With No Man's Sky's highly anticipated release just weeks away, a Dutch company is objecting to the game's alleged use of a patented "superformula" to generate landscapes and terrain.

The brewing conflict, first reported earlier this week by Dutch newspaper Telegraaf (Google translation), centers on a geometric transformation formula developed by University of Antwerp professor Johan Gielis in the early 2000s.

The formula's penchant for creating naturalistic shapes with gentle curves using just a few parameters led some to nickname it a "superformula." Gielis received a patent on the superformula in the European Union in 2002 and a US patent was granted in 2009 (in addition to a few other related patents). He then founded Genicap to monetize the formula by "develop[ing] innovative technologies and products for today’s and tomorrow’s world," according to its corporate webpage.

Fast forward to 2015, Hello Games' Sean Murray said in a wide-ranging New Yorker interview that Gielis' superformula formed the basis for much of the game's procedurally generated universe. A relevant passage:

Murray, sitting before his monitor, typed the Superformula into the terrain of a test planet. He began simply, creating walnut-shaped forms that floated in an infinite grid over a desert. The image resembled a nineteen-eighties album cover, but the over-all look was not the point. Whenever he refreshed the rendering, the floating shapes changed. Many were asymmetrical, marred by depressions and rivulets. Game designers refer to lines of code that require lots of processing time as “costly.” The Superformula is cheap. “One of the hardest things for us to do is to create coherent shapes,” he told me as he worked. In order to produce varied landscapes, a formula must be able to cope with a wide range of random information without generating mathematical anomalies that cause glitches. “This sounds ridiculous, but it is hard to find a formula that you can rely on,” he said.

In a machine translation of the Telegraaf article, Genicap business developer Jeroen Sparrow said the company "certainly [does] not want to stop the launch [of No Man's Sky], but if the formula is used, we will have to sit at the table at any given time." Sparrow expanded on that thought in a statement provided to Eurogamer:

It would be great to exchange knowhow with Hello Games. We believe No Man's Sky is the beginning of a new generation of games. What Hello Games did with the formula is very impressive. Johan Gielis, the founder of Genicap and the one who discovered the superformula, is extremely proud. If Hello Games used our technology, at some stage we will have to get to the table. We have reached out to them but understand they have been busy. We trust that we will be able to discuss this in a normal way.

(In a statement to Eurogamer, Sony, which publishes the PS4 version of No Man's Sky, passed questions about this issue off to Hello Games. Hello Games representatives have yet to respond to a request for comment from Ars).

Despite the noise being made by Genicap, there's some question as to whether the company's patent actually applies to No Man's Sky. The European Patent Convention says directly that "discoveries, scientific theories, and mathematical methods" are not directly patentable, and US patent law also excepts "disembodied mathematical algorithms and formula" from patentability.

But that doesn't mean Genicap's patent is invalid. "Copyrighting a mathematical formula is actually a difficult feat," Law of the Game blogger and attorney Mark Methenitis tells Ars. "You can, however, patent the practical application of a mathematical formula... So while you can't make the formula itself a claim, you can make using the formula to achieve specific outcomes 'claims' in the patent. Looking over the patent here, it does seem like that's [what Genicap did]."

In other words, Hello Games can't get in trouble for simply using the basic superformula. But it could run into legal trouble for using the formula in a specific way that's outlined in the patent. And while Genicap's patent calls out the formula's potential use in "graphics programs (e.g., 2D, 3D, etc.); CAD software; finite element analysis programs; wave generation programs; or other software," it doesn't specifically mention game design (procedurally generated or otherwise).

Regardless of the state of the law, though, Genicap could still cause headaches for Hello Games simply by trying to bring a case to court. The timing is certainly suspect; Murray talked to the New Yorker about his use of the superformula more than a year ago, yet stories about the patents are only leaking to the press now that the game has been finalized and is mere weeks from its planned August 9 launch date . While Genicap isn't publicly asking the game be pulled from release or demanding a share of the profits, the company must realize it currently has a lot of leverage in even asking for discussions.

"The funny thing, even if it's a bad patent or a bad claim, the cost of defending the potential suit could be a deterrent to releasing the game," Methenitis warns. "Defense costs to the Markman hearing can still get up to a million dollars (but average at least a couple hundred thousand), and going through an entire trial is usually multiple millions ($2-$5 million is a pretty typical range). Certainly not a small amount."

Update, July 25: Responding via two public tweets this weekend, Hello Games founder Sean Murray said that No Man's Sky "doesn't actually use this 'superformula' thing or infringe a patent. This is a non-story... everybody chill... I wish Johan Gielis, the author, all the best in future. We're going to meet and chat maths once the game is out."

Murray's statements seem to contradict that 2015 New Yorker article mentioned above, which includes lengthy discussion and demonstration of Gielis' superformula being used to populate the game's planets. Even being charitable, and assuming the formula is no longer directly extant in the game as it exists currently, it seems relatively clear that the formula was used heavily at some point in the game's creation. We'll let you know if and when we hear more from Murray or Genicap on the matter.