The Planiverse: Computer Contact With a Two-Dimensional World by AlexanderKeewatinDewdney
(ISBN 0387989161 ) -- amazon.com provides sample pages, I highly recommend checking them out.
The author is a particularly well-published computer scientist and mathematician.
In it, a computer science class embarks on a project to simulate a two-dimensional universe. After a few semesters of development and upgrades, a mysterious glitch in the program allows them to contact and observe a being in what appears to be an actual two-dimensional universe.
The contact is with a being named Yendred on the planet Arde, the son of a fisherman who leaves his family to venture on a spiritual journey to the nation of Vanizla, to learn of the knowledge beyond thought. And since his journey crosses most of the continent, his friends from Earth get to learn a great deal about his world and how it works. The story of Yendred and the story of the computer scientists who must keep their project secret, both of these form the backdrop against which we learn about the physics, creatures, technology and culture of Arde.
The book takes a more hard-science approach than FlatLand. Flatland's inhabitants are geometric shapes, and live in a world with no up or down. In contrast, Ardeans are organic beings, and their world has no north or south.
Some aspects of the second dimension include the following: