If we define samples manually how could there be a Sampling Frequency? I just got a thought when generating matrices , plotting it and taking its FFT,

Lets say, I have randomly input a matrix of length 256,

[1 7 9 5 7 1 -2 0..................8]


According to the FFT, the resulting 256 FFT coefficients correspond to the following frequencies:

0, $f_s/256$, $2 f_s/256$, $3 f_s/256$, $\ldots$, $255 f_s/256$

but since the samples i taken has no sampling frequency defined how could there be some sampling frequency ? Like in an image ,

Since the image is just a 2 dimensional Matrix , if i randomly generate an image in a matlab with random pixel values (sample points) and plot its FFT , the matlab will show the frequencies of that 2-D matrix but since there is no Sampling Frequency is defined how matlab calculates the frequency for each of the coefficient ?
Units can be arbitrary, such as ISO Meters, or the length of the current king's foot (maybe longer than last year after the assassination of some shorter king).

A good default unit if there isn't some ISO standard, useful natural unit, or you can't think of one to make up (how long is your monitor's display, or your left foot, etc.), is the length of your window of data.  e.g. 1 cycle per your vector of 256, 2 cycles, 3 cycles, etc. per your vector length.  If your vector displays as 3 inches long on your display, then you can also easily convert cycles/vec into cycles/inch, or per/mm, per/fortnight, etc.