Note: this question is not a duplicate. The accepted answer to the question "Anatomically correct Medusa" explains the petrifying vision via calcifying toxins spat from the snake hair. This a) wouldn't work with a cockatrice, and b) spitting venom does not achieve the desired effect of petrifying vision in my opinion. The external anatomy made up a big part of that question, so the petrifying part wasn't needed to be really believable.
Many of you will know about tales of of the basilisk, gorgon and cockatrice, who can turn attackers to stone merely by looking at them.
It seems absurd, and probably is, but is there any conceivable way that an animal could transform other animals to a stiff, rigid state without any visible physical connection?
One of the obvious implications of this is: How does it not petrify everything it sees? Well, I came up with two theories for this,
They have retractable membranes over their eyes which shield the world from petrifying until the animal desires otherwise,
The petrifying organs are not actually the eyes, but are located somewhere on the front of the head. This would convince people that it petrified things by looking at them, without the consequences of such an arrangement.
But the most absurd and puzzling thing about this topic is "How does it actually petrify?" I came up with a few ideas here too. The main one is that it sprays colourless gas which, upon reaching the target, dramatically lowers the body temperature and freezes the quarry.
Would that work? Or is there some other method that could give the effect that an animal could turn people "stiff" just by looking at them?
Note: And I mean physically, actually rigid/stiff, so please don't answer "They were rooted to the spot with fear."