If you knew the algorithm and fed it back say ten thousand times, each time there'd be a dot somewhere on the screen. You'd never where to expect the next dot. But gradually you'd start to see this shape .
Here, Valentine explains the chaos theory to Hannah Jarvis. Like the story of Hannah and the story of Thomasina, the stories are chaotic—they feed into themselves with unpredictable results. Chaos theory is one of the central metaphors in Arcadia and influences the structure of the work itself. What is important about Valentine's description of chaos is that it links mathematics directly into the world of art, the same place Stoppard desires to take it. Valentine describes the new math as he does a Picasso, with the language of modern art. Like Thomasina's algorithm, the structure of Arcadia is equally plotted and planned. Stoppard leaves behind old modes of theatre—the three act well made play—and presents a chaotic, if not unpredictable algorithm of stories. Stoppard creates his own set of points and equations that form a picture, not unlike Thomasina's. Arcadia is a test of the algorithm forming a fractal form of a play that attempts to imitate nature through the realities of mathematics.