So I just bought Minecraft. This decision took me a few months to make, mostly because I was debating between not wanting to buy such a low resolution style game, but at the same time it looked like a lot of fun when watching those crazy guys over at Rooster Teeth and their Let’s Play Minecraft videos. It all started in the subreddit of TheyDidTheMath when someone asked how big a single generated world in Minecraft was, in kilometres. My response was simple, because the data was already available on the Minecraft Wiki.
In practice, technical reasons (the limits of 32-bit math) force the maximum map size, including the Far Lands (unrendered chunks of the map), to be around 9.3 million times the surface area of Earth, which comes out to about 4.7 quadrillion km² (The hard limit where chunks are overwritten is at X/Z of ±34,359,738,368, making the world at most 68,719,476,736 meters wide and long, which is about 4,722,366,482,869,645 km². When compared to Earth’s total surface area, 510,072,000 km², this works out to be about 9,258,235 times that).
I slightly modified this quote from the wiki, to clarify a few terms for non minecraft players 🙂
Then someone asked in a different thread, how many unique worlds can spawn in Minecraft, assuming that once a world is generated, it can never be generated in that exact configuration again. This means that if you generate a world, and then generate a 2nd world that’s identical in every way except one block of dirt is located one block over, then that world is unique compared to the first. Now then, assuming Steve (this is the name of the character you’re controlling in Minecraft) is 1.828 metres tall (6 feet), and the maximum size he can fit into without crouching is 2 blocks, we can assume that each block is 0.762 metres (2.5 feet) in height. Why 0.762 and not 0.914m (3 feet)? In a two block height tunnel, Steve can still jump slightly. We can only estimate that there is a 0.3048m gap (1 foot).
Using the data provided further down the wiki page, we get the list of naturally generated blocks. We’re going to ignore snow blocks for the time being, because those are randomly generated and could be completely omitted entirely, plus they don’t count as a full block. We’re also going to ignore vines as well. We can safely skip these two and still get an accurate number because in The Overworld (the name of the planet you’re on), an “air” block takes up the same space as a snow and vine block. We’re just not calculating in their value, but are replacing them with air. We’ve turned off structure generation as well. There are 50 naturally occurring blocks.
Multiply 921,600,000,000,000,000 by 50 and we get the total combination number, and multiply that number by 921,600,000,000,000,000 again to cover all possible combinations, and we get:
424,673,280,000,000,000,000,000,000,000,000,000,000. That’s how many unique worlds the Minecraft engine can create, if we assume that there’s no “seed value”. Some people have pointed out that it’s really 2^64 because of the seed generation limit of 32 bit math in computer language, but we’re ignoring that simply because it’s the lowest possible number. We’re not about limiting ourselves here at Everyday Science Stuff. To put the total worlds number into perspective, if we joined each unique world end to end, and made one massive “planet” that was flat, it would be roughly 200,546,286,364,231,595,458,560,000,000,000,000,000,000,000,000,000,000 km, or 5 septillion times the size of the observable universe.
That’s quite big.. (that’s what she said..)