TITLE: Intuitive pictures in characteristic p
QUESTION [27 upvotes]: This is a tough one, but does anyone know of any images that recall characteristic p geometry (over algebraically closed fields) in some sense? It is not enough if it is some picture that can be also understood solely in characteristic 0.
A quick search through the literature has proved fruitless.
I have been thinking for a while of asking this question, but I never had a pressing need rather than my own curiosity. However, now I am trying to improve a poster by including pictures but the topic is algebraic geometry in characteristic p. 
An example of such an image in Complex Geometry would be the arrangement of contracted and blow up curves in the standard Cremona transformation of the projective plane. The one in this poster is simple but effective.
I believe this question also might be of interest for people who try to explain research to non-mathematicians or simply to mathematicians who are not geometers.

REPLY [3 votes]: This is not nearly as nice an example as the others, but I always imagined the line in characteristic five geometry as a countable set of points that glow like blue Christmas tree lights vaguely in the shape of a narrow paraboloid, with 0 at the vertex, with 1, 2,3, and 4 at the next "height", with the quadratic "irrationals" next, etc. although the makes it seem like each field of order $p^n$ contains the field of order $p^{n-1}$. Like in Carnahan's answer, I imagine the Frobenius automorphism shuffling around everything in each fixed ring. Finally, I imagine the Zariski topology as a glowy light filling in the paraboloid representing the forces that each point exerts on all others; it's constant everywhere, as in the Zariski topology, there's no real sense of distance.
More complicated varieties I imagine as a double cone with glowy lights (two Christmas trees!) or as the paraboloid distortedt to have self-intersections in some of the lights.
something like the galactic gravity simulation or spherical pendulum in this website