Here's what Prof. Andy Adamatzky has to say about Physarum plasmodium doing thinking:
"Plasmodium’s foraging behaviour can be interpreted as computation, when data are represented by spatial configurations of attractants and repellents, and results by structures of protoplasmic network . Plasmodium satisfactory solves many computational problems with natural parallelism, including shortest path, implementation of storage modification machines, Voronoi diagram, logical computing, process algebra... "
Read all about it in his nice paper "Slime mould computes planar shapes" here.
Well that's very nice for me that somebody has gone to the trouble of doing sums to prove that the thinking of bodies can indeed be thought of as thinking, that Ms. No-brain, No-symbolic language here is doing the math all over my pictures. Maths even.
I don't know if it has any kind of memory. Or even what I think I might mean by memory here.
I have no idea why it seems to be happy to forage endlessly across paintings carrying a burden of fluorescent powder with only the occaisional break with a clean oat flake on a bit of damp kitchen roll. But then I can't say I understand why I do, either.