Math that makes worlds

From the May 18 New Yorker article World Without End, by Raffi Khatchadourian:

The design allows for extraordinary economy in computer processing: the terrain for eighteen quintillion unique planets flows out of only fourteen hundred lines of code. Because all the necessary visual information in the game is described by formulas, nothing needs to be rendered graphically until a player encounters it. Murray compared the process to a sine curve: one simple equation can define a limitless contour of hills and valleys—with every point on that contour generated independently of every other. “This is a lovely thing,” he said. “It means I don’t need to calculate anything before or after that point.” In the same way, the game continuously identifies a player’s location, and then renders only what is visible. Turn away from a mountain, an antelope, a star system, and it will vanish just as quickly as it appeared. “You can get philosophical about it,” Murray once said. “Does that planet exist before you visit it? Sort of not—until the maths create it.”

This article gets to something fundamental about the mathematical experience for me: even when you’re making the rules, the rules talk back, and give you worlds to explore that you couldn’t even have conceived of. The description of the programmers being drawn into exploring their own, unfathomable creation resonates; that’s the story of mathematics from the beginning. They found a way to make it visual and more broadly experiential.

Hopefully the game, No Man’s Sky, will be fun for everyone who plays it!

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