[teo_zero]

The structures that emerge from a series of transformations applied to an initial field (be it the natural numbers or the complex set), could be due to the transformations, or intrinsic of the underlying field. The parent comment stated that we're in the former case, i.e. we are seeing artifacts due to the transformation itself and we're not in front of some new properties of the numbers. It implied that this is a bad thing, or at least that's how I read that 'merely'. My (admittedly cryptic) reply was meant to show that similar results are worth attention as well, just like the Mandelbrot set, and should not be quickly dismissed as an unwanted effect.

[2-718-281-828]

so, your point is that the mandelbrot set isn't merely an artifact, if i understand you correctly.

[teo_zero]

Wait... I'm not sure where this conversation is going.

I say that the beauty (or value or worthiness) of the pictures of the Mandelbrot set comes from the transformations we apply to uninteresting complex numbers.

Similarly, the beauty of the pictures in the article may come from some hidden properties of the underlying prime numbers, or from the transformations themselves, and I don't think that either case would be better than the other.

I said this in reply to a comment that seemingly stated "what a pity, these images are 'merely' due to the transformations". I was objecting to the tone of disappointment that I read in that message.

[expazl]

Convergence artifacts are due to the algorithm converging poorly. This is why it's a "pity" the interesting structure you see in the picture has nothing to do with the distribution of numbers and is just a bug in the algorithm that happens to look nice.

So no, it's not like the Mandelbrot set. It's more like if you wrote a script to visualize the Mandelbrot set and created a bug that made part of the visual you created look like there was an interesting structure by accident, then shared your pictures with a wide audience going "look at this interesting structure I found in the mandelbrot set!" and then someone replies on Twitter with "you have bug in line 124 and when I correct it the structure disappears". Which is why it's a pity.