2D creature speculation

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A hypothetical creature living in 2 spatial dimensions can't have a continuous running mouth-anus tube, because it would fall in half .

It would likely have a big hole in which it sucks food, digests it, and ejects it through the same hole. But the question remains how to get molecules from the food chamber into the organism. One single hole in the cell membrane would work, but that is likely not enough for a large complex cell. Alternatively the organism would need some kind of interlocking section that pumps matter in or out like a canal lock system [II].

Because of the complexity and size of that (if even one of the pumps fail to interlock the cell disintegrates) I think for a 2D creature the classic cell structure of a membrane surrounding a large pool of chemicals inside doesn't make as much sense. Instead it would look more like figure [III], kind of like a pompom, where lots of non-essential extensions dangle from a strong core, with many concave indentations to process food or do other necessary reactions. All the green walls here consist of thin, strong, floppy, but actuated, material, with no need to put anything inside. Inside the indentations there are free floating proteins and maybe even helper cells like mitochondria.

What do you think? This is only about the basic topology of the cell (mug = donut), and a real cell would likely use a combination of both [II] and [III].