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Disclaimer: This isn’t a review of No Man’s Sky, nor is it a critical teardown of what’s in it and what isn’t. This isn’t an expose on Hello Games or their development practises, and it certainly isn’t a litany of complaints about the things Sean Murray may or may not have said to the press in his unchecked enthusiasm. We might touch on those things occasionally, but there have already been more than enough think pieces and hot takes on No Man’s Sky the finished product versus No Man’s Sky the expectation; probably around 18 quintillion, at last count.

What this is, however, is a discussion about mathematics and – more specifically – the mathematics of procedural generation.

Additional disclaimer: There’s also some swearing. For emphasis.

Good at Maths

When I was at university, we lived next door to a bunch of lads from Northern Ireland, in our first year in student housing. Long story short, and I don’t remember the exact details of who broke into whose kitchen via the fire escape to play Pro Evo… in any case, we all got like a house on fire; ironic really, as the fire escape door was broken in doing so. Stick with me folks, there’s a point to this sentimental rambling.

The Northern Irish chaps, all friends from school who had travelled to England together, often had an interesting turn of phrase that the English (and to be fair, the Scottish and Welsh) would need explaining. An example:

Brian came home one morning, still wearing the clothes he had on the night before, having done the walk of shame across campus. Paul and Ryan asked Brian (yes, these are their real names) about who he’d hooked up with the night before, but rather than immediately show us a photo on his phone or wax lyrical about the girl he’d just met, he was rather cagey and quiet.

“Ah, she must be good at maths then, is she Brian?” Came the inquest from his oldest friends. The rest of us, unaware of this expression, asked for an explanation.

“It’s basically, if you’re going out with a girl and she’s not much of a looker or she comes from a rough area or whatever, and you’re a bit embarrassed,” they explained, “then you figure she must have something else going for her, you know? So like at school, you’d go out with a girl, even if she wasn’t very attractive, if she could help you with your maths homework. So, you know, they’re good at maths.”

Sean Murray and Hello Games – and ultimately, No Man’s Sky itself – are very good at maths.

‘Superformula’

There’s an algorithm used, in No Man’s Sky, that sits at the core of everything the game promises. Over 18 quintillion planets, all birthed randomly out of pure mathematics by procedural generation; it’s a fairly serious undertaking by a small development studio.

There was a concern, following the game’s initial delay and the secret legal wrangling with the Sith Lord owner of Sky Media Rupert Murdoch (over their permission to use the word ‘Sky’ in the name) that another hiccup could interfere with No Man’s Sky’s release: the suggestion by a Dutch botanist Johan Gielis that Hello Games has used his patented ‘superformula’ without permission in the creation of their near-infinite universe. Sean Murray quickly nixed those qualms with a tweet stating that the Dutch ‘superformula’ wasn’t used in No Man’s Sky, and asked that “everybody chill”.

I bet he’s wishing for those days of people agonising over a potential name change or a mathematical patent right about now, incidentally, and everybody really does need to chill.

But there is a formula used to create the 18 quintillion planets in No Man’s Sky, and while we don’t know the details of the algorithms Hello Games used – and Sean, if you ever want to get together and discuss hardcore maths, then please get in touch – it must be pretty a pretty super formula to do it.

18 quintillion planets. Just take a moment to stop and think just how big that is. No, seriously. Stop flinging your excrement at Sean Murray and Hello Games on Twitter and Reddit for one sodding minute to think about just how brain-meltingly, calculator-crushingly large a number that really is. To put that in a little – or rather, very large – bit of context, our home galaxy, the Milky Way, upon whose sweeping spiral our insignificant blue speck drifts giddily through the universe, is thought to have at least 100 billion planets. “At least” means it could well be more, but that’s a good low-ball estimate.

No Man’s Sky contains over 18 quintillion planets. That’s over 180 million times larger than the Milky Way, and the install is about 6GB in size. Those are utterly bewildering numbers. It’s one of the technical achievements of the century.

