On the Matrix wiki, there's an article about the Nightmare Matrix which says:
The Nightmare Matrix was the second prototype Matrix, designed by The Architect after the massive failure of the Paradise Matrix in the hope that human minds would more readily accept an imperfect world with suffering. Unlike the first version, this Matrix instituted a basic cause-and-effect programming and forcibly made those connected to it accept the program.
Vamp Prime, a possible remnant of the Nightmare Matrix. It also featured programs that resembled mythical evil creatures in various human mythologies such as vampires, werewolves, zombies, aliens, etc. It also failed, but many of the programs who were designed for it survived deletion in exile.
The Merovingian and his wife, Persephone may have had their roots in this version of the Matrix. Upon its failure, the Merovingian started a smuggling ring of programs and information to provide a haven for exiles that would last for 6 cycles in the final version of the Matrix.
The Nightmare Matrix is also featured in the Matrix Online.
But like many articles on the Matrix wiki, it doesn't really give any specific references that would allow readers to verify what it says. The only evidence I know of is this bit of dialogue from Persephone in The Matrix Reloaded, right before she shoots the Lupines Cain and Abel:
They come from a much older version of the Matrix, but like so many back then, they caused more problems than they solved. My husband saved them because they're notoriously difficult to terminate. How many people keep silver bullets in their gun?
Does anyone know exactly what was "featured in the Matrix Online" (or any other published sources like comic books)? Did they explicitly use the words "Nightmare Matrix", or specifically say that programs with "supernatural" characteristics, like the ghost-like Twins or the Lupines and Vamps, came from the second iteration of the Matrix after the original Paradise Matrix which was mentioned by the Architect (though he didn't use that exact term)? And even if there was a Matrix with many "supernatural" programs, do we know that this version was especially "nightmarish" for inhabitants, as opposed to these programs just showing up rarely and possibly playing a similar role to Agents in the later versions of the Matrix? Finally, is there evidence for the idea that the second version of the Matrix was the first to institute cause-and-effect, and that this was the reason for the Merovingian's emphasis on the idea, as opposed to it just being his personal philosophy to emphasize cause and effect over choice?
Edited to add: Richard mentions there was nothing about this in the Matrix comics, and it wasn't in the Animatrix either, so I think that just leaves The Matrix Online for a source...I know that monstrous programs like vampires were featured, does anyone know if anything further was ever revealed about their background, as there was with Seraph according to the "Online" section of his wikipedia article? Or about the origin of the Merovingian's fixation on cause and effect?