The question of pattern recognition in random noise is interesting and a legitimate question. Animals (given our propensity to see then) and an interesting subject matter.
Generating random noise and then filtering it to "find" patterns seems dubious, at best. Why not just generate animal shapes in the first place?
Starting from a random image it's possible to manipulate and filter it to find literally anything. It doesn't mean there are "animal pictures" in the random data; it means the image has been manipulated to look like it. It's a tautology.
In a sufficiently large random image, you'll (probably) find as detailed of a picture of a rabbit as you like.
The question is about how often image recognition (either human or algorithmic) picks up a signal in random noise -- that is, how often we see things that aren't there (or if you prefer, are there, but by chance). Of course you can find anything, the question is with what frequency.
If you've ever spent much time looking at random patterns, you'd know that we're prone to seeing things that aren't there in noise. Modeling that phenomenon is interesting (at least to me).
I don't know much about wolfram things, but just looking through it, it appears that the manipulation and filtering is grouping the randomly generated data (I would argue it's still random), taking only groups between a certain size(this is the least random part, it makes sure there are enough "features" yet not too many), and then smoothing out the groups for display (still completely dependant on the data, which was random).
As the "animals" are smoothed groups of random data, (and differ every time) , I'd argue it's still (basically) random.
The premise of extracting meaning from noise is flawed. It doesn't matter what process you use to arrive at the meaningful conclusions if the source material is completely meaningless. It's analogous to a fallacy of false premise: you can literally arrive at any conclusion given a false assumption.
"random" encompasses an infinite array of variable parameters -- linear blur, Gaussian blur; white noise, brown noise, pink noise -- some of these can tend to make animals appear in dot patterns, or melodic phrases arise from static, or whisky taste of butterscotch and leather
The question of pattern recognition in random noise is interesting and a legitimate question. Animals (given our propensity to see then) and an interesting subject matter.