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 design a vertical 2D world (i.e. East-West and Up-Down, no N-S) and consider 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 (Arabic 'Ardh = Earth'). 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; Like many other terms this comes from Maltese Arabic: 'insan = human'), as he begins a journey across the western half, Punizla (Arabic 'Punent Nizla = ‘West Slope’) of the single continent Ajem Kollosh (Arabic 'ajm Kull shay = home of all things') to learn more about the spiritual beliefs of the people of the East, Vanizla (Arabic 'Levant Nizla = East Slope’). Yendred mistakes the watchers on Earth for 'spirits', hence his interest in communicating with them.
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 (this is 1980s technology). The name Yendred (or "Yendwed", as pronounced by one of the students, who has a speech impediment) is simply "Dewdney" reversed. The novel is in fact an allegory of Yendred/Dewdney's search for a reality deeper than that of scientific enquiry.
Written as a travelogue, Yendred's journey through the West takes him through three cities. In Is Felbelt (Arabic 'Asfal Balad = Lowest City'), the capital, he observes the chaotic politics of democracy, contrasted with the orderly kingdom of the East. In Maj Nunbilt (Arabic 'Majnun Balad = Mad City' he visits the Punizlan Institute for Technology and Science, 'the PITS', and hears about the vain search of scientists for truths beneath the surface reality of existence. In Sema Rhublt (‘In-Between City’ according to Dewdney), a colony of artists, he learns about their futile attempt 'to create random forms in the hope of obtaining something which looks like nothing else'.
The Technology of Arde is explored in great detail. For example, all houses are underground, so as not to be demolished by the periodic 2D rivers; nails are useless for attaching two objects, tape and glue are used instead, most Ardean creatures don't have deuterostomic digestive tracts since they would split into two, and have instead evolved alternatives; and even games such as one-dimensional Alak, everything is designed to work in 2D. An appendix explains some fundamentals of Ardean two-dimensional physics and chemistry.
The underlying allegory culminates in Yendred's arrival at the watershed of the continent, where he at last finds a teacher, Drabk, who can give him spiritual enlightenment. Together they fly into the Shrine that stands on the edge of Vanizla; it is square - the 2D equivalent of the Kaaba, the cubic shrine at the heart of Islam. Yendred has no more need of the failed 'spirits' of the watchers on Earth, and contact with Arde is lost.
Kirkus Reviews considered it "an ingenious intellectual exercise—amusing, edifying, sometimes tedious"  At Tor.com, Jason Shiga found it to be a "tour de force followup" to Flatland, and found the appendix to be the "most impressive section" of the book.
- 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.
- Author's bibliography
- Kontrol An online action game and 2D universe simulation inspired by The Planiverse
- |authorlink=Philip Stewart |journal=Sufi |issue=9 |date=spring 1991 |pages=26-30|"Allegory through the computing class: Sufism in The Planiverse by A. K. Dewdney".
- THE PLANIVERSE: Computer Contact with a Two-Dimensional World, reviewed at Kirkus Reviews; published March 16, 1984; retrieved June 5, 2017
- Revealing Demon: Volume 3, and Five Other Sci-Fi Books About Math, by Jason Shiga; published September 15, 2016; retrieved June 5, 2017