Human brains are quite good at spotting some kinds of patterns. A visual representation is a trivially easy way to access that pattern spotting ability. Trivial as in you can do it in the time it's taken me to write this reply. It also communicates well.

isn't fft just a different way of looking at the data?

A Fourier transform is not merely another graphical representation of data (although, it could be used as such). Among other things, it lends itself to generating features and analysis that can be used for detecting patterns by computer, not just humans.

Essentially, yes, that was my understanding, too. I've only used in in signal processing - converting from the time domain to the frequency domain. Not sure how that would apply to this.

I was thinking specifically of this:

  When i look at the FNV-1a "number" map, i think i see subtle
  vertical patterns. With Murmur i see no patterns at all. 
  What do you think?

Wouldn't that vertical repetition, and the other repeating patterns the other hashes form, show up as a nice spike in the frequency domain? Whereas I would expect uniform hashing to generate a flat, white-noise spectrum.

I find the avalanche maps used here easier to grasp: http://home.comcast.net/~bretm/hash/5.html

Here is FNV, quite a lot of reds: http://home.comcast.net/~bretm/hash/6.html And of course all green for SHA-1: http://home.comcast.net/~bretm/hash/9.html