I think the article is very honest about this just being a fun exploration. They even show how you can get similar patterns with newton's algorithm which is a more "classical" take
Inter dimensionality is the defining feature of fractals.
A multilayer ANN will have compression that may be fractal like. But in theory a feed forward network could be single layer but will a lot more neurons.
I have the feeling this result was due to representation but there are some features that look like riddled basins.
Riddled basins do arise in SNN or spikey neutral networks that have continuous output bs the binary output of ANNs.
But as all PAC learning is just compression that may be the cause also.
I'll be digging into this on the weekend though.