How far do I have to place torches so that mobs will not spawn near me?

Question

Since torches prevent mobs from spawning, is it possible to place enough torches within a specific radius to ensure safety during the night? I'm thinking of a situation without any shelter built, more along the lines of a flat plain. If it is possible, how many torches/how far out do I need to go to make that area safe?

Answer

1. Learn about light:

   • Sunlight gives 15 luminance to the blocks it hits directly, or through half steps.
   • Lava gives 15 luminance.
   • Lightstone gives 15 luminance.
   • A jack-o-lantern gives 15 luminance.
   • A candle gives 14 luminance to the otherwise empty block it occupies.
   • A redstone candle gives 7 luminance to the otherwise empty block it occupies.

   • Every tile that isn't a light source has a luminance of one minus the luminance of its neighbors. For example, if you had a 6 and a 4 luminance sources close to each other, attached to a wall, you'd have this distribution:

                 1
                121
           1   12321
          121 1234321
         1232123454321
        123432345654321
         12┴─────┴4321
          1     12321
                 121
                  1  
     

     ...except this works in three dimensions instead of two!

2. Learn about spawning:

   1. The following applies to any difficulty, except for Easy.
   2. Every tile within 24 distance of the player is not eligible.
   3. Every tile outside a 144×144 square centered on you is not eligible.
   4. • Every non-glass, non-half step surface in the outer world with 7 or less luminance is eligible for spawning.
      • Every non-glass, non-half step surface in the Nether is eligible for spawning.
   5. Mob spawners cause mob to spawn at a high rate in any surface within 5 distance of it.
      
      

3. In practice:

   Here's what I try to do to ensure a luminance of 7 consistently along a line:

   1. Place the first torch. Pardon my hexadecimal one-sided luminance graph:

      EDCBA98765432100000000000000000
      ↑
      

   2. Proceed until you find two tiles looking exactly like the next, then go back one.

      EDCBA98765432100000000000000000
                   ↑
      

   3. Plant a torch there. Lo and behold, minimum luminance there will be 8!

      EDCBA9889ABCDEDCBA98765432100
                   ↑
      

   4. GOTO 1

   You can adapt this algorithm to your necessities with ease. Just plant a torch in the darkest area when in doubt. (Duh.)

   Also:

   • Put torches directly onto surfaces for best results.

   • In your mining, be aware that any surface is good enough to spawn...

     ↓↓↓ ↓↓    All positions marked with an arrow are valid
     ███ ██↓   spawning points, to the best of my knowledge,
     █     █↓  and they all can lead to the just spawned mob
     █      █  to reach you.
     █     ↓█
     █↓↓↓↓↓█   Be vigilant and don't mine caves from the
     ███████   bottom up :(
     

4. Learn how to keep mob that has spawned outside: make traps.

   • Mobs can only jump up one tile. Make pits deeper than that and, once in, they will be trapped (skeletons are still dangerous and spiders can climb out).
   • Mobs cannot deconstruct. Make walls. (Be aware creepers do explode, if they get close enough.) Use cobblestone: they have high explosion resistance and can't catch fire.
   • Mobs cannot use items. Protect your entrance with a wooden door. Plant it from the outside, or skeletons will be able to hurt you with their arrows!
   • Mobs' path finding is somewhat dumb. Protect your spawn point with water and liberal amounts of cactus (arrange them in a chequered pattern.)

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