I shall use the random reduction algorithm this time. Let's see what happens with the mother and daughter chicks this time.
There are two interesting things about quines in a random environment. (1) They have a life, in the sense that their evolution under random reduction breaks the perfect equilibrium which makes them to regenerate themselves, as quines, in the deterministical reduction algorithm. Instead, they turn into alive creatures which are only in a statistically defined equilibrium. But they are individuals who may live and even die. (2) Related, their metabolism becomes obvious. While in the deterministical reduction algorithm they practically regenerate most of their body by releasing and receiving the same number of nodes, in the random reduction algorithm they keep their body by releasing and replacing sometimes more, sometimes less nodes.
As a visual proof of the existence of a metabolism, after the two "chicks" appear the colour of the new nodes is turned off and on periodically in time, so that you can see that the nodes which form the two creatures are constantly replaced. You can also see that the two "chicks" are not identical during their life, each one taking it's own shape. No chick dies in this simulation, however, at least not during the reduction steps shown.