David, a young boy who lives in a community of religious fanatics, dreams of a city and the Old People who lived long ago. While David is exploring, he meets a girl named Sophie. While they are playing, Sophie sprains her ankle and David finds out that Sophie has 6 toes on each foot-something that is forbidden in the community. Rosalind, David's cousin, can communicate with David and others by reading each other's thoughts. Fringe people, those who have Deviations, raid the community of Waknuk. David sees someone who is remarkably familiar-he looks just like David's dad. Sophie and David go swimming in a stream and an intruder, Alan Ervin, finds out that Sophie is a Mutant. Sophie and her parents leave Waknuk so they can escape the harassment of the community. Alan tells everyone that he saw a Mutant and when David returns home, he is beaten for associating with a Blasphemy.
David's mother gives birth to a daughter Petra who is declared normal. Aunt Harriet arrives with her new baby which happens to not be normal. She wants her sister to lend her Petra so her child will be able to grow up in the community pretending to be normal. Aunt Harriet is found dead the next day but no one says where the baby is. David dreams of Aunt Harriet and her problem and is scared that it will be found out that he is different because he can read thoughts.
Once Petra gets older, the shape-thinkers learn that Petra, too, can communicate with shapes in their minds. Petra is different though-she has extraordinary powers. Anne, one of the shape-thinkers, announces she is going to marry a norm-Alan Ervin in fact. The shape-thinkers are scared because they believe she will tell him about her difference. Alan is killed though by Uncle Axel, David's uncle, and Anne commits suicide. Rachel finds a note written by Anne to the inspector denouncing the shape-thinkers. Rachel burns this letter so that no one finds out about them. Mr. Skinner, a community member, becomes suspicious of the shape-thinkers and is believed to tell the inspector abount them.
David, Rosalind, and Petra must run away to escape being exposed. Sally and Katherine, two other shape-thinkers, however are captured and tortured. Petra, with her exceptional powers can communicate around the world. She contacts with a women from a country named Sealand. People from Waknuk start after David, Rosalind, and Petra. Along with those people is another shape-thinker, Michael, who acts as a spy. Petra learns that in Sealand, almost everyone can communicate to each other through thoughts. Eventually, David, Rosalind, and Petra reach the Fringes and meet with the man David saw long ago. He learns that this "Spider-man" is actually his uncle. David is thrown out of the Fringes camp because he attacked Spider-man. A grown Sophie, who has been living in the Fringes, rescues David and hides him in her cave. Sophie rescues Petra and Rosalind and has to kill the albino watchman. The Waknuk people are getting closer to the Fringe camp. The Fringe people and the Waknuk people fight each other. It is at this time, that the Sealanders start to arrive to rescue the shape-thinkers. Spider-man kills his brother for revenge. Sophie and Spider-man are both killed in the fighting. The Sealanders arrive in a big helicopter and send special white threads onto everyone. These threads kill all the Waknuk inhabitants who were fighting and the Fringe people. David, Petra, and Rosalind go with the Sealanders back to their country and David sees the real-life version of his fantasy city.