In 1977, Dewdney was inspired by an allegory of a two-dimensional universe, and decided to expand upon the physics and chemistry of such a universe. He published a short monograph in 1979 called Two-Dimensional Science and Technology. In July 1980, this was reviewed by Martin Gardner in Scientific American, and shortly after this, all copies of the monograph were sold out. In 1981, following the success of the monograph, Dewdney published A Symposium on Two-Dimensional Science and Technology, which contained suggestions for how a two-dimensional universe would work from scientists and non-scientists on varied subjects.
In the spirit of Edwin Abbott Abbott's Flatland, Dewdney and his computer science students designed a vertical 2D world (i.e. East-West and Up-Down, no N-S) and considered the issues of biology and society for the inhabitants.
To their surprise, they find their artificial 2D universe has somehow accidentally become a means of communication with an actual 2D world – Arde. They make a sort of "telepathic" contact with "YNDRD," referred to by the students as Yendred, a highly philosophical Ardean (or Nsana, as they call themselves), as he begins a journey across the single continent Ajem Kollosh to learn more about a mysterious philosophy the inhabitants of his destination have.
The students and narrator communicate with Yendred by typing on the keyboard, and Yendred describes how he "feels" their thoughts in his head. For Yendred's replies, he thinks an answer, and it appears on the computer's printout. Yendred's name is actually "Dewdney" reversed, or "Yendwed", as spoken by one of the students with a speech impediment.
Written as a travelogue, Yendred crosses the world to reveal its features, explaining to the students diverse topics such as the politics, geography, construction (all houses are underground, for example, so as not to impede movement), tools (nails are useless for attaching two objects, tape and glue are used instead), biology (most Ardean creatures don't have deuterostomic digestive tracts since they would split into two, and have instead evolved alternatives), astronomy, and even games (such as one-dimensional Alak), all designed for fit in 2D. An appendix explains some fundamentals of Ardean two-dimensional physics and chemistry.
- Kontrol An online action game and 2D universe simulation inspired by The Planiverse
- Creatures (inspired by The Planiverse)
- Begley, Sharon. 1982. "Life in Two Dimensions." Newsweek. January 18, pp. 84–85.
- Dewdney, A.K. 1979. "Exploring the Planiverse." Journal of Recreational Mathematics. 12:16–20.
- Dewdney, A.K. 2000. "The Planiverse Project: Then and Now." The Mathematical Intelligencer. 22:46–51.
- Gardner, Martin. 1980/2001. "The Wonders of a Planiverse." Scientific American, July 1980; reprinted with appendix in The Colossal Book of Mathematics (New York: Norton).
- Sandberg-Diment, Erik. 1984. "Review of Dewdney 1984/2001". New York Times, November 6.