Valentine, Chloe, and Gus are together in the room. All of the characters are dressed in Regency clothes, and Gus pulls more out from a hamper to try on. Chloe is reading a newspaper featuring an article about Bernard, and Valentine is typing on a computer. Chloe asks Valentine if the future is programmed like a computer. Valentine replies that the universe is deterministic; one might be able to predict everything to come if he had a computer large enough. Chloe interjects that the formula wouldn't work because of sex; people might fancy people who weren't part of the plan or proper formula. Hannah enters the room carrying a tabloid with an outrageous headline about Bernard's theory: "Bonking Byron Shot Poet." Hannah at a form made from Thomasina's equations. Putting Thomasina's equations into a computer made the shape. The results of the equation are called the Coverly set. Valentine tells Hannah that the results are publishable and that Thomasina would be famous. Hannah reminds Valentine that Thomasina couldn't be famous, since she died in a fire the night before her seventeenth birthday.
The scene switches now to the early nineteenth century. At this point, the stage shows two rooms, one of the past and one of the present; or possibly there would be brief lighting changes to distinguish from the nineteenth century time period and that of modern day. Thomasina is now sixteen and chases Lord Augustus, age fifteen, around the house. The two are stopped by Septimus, who calls Thomasina to begin her lesson. Thomasina is upset that Septimus gave her no marks for her rabbit equation; Septimus tells Thomasina the equation had no resemblance to a rabbit. Thomasina protests that she had no room to finish it.
The action shifts to the present. Valentine and Hannah are working on their separate projects, and Valentine reminds Hannah that her tea is getting cold. Tea, like the swirl of the jam in rice pudding, cannot be made warm again. The scene returns to the schoolroom. Thomasina asks Septimus if she will marry Lord Byron, and Septimus tells her that it would be highly unlikely. Thomasina reminds Septimus that he must teach her to waltz. Septimus gives Thomasina an essay from the Scientific Academy in Paris that is like Thomasina's own work—the scientist has found a contradiction in Newton's theory of determinism.
The focus is again drawn to the present day. The scenes at this point overlap, and the characters overlap dialogue. There is little separation between the past and the present. Chloe enters the room looking for Gus to be in a photograph. Chloe is still dressed in regency clothing. Lady Croom has come in the schoolroom looking for Mr. Noakes. Lady Croom is upset about the sound of Mr. Noakes's engine. Thomasina slams the book, containing the essay about determinism, down on the table. Thomasina tells Croom and Septimus that she was right; the problem with determinism is likely hidden in the author's observations about the action of bodies in heat. Mr. Noakes enters the room, and Lady Croom lectures him again about his landscaping. Lady Croom doesn't understand the reason why he is draining the lake, nor why he has built a hermitage without a hermit. Septimus asks Noakes if there might be room for a piano in the hermitage.
Bernard enters the room, followed by Hannah who is carrying a garden book. Inside the garden book there contains an entry from October 1st that proves that Chater the poet was the same Chater that was killed by a monkey bite in Martinique in 1810; thus, Bernard's theory is destroyed—Byron did not kill Ezra Chater. Hannah tells Bernard she intends to write a letter to The Times explaining the letter. Septimus enters with an oil lamp carrying Thomasina's primer. Thomasina enters secretively, barefoot in her nightgown and holding a candlestick. It is the night before Thomasina's seventeenth birthday, and she wants Septimus to teach her how to waltz. It is also the night of the annual dance, and Hannah enters, dressed for a party. Valentine stumbles in and tells Hannah that Thomasina's diagram is of heat exchange. Septimus and Thomasina discuss Thomasina's diagrams, too, while she tries to get him to dance. The music heard from inside the house changes to a waltz ,and Thomasina and Septimus begin to dance. Septimus kisses Thomasina on the mouth and the couple begins to dance again. Septimus sends Thomasina up to bed with a lit candle. Gus enters and gives Hannah a picture that Thomasina drew of Septimus and Plautus. Gus and Hannah begin to dance.
Not only is the content of Arcadia an experiment with chaos theory, but the structure of the play itself has been sighted as an algorithm for a random, if not chaotic conclusion. This idea is best expressed by Lucy Melbourne in her essay, "Arcadia as Iterated Theatrical Algorithm." Valentine, the graduate student of chaos theory, enthusiastically explains the new math as extending into art itself, "then maths left the real world behind, just like modern art nature was classical, maths was suddenly Picassos." Stoppard has attempted to create the structure of a play like an algorithm that feeds into itself. In other words, the story of Thomasina is iterated to finally result in the story of Hannah Jarvis. The formal structure of the play, the division of scenes and acts, are plotted and planned like the fractal image Valentine creates on his computer. Stoppard leaves behind old modes of theatre—those of three or five act plays—to form a new play structure that abandons convention in favor of a chaotic, if not unpredictable algorithm of stories. The result of the picture formed or fractal, is two sets of dancing couples at the end of the work-constantly changing and moving but headed toward an inevitable end.
Stoppard has thus, as many before him attempted a new form of realism. Like Thomasina's desire to get away from typical forms of geometry that, in no way describe nature, Stoppard uses the unpredictable algorithm and play to plot the intricacies and outcomes of life itself. The structure of the play would seem to defeat any sort of reality, but the usage of an equation—the algorithm that can be repeated over and over—seeks a different sort of realism that can be repeated, a process that is constantly in flux. The play is divided into two acts and seven scenes. There is initial order between the scenes, switching back and forth from historical to present day scenes, but then the back to back modern day scenes throw this order. There is no symmetry between the acts or in the scenes; some scenes are four pages, and others are over twenty. The only stable element of Stoppard's form is the environment, the setting of both time periods is the same, although Sidley Park changes considerably over two centuries. The audience cannot predict the progression of the plot nor suspect Thomasina's untimely end. Stoppard has created a random and chaotic play (as possibly as a playwright can manage) that tests and crumbles our notions of the play in an effort to create reality. Stoppard strives to bring playwriting from arcs and angles to organic, unordered, and chaotic forms.