Friday, October 8, 2010

Some Math

[Hello. Sadly, the regular Towards Dawn update won't be appearing today as I just simply have not had the time to play or write it. I'll make up for it by doing at least one post over the weekend! In the meantime, my good friend Sean Di Lizio has been doing some math, and I thought I would share them with you. They may be considered depressing, if you see the goal of Towards Dawn to circumnavigate the globe or to see the 'entire' world. Rather, though, I just see them as exciting. So much left to see!]

I did some calculations that might be interesting to you.

I’ve listened to an interview where Notch said that the world is the equivalent of having 8 times the surface area (n.b not volume, not circumference) of Earth.  As Earth’s circumference is just over 40,000km, we’re talking roughly 113,000 kilometres to circumnavigate the Minecraft planet.  (It works out to the square root of 8 for the increase in circumference for a world with 8 times the surface area.)

Thus, being that the character walks at about 4.25 m/s (or so I’ve read on the wiki).  Doing some rough calculations, that works out to about 7,400 hours to walk around the world.  Of course, crossing mountains and taking detours slows that pace to half, and you’re only able to walk for about a third of the time due to the day / night cycle and the need to gather some resources.  So, we’re talking about 44,400 hours of gameplay, or just over 5 years.  (Boating is slightly faster at max pace, but works out much better in reality due to a lack of obstructions.)

Thus, Towards Dawn is probably unlikely to achieve a circumnavigation of the planet, but you could start calculating percentages.

A complete day / night cycle is 20 minutes.  After 18 days of travel, assuming you’re only walking for 8 hours on average due to other tasks that need doing, then we’re talking 8/24 * 20 minutes = 6.67 minutes of forward travel time per day.  Giving you an average pace of 2.5m/s due to hills and obstructions, that works out to traveling about one kilometre per day.  So you’re now probably 18 kilometres from spawn.  To date, you’ve walked 0.016% of the world’s circumference.  By Minecraft day 113, you’ll have achieved 0.1%. :)

Also, doing the maths for Minecraft years, then it would take 310 Minecraft years at your current pace to circumnavigate the planet.


  1. Are these calculations of Minecraft years based on 365.25 day/night cycles? Is it possible to calculate how long it takes the Minecraft world to orbit its sun?

    On a similar topic, I wonder if Notch plans to introduce seasonal variation in day/night cycles...

  2. I just made the assumption of the calculations of Minecraft years based on the standard 365 day cycle.

    We'd probably need a little more info from Notch to make any calculations of orbit durations, like seasonal variations as you've suggested.

    It would be possible to get a rough estimate if we assumed a similar mass to volume ratio as earth, and then calculated orbits based on an estimate of the sun's volume and distance from the planet. However, that's two unknowns and I can only think of one piece of information to solve that - the size of the sun in the sky.

    Any ideas, peoples?

  3. Dont worry, it will all be scenic!

  4. Given the minecraft sun appears in the sky very much like our own, doesn't this suggest the minecraft sun would have a similar size, output intensity and distance?

  5. I think you're making a big assumption in how long he typically travels per day.

    I think it should be possible to more accurately calculate distance traveled from the size of the save file. As the world is continuosly generated as you travel, the file will grow ever larger.

  6. This doesn't match with the numbers you presented before. You km² size of your minecraft world is considerably lower than earth's, it was less than a new york iirc.

  7. Anon: The world generates in chunks as you go. So *all* that world doesn't currently exist, no. But all that potential world exists, up to 8 times the surface of earth. I think the procedural algorithms start screwing up after that (or so I heard). THis is why the file size grows, because more world is generated as I move into new lands.

    Simon: Last itme I attempted Cartograph, I could see the pictures dimensions, even if I couldn't see the picture itself. It was about day 13 or 14, I believe, and the image was 800x12000 or 14000 or something like that. If 1 pixel is one cube is one meter, then that would be round about right for Sean's equations, i think. That said, it does still need some assumptions, of course.

    I for one would like to think I an walking more than a kilometer a day :p

  8. You could try other map generators, maybe they'll work. I know of 3 other than Cartograph: C10T, AlphaVespucci and mcmap. Mcmap is the simplest, which could make it the most robust.

  9. 1 more: Minecraft Topographical Survey :)

  10. @Brendan

    I see, thanks :)

  11. It isn't the destination, it's the journey.

    And the book deal.

  12. if your walking a kilometre per day, check out your map: your camps should be about 1000 blocks from each other.