Speculation time: As I said earlier, I don’t know any details of the formula that Hello Games used in the procedural generation in No Man’s Sky (and they’re more than welcome to enlighten me) but I’d be willing to bet there’s a healthy amount of just-in-time instantiation – that is, only creating objects when called upon by the algorithm, i.e. things popping in as you fly towards them – combined with some prodigious deduplication.

Deduplication, in the world of information technology, is a method of reducing storage usage by marking pieces of data as duplicates of one another and only keeping one master copy (with pointers to where it can be found in place of the deduplicated data). On a really basic level, that’s like only keeping one version of a Word document even though you might have the same thing stored in ten places. In reality, that happens at the block level – as small as 4KB in size, the storage equivalent of atomic particles – which probably explains how No Man’s Sky is able to fit so much into so little. It builds the universe on the fly, and it’s really efficient in only storing deduplicated copies of the absolute base components, the atomic building blocks it needs to build said universe.

But when you’re building 18 quintillion planets from shared building blocks, that level of procedural generation and hardcore deduplication is going to show. Unfortunately in No Man’s Sky, it can show pretty early on.

Attack of the Clones

One of the chief concerns being levelled at No Man’s Sky – and certainly one of the more founded ones that, isn’t just teen angst and base internet rancour – is that it can be somewhat repetitive. Though to some, that’s entirely the point.

Anybody who spent years of their life trading commodities in the original Elite can tell you that there was no real aim to that game; the joy was in Littlest Hobo-ing your way around the galaxy, occasionally getting into scrapes and adventures, but mostly just wondering in the vast black expanse of an infinite universe. If that’s your interpretation of No Man’s Sky – as it is ours, here at Thumbsticks towers – then you’re probably the ideal person to play No Man’s Sky, and will get the best out of it in the long run. You should also read Keith Stuart’s piece over on The Guardian on that very subject; it’s really rather good.

But No Man’s Sky is repetitive, nonetheless. I’ll concede that the inventory is too small, and managing it is a constant juggling exercise. I’ll concede that resource mining is a bit of a grind, and can be tedious and frustrating in equal measure. I’ll concede that the trading posts and alien encounters are cookie cutter, and may as well just be text-based menus after you’ve seen the animation once (like the interminable, un-skippable guardian summon monsters in Final Fantasy VIII).

And while I will also concede that the planets can be a bit samey and ultimately repetitive, I’m afraid I’ll have to step in at this point if you’re using that as one of your many slings and arrows with which to attack Sean Murray and Hello Games. The planets have to be similar, or at the very least repeatable or formulaic, because if they weren’t? We’d never be able to get anywhere.

Let’s take a look at those 100+ billion planets in the Milky Way again for a moment. Do you know how many of them are habitable or hospitable? To our precise knowledge, exactly one: Earth (though there has been a good candidate for a second found orbiting Proxima Centauri very recently). And never mind whether they’re actually hospitable; do you know what percentage of them would even have a crust, mantle or surface that you’d be able to walk on, or land a dinky little starship on? The percentage is probably stupendously tiny.

If Hello Games had, with their formula for procedural generation, allowed the galaxy of No Man’s Sky to form in any old way it wanted, then there would be no game, kids; or at least, it would barely be playable. Here’s a fictional diary extract of what would happen if the game were truly random:

Day 1.

I awoke on an alien planet, stranded with my stricken ship, unable to escape this bizarre world. After some time wandering, it seemed that I could scavenge the resources I needed to repair my ship, and set about the task. After several hours of shooting rocks and trees to garner mineral deposits, I was able to craft the requisite parts and fuel up my ship for departure. I only hope the next world I find is friendlier than this one.

Day 287.

I have died so many fucking times it isn’t even funny any more. The first eighteen planets I tried to land on were all gas giants, and my ship simply sank to the core of the planet and, if I wasn’t burned up by whatever hellish gas composed the planet’s surface, I was crushed by its gravity at the centre. The next dozen or so were so hot that my ship melted and I was boiled alive before I even touched the surface. Then the next few months have been spent in a vicious cycle of the two; of finding a new planet, attempting to land, dying, and reloading my fucking save. I’m going to try planet 13,722 now. Wish me luck.

