Good point. I was mostly thinking about the short axis, but you’re right – both the arrow and these circle shapes are mirrored along one axis and asymmetric along the other. I guess my cultural bias got the better of me.

You can take a smooth stone or a thick branch to make a depression, which will end up as a filled circle.
A sophisticated example of a writing tool could be a conical stake; the tapered end is for empty circles and the circular end for filled circles. (In a hypothetical technological level of the culture, comparable with our era of pens and inkwells, the tool could be a combined pen and a stamp.)

» the smaller circle designates the direction of motion just as much as the larger one

That’s true, I only made the assumption that the creatures have a strong and fundamental sense of the individual point-of-view, therefore “what is coming towards me”.
The creatures could be highly social, and meetings are always important events :3

But I don’t understand what makes an arrow asymmetrical; like these symbols, the arrow is mirrored along its long axis.

One obvious problem is that it’s relatively time-consuming to fill in a circle (or any shape) you’ve drawn, while an arrow only requires a few lines. In spoken languages, words that are frequently used become increasingly shortened down, and I would expect the same to happen with a pictorial language. But this isn’t a major problem, as non-filled ones work just as well.

I’m not sure if the larger circle designating the direction of motion (well, to be exact, the smaller circle designates the direction of motion just as much as the larger one, but you know what I mean) is the most intuitive one. It’s the most appealing in the “down-arrow” case, where it feels natural that the biggest object is the one that falls down first, but for the other images I find either interpretation equally easy to construct. The issue might be helped by the introduction of an asymmetry of some kind – note that arrows aren’t symmetric in the same way that your symbols are. (It also feels to me that the *way* arrows are asymmetric easily leads you to the correct interpretation, but of course that might just be the cultural conditioning.)

On the other hand, your “plus” and “minus” signs are very intuitive and natural. The “in” and “out” symbols also feel more intuitive than the “arrows”, though on further reflection I’m unable to say just what makes these interpretations of “in” and “out” so natural as compared to the opposite interpretation. Maybe it’s because the “in” icon seems to signify entering openly, while the black circle in the “out” icon is partially hidden, as if sneaking out from the back door. How cultural/universal are these feelings, I wonder?

Btw, you might be interested in this article on typographical logos for towns and wards in Japan: http://www.pinktentacle.com/2009/09/typographic-town-logos-in-hiragana-katakana/

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