Slime molds are very different organisms, from plants, animals or fungi, and their taxonomy is the subject of much current research.  They  fall into three groups: 1: plasmodial slime molds in which a single huge cell may have thousands of nuclei. 2: cellular slime molds existing a s single cells which can aggregate together on a chemical signal and move and behave like a single organism before sporulating  3 Amoeboid slime molds; similar to the cellular, but smaller .

I quote from wikipedia:

When a slime mold mass or mound is physically separated, the cells find their way back to re-unite. Studies on Physarum polycephalum have even shown an ability to learn and predict periodic unfavorable conditions in laboratory experiments.[18] John Tyler Bonner, a professor of ecology known for his studies of slime molds, argues that they are "no more than a bag of amoebae encased in a thin slime sheath, yet they manage to have various behaviors that are equal to those of animals who possess muscles and nerves with ganglia – that is, simple brains."[19]

Atsushi Tero of Hokkaido University grew Physarum in a flat wet dish, placing the mold in a central position representing Tokyo and oat flakes surrounding it corresponding to the locations of other major cities in the Greater Tokyo Area. As Physarum avoids bright light, light was used to simulate mountains, water and other obstacles in the dish. The mold first densely filled the space with plasmodia, and then thinned the network to focus on efficiently connected branches. The network strikingly resembled Tokyo's rail system.[20][21]

Slime mold Physarum polycephalum was also used by Andrew Adamatzky from the University of the West of England and his colleagues world-wide in experimental laboratory approximations of motorway networks of 14 geographical areas: Australia, Africa, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, the Netherlands, UK and US.[22][23][24]

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