Day 288.

I’ve made a massive fucking error. Planet 13,722 is even worse than all the others! I’ve finally found a planet I can land on, but there’s literally nothing here. It’s just a fucking rock, floating in space like a giant, frozen turd. There’s a relatively hospitable atmosphere and a stable mantle, so it didn’t insta-kill me when I landed, but there’s literally nothing here. There’s no fuel. There’s no minerals or resources. There isn’t another living creature or useful thing on here, and my ship is out of fuel. I spent months wanting to land on a fucking planet that wouldn’t fucking kill me, and now I finally have, I can’t get off the fucking thing. Ever.

Doesn’t sound like much fun, does it? Anyway, back to the maths.

Sean Murray is a Generous God

Hello Games have had to create the procedural generation algorithm for No Man’s Sky with a number of parameters and variables locked in, to result in an actual, playable experience.

Think of it like generating a random world map for a game of Civilization: You pick the size of map you want, you pick what percentage of water, what density of forest, what global temperature range, what distribution of resources, and the game builds you a random world based on those parameters. Do that a thousand times and you’ll never end up with the same map, but you might get some that are very similar if you punch in comparable starter variables. That’s procedural generation at work, folks, and it was foolish of people to expect anything different from No Man’s Sky.

Yes, there’s a hell of a lot more variables, and yes, the results are a hell of a lot stranger than anything we’re used to – and the created universe is still unimaginably large and entirely unfeasible to even comprehend – but it’s still just procedural generation. It’s like one of those children’s games where you can jumble up the face, legs and torso of different characters to produce some comical results, but on a bewilderingly large scale.

I’m willing to bet that the procedural generation algorithm behind No Man’s Sky does the same thing as Civilization’s map builder, just hidden in the back end and with a truckload more variables. Here’s some to get you started:

  • Planet’s radius.
  • Percentage of water.
  • Density of foliage.
  • Temperature.
  • Resource distribution.

Thus far, all pretty similar to Civ, just a bit more spacey. But No Man’s Sky goes a lot further than that, delving into the funky and the fantastical:

  • Monoliths.
  • Artefacts.
  • Alien races.
  • Colour of ground.
  • Colour of foliage.
  • Colour of water.
  • Atmosphere.
  • Toxicity.
  • Radioactivity.
  • Types of plants.
  • Types of animals.

There’s probably several hundred variables for each planet – and consequently some components like plants and animals will have their own sub-procedural generation and their own individual base variables, based on the planet they inhabit – and the formula will be incredibly complex, but they all have to stay within a liveable set of parameters, because to leave a player stranded on a planet they’re unable to leave would be unforgivable.

That’s ultimately why No Man’s Sky feels repetitive, and it’s also why it feels easy (bordering on the mundane) at times: there’s a benevolent deity, in the form of Sean Murray’s mathematical formula for procedural world-building, watching over you at all times, making sure that you’re always able to progress and keep on trucking with your interstellar gap year. No Man’s Sky is not a hardcore game with procedural generation attached (as you’ll see in other survival roguelikes The Long Dark and We Happy Few), rather it’s a procedurally generated universe with a game attached, and there’s a finite limit to how challenging that game can be while also remaining playable for all possible eventualities (of which there are also quintillions, most likely).

No Man’s Sky is a an astonishing mathematical algorithm for procedurally generating 18 quintillion worlds in 6GB of space, created by a tiny team of enthusiastic coders in a meagre office in Guildford – which in itself is remarkable enough – but it’s not the pillars of fucking creation. It’s a mathematical framework, a complex formula for spitting out odd planets and weird life-forms, but it’s still just procedural generation. Stop treating it like it should be an entire living, breathing universe, with a history of billions of years of evolution and chaos theory in action, because that’s simply not possible.

I’ll repeat that point in case you missed it, because it’s really important and I think some people out there aren’t fully taking it on board: No Man’s Sky does not contain the pillars of fucking creation. It’s still just maths – enormous, staggering, overwhelmingly clever maths, admittedly – but at the end of the day?

No Man’s Sky is just really, really good at maths.

