This is what I Initially thought too but I am less certain now - I assumed Fractal implied self similarity (which this doesn't seem to have) but this is in fact not true - I think to actually say if its fractal or not someone needs to estimate its dimension using box counting or some, way beyond me, analytical method.

They should have definition at arbitrary scales. These images do not, they are built from a fixed sized matrix. Beyond a certain point you are between the data points.

Same can be said for the madelbtot set or any other fractal - there is a physical bound on the precision of the values - you can in theory run a NN with arbitary precision floats...

But the image is based on the attributes of each node in the NN matrix. The Mandelbrot set can be calculated at any precision you desire and it keeps going. An NN is discrete and finite.

That's not what it shows at all - it shows how varying hyper parameters (which are floats and thus can be set at any arbitary precision) effects the speed at which convergence happens - so its some function F: R^n -> Z - it has literally nothing to do with the nodes in the neural network...