Fibonacci chain with two
lengths, L and S, where L/S = \{phi}. The corresponding pointwise dimension is
0.7. Various modifications, such as truncation from the head or tail,
scrambling the orders of the sequence, and changing the ratio of the L and S,
are done on the Fibonacci chain. The resulting patterns in the Fourier space
show that that the fractal signature is very sensitive to changes in the
Fibonacci order but not to the L/S ratio.