About the Author

Tom is an itinerant freelance technology writer who found a home as an Editor with Thumbsticks. He especially loves coffee, role-playing games, and anything he can play co-operatively with his wife – they make an awesome co-op team.

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23 Comments

  1. A. Vlasenko / 31st August 2016 at 9:33 pm /Reply

    The argument that in the real Universe, only one in 13,722 planets has a surface you can land on is preposterous. Look at the Solar System: there are only four gas giants and one planet where you would need a seriously reinforced hull if you want to fly to the surface (Venus), the rest of the planets, moons, asteroids and comets are perfectly fine to land on (though you might want to avoid the dayside of Mercury). Sure, life may not be common: but in the Solar System, there is abundant life on the surface of Earth, there are ice-covered oceans on Europa and Enceladus that could possibly have life (a game could give you the ability to drill through the ice and drop a submersible into the ocean to find this potential life), there could be subterranean microbial life on Mars, and there could be exotic cryogenic life on Titan, if evolution can come up with such a thing. In addition, the Kepler survey of transiting exoplanets shows that plenty of stars (maybe 1 in 5) have a planet in the habitable zone that is too small to be a gas giant. This isn’t to claim whether any of these places have life, we simply don’t have enough information to know this right now, the point is simply that there is a believable way for a game to put in life on a relatively high proportion of planets without being ridiculous about it. And there is no reason for (1), every planet to be single-biome and devoid of large-scale features (mountain ranges, canyons, polar ice caps, climate that varies depending on latitude, etc.) and (2), for every system and planet to have goddamn galaxy-faring aliens on it. I thought this game was supposed to be about exploration? Do you not think that finding a piece of alien junk or an identical single-occupant alien house on every single acre of every single planet ruins that impression?

    • Tom Baines / 31st August 2016 at 9:44 pm /Reply

      That wasn’t my argument at all. My argument was that, in a universe of 18 quintillion possible planets, the probability of you landing on one that is not only survivable but also contains everything you need to be able to hop to the next planet every single time is unreliable at best (at least without the parameters of the formulae being skewed in your favour). 13,722 was simply a hyperbolic example (to illustrate the need for that parameter-based oversight in a colourful way) which you’ve apparently read a little too literally, but thanks for playing!

      • Eric Richardson / 1st September 2016 at 2:43 am /Reply

        Lol we have a term for when a point goes over ones head.

        whoooooshhhhh

      • A. Vlasenko / 1st September 2016 at 3:42 am /Reply

        Well, then the requirement that you must get everything you need from scratch every you time you land on a planet, before you can move to the next one, is silly and a bad game design choice (since it basically forces all planets to be the same in terms of resources and survivability, and because the only way to get some resources is from intelligent aliens, every planet must be populated with them, ruining the sense of exploration). The spaceship should be capable of exploring several planets in a row before requiring a complete recharge, and the player should also be able to do some kind of scan from a distance to determine if a planet or star system is worth going to. For example, look at Elite Dangerous: most of that game’s universe is fairly empty and inhosipitable, but it is still possible to go on long trips across the Galaxy, tens of thousands of light-years away from any populated systems. Sure, if you’re not careful and make bad decisions, you can get stranded, but a game is not required to guarantee easy victory regardless of the player’s choices.

        • SghnDubh / 1st September 2016 at 12:12 pm /Reply

          Your 48-slot starship *is* capable with the correct modules and a full charge of warp cores, to travel many systems in one jump.

          Most critics including possibly this author expect to do and see an unreasonable amount of variation possible within a small window of play time. There is much more terrain, flora and fauna variety as you venture off the ‘center of the universe’ path and away from Class G stars.

          Though yes, I concede there are many redundancies including building models and NPC encounters…which I expect HG to improve with DLC.

          In short, sheesh, get some patience people.

          • KDerby42 / 10th September 2016 at 12:41 am

            Dude, I have over 100 hours in this game, I maxed out all my slots, finished the atlas quest, realized I would never have the patients to get the the center of the galaxy and just bounced around randomly after that. Your statement that: “There is much more terrain, flora and fauna variety as you venture off the ‘center of the universe’ path and away from Class G stars.” simply isn’t true. After you have seen 10 or so different planets the rest always variations of the same. I have taken a lot of black holes which take me to different parts of the galaxy, I see no galaxy wide variation.

