radially averaged power spectrum of a binary image does not look like power law

It has been known that Fourier power spectrum somehow obeys power law therefore the slope of the spectrum can be used to calculate the fractal dimension of an image. Many people have used it for texture analysis.

I wanted to calculate the Fourier fractal dimension of a binary image and have produced radially averaged power spectrum, using the matlab code here: http://www.mathworks.com/matlabcentral/fileexchange/6167-calculation-of-fractal-dimension-of-fractal-surfaces-using-fft

the spectrum I have plotted is like this,

However, I was told that this curve does not look like power law. I want to ask whether the comment is true and why, and is it because I'm using binary image rather than gray-scale?

[Image Analyst]

Please also attach your original spatial domain image(s).