I am trying to apply Arnold cat map function to the matrix form of digital image to scramble the pixels. Please help me to calculate the periodicity of the Arnold scrambling function.
Please see if the answers and pdfs attached .from another similar q. on RG is useful.
"Swati Khare 12.13
Barrow Neurological Institute
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Good luck
Cheers
I didn't know what that cat map is, so, thank you for pointing this out.
It seems you can find the period by subjecting the output image of the Arnold function, to the same Arnold function, until your original image reappears. The period depends on the X dimension and possibly also on the Y dimension of the input image; it does not depend on the pixel values.
Thanks, Narasim and Lambert for your help. Yes, periodicity depends on matrix dimension but just want to know is there any method to calculate it directly. Otherwise, I can use loop and run it until we get the same image.
Just a hunch ..approx p where p =periodicity maybe :
p= n +1 + j*2pi/ log(lambda) where lambda = min ( negative ) eigen value of the permutation matrix( ie Arnold matrix) of order n. In the example of n=3 in pdf we get approx p= 5 close to 6.
Cheers
Hi Narasim,
I appreciate your hunch, but I don't think using 'pi' and a 'log' will lead to an integer number of iterations at which the original image will reappear.
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