  2. Thomas Bartholomew / 1st September 2016 at 12:31 am /Reply

    Oh, after reading the reviews and not the least of all your amusing piece, I think that I will stick with Roblox.

  3. Adam Cass / 1st September 2016 at 1:28 am /Reply

    Great article, but what occurs to me most after reading it is: isn’t the universe itself, the one we live in, just the result of a kind of maths and procedural generation? Aren’t the only differences, really, that the supercomputer made to create it was far more advanced than anything we currently possess, and that there is no requirement for even one millionth of the worlds to be ‘habitable’? The thing that I celebrate most about NMS is that thing you said, perhaps with a bit of hyperbole but only a BIT, that it’s one of the technical achievements of the century. And hooray for that!

  4. Dave / 1st September 2016 at 4:24 am /Reply

    Sean Murray and Hello Games’s maths needs to seriously improve and make the galaxy interesting and varied, where there are the desert planets, water worlds, ice planets, ringed planets, unexplored planets, gas giants, planetary physics, solar system physics, day/night cycles, mountain ranges, rivers, valleys, polar ice caps, civilizations, dead civilizations, warring civilizations, warring factions, realistic creatures, ecosystems, etc…

    The original vision that Sean had for this game was wonderful, like living and breathing a sci-fi exploration novel from the 70s, but in reality the game has been stripped down to the bare bones of that vision, in reality I think due to the 15 man Dev team being so small. Game development is hard and needs lots of manpower, I would like to see a AAA studio with 100’s of Devs take this on and make the original vision that Sean had, maybe a No Man’s Sky 2.

  5. M. Twigg / 1st September 2016 at 6:04 am /Reply

    Mr. Vlasenko and Mr. Baines, you both put forth extremely valid and well thought out arguments that were both intelligent, thorough and show proof of your research and expertise in the fields of space exploration and mathematical theory. Without having done the same research myself, all I can contribute to this discussion is that I regret I was born about 200 years too early.

    No Man’s Sky offers me a fantasy in which I can explore an expansive, albeit repetitive and abbreviated universe. I acknowledge that the game does fail to shoulder the burden of creating a uniquely authentic experience for every system and planet that I have discovered during my journey towards the galaxy center.

    I find that in order to enjoy the experience fully I am forced to use my imagination to build upon the framework Hello Games has provided. I am an explorer, plain and simple, and I create my own unique and wondrous experience on every uncharted system I enter. Call me old fashioned, but using my imagination has consistently recreated the wide-eyed and child-like wonder in me that I so often feel when I look at the stars from my backyard and think, “what is really waiting for us out there?”.

    I understand what the intent of this piece is. You respect the ingenuity of the mathematically-powered algorithms that allowed a massive game board to be delivered in such a modest package, but that at the end of the day this game can be summed up as simply one thing; an equation. I can respect that, but I feel this synopsis is indicative of the opinion of an over-stimulated generation. The issue most folks seem to have is the lack of any meaningful storyline. Modern gamers are used to having linear quest lines spoon fed to them without having to contribute anything in the form of imaginative thought. To each their own, but there are 18 quintillion different experiences waiting for them in No Man’s Sky if they allow their imaginations to set the stage.

    A bit of a dreamer’s notion I know.

    Thanks very much for your article. I enjoyed reading it!

  6. Trevor / 1st September 2016 at 8:45 am /Reply

    It isn’t some specific number around 18 quintillion. The algorithm can generate an infinite number, but that sounds less impressive than 18,435,294,…….etc. In truth it’s really just one planet, with randomly generated computer landscapes. That’s an achievement of some sort, but makes for poor gameplay if interesting stuff isn’t manually added in. There are lots of games out there – choose carefully.

    • Daniel New / 1st September 2016 at 9:10 am /Reply

      Each Call of Duty is like that for me. It’s just one corridor, with different wallpaper.

  7. Jim E / 1st September 2016 at 9:04 am /Reply

    Nice article; many thanks. Having played too long to get a refund, I swallowed my disappointment and kept playing, and I’m glad I did. There are lots of problems with the game, but I hope it will be added to and improved over time (early mods, like low flight, are already an improvement). Having read your piece, however, I find myself wondering whether a slightly smaller universe (say the size of our Milky Way) would have allowed more time, energy and mathematical ingenuity to have gone into making the planets more varied? Did the “good at maths” crew at Hello Games push the mathematical boundaries at th expense of playability, perhaps?

    • AluKed / 1st September 2016 at 9:27 pm /Reply

      A smaller universe would make very little difference – the algorithm created is probably infinitely scalable, so the size of the universe is a trivial decision – small or humongous, the workload is the same.

      To get more planet variety, they’d need to spend more work to increase the depth of planet gen simulation and, thus, algorithmic complexity.

  8. Mat Hall / 1st September 2016 at 9:48 am /Reply

    Yes, the fact that if you have 2^64 planets they’ll be s bit samey is inescapable, so to my mind the question becomes why not have fewer, and mix it up a bit? Knock it down to 2^60 planets (still a metric fuckton), and give each one 16 biomes?

    (Also “one of the technical achievements of the century” is hyperbole; Minecraft has 2^64 “planets”, not to mention the additional options (single/multi/large biomes, etc.) that further boost the numbers. Heck, sometimes it feels like there’s more variety in a single Minecraft world than the entire NMS universe…)

    • AluKed / 1st September 2016 at 9:33 pm /Reply

      Number of planets and complexity of the planets is not an OR proposition; it’s a matter of algorithmic depth complexity. If they added biomes to planet gen (and they should, at the very least polar dynamics), there would be no difference at all between generating 2^60 or 2^64 planets.

  9. Trevor / 1st September 2016 at 8:37 pm /Reply

    The game might have greatly benefited from a feature that allows the lifeforms in it to evolve. Absent that, the best one can really do with procedural generation is to have it be 50% algorithm, 50% hand-crafted. I think they should have spent a lot more time on hand-crafted lifeforms. Multiplayer and some cutscenes wouldn’t have hurt either.

  10. David Mielcarek / 1st September 2016 at 11:32 pm /Reply

    Good article, really enjoyed your writing and viewpoint. And I fully agree. Though I have not gotten the game yet (still waiting to get), I have read/watched/consumed loads of reviews/journals/etc. There seems to be 2 sides. The gamers who approach the game as an adventure, relaxing, puzzle solving game have fun, those who like to buy a game, solve it as fast a possible and become a god among other players, hates it. I am a die hard vanilla minecraft player (no mods) and love when I can just sit, relax and explore/build. Minecraft is also a very repetitive game, break blocks, get resources, build/improve things, but, there are tons of people (like me) who love it.

    • KDerby42 / 10th September 2016 at 12:49 am /Reply

      Now, imagine that Minecraft was just the same as it is, but no ability to build anything…. That is “No man’s Sky”.

      • David Mielcarek / 20th September 2016 at 10:22 pm /Reply

        Yep, I would have to agree. I still have not gotten NMS, but, it does seem that ‘building’ stuff in it would make a lot better play, and make people feel they ‘own’ their areas.

  11. David Mielcarek / 1st September 2016 at 11:35 pm /Reply

    Also, the 1/2 that seem to dislike also focus on ‘quick’ rewards, like complaining that the Monolith Portals secrets have not been solved. They focus more on ‘now’ and less on enjoying the journey, not the goal. Relax, enjoy your game/life and pat yourself on the back when goals are met, but, don’t make the goal your goal.

  12. ThomasJeromeNewton / 10th February 2017 at 1:47 pm /Reply

    Intelligent article and a great read. I have 300 hours played already and i still haven’t become bored with what i’m finding.

  13. NPH / 17th February 2017 at 11:00 pm /Reply

    Minecraft is so much better, nms simply failed. Progen isnt new, and nms did nothing new.

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