409 lines
11 KiB
Typst
409 lines
11 KiB
Typst
#import "/lib.typ": diorama, example, note, todo
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= Tilesets <tilesets>
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The protocols as described are very sensitive to the exact timing that the EID counter is
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incremented. The fundamental cause for all types of interference is that there is a chance for
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unexpected entities to spawn in-between the measurement items, which increments the counter and
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corrupts the data. The solution, then, is to make that window *as short as possible* so the chance
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for interference is minimized.
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The fundamental principle is to use the game scheduled tick priority queue to do this. A *tile
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sequence* is a chain of redstone components that all update in the scheduled tick phase. A *tile
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set* is a system of constructing tile sequences that enforces a particular global ordering.
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#show raw.where(lang: "mc-diorama"): it => diorama(autoplay: true, loop: true, theta: 160, phi: 20, it.text)
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```mc-diorama
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p 0 -1 0 smooth_stone_slab type=top
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p 1 -1 0 smooth_stone_slab type=top
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p 2 -1 0 smooth_stone_slab type=top
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p 3 -1 0 smooth_stone_slab type=top
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p 4 -1 0 smooth_stone_slab type=top
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p 0 0 0 repeater facing=west powered=false locked=false delay=1
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p 1 0 0 observer facing=west powered=false
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p 2 0 0 repeater facing=west powered=false locked=false delay=2
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p 3 0 0 comparator facing=west powered=false mode=compare
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p 4 0 0 repeater facing=west powered=false locked=false delay=1
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t 2
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p 0 0 0 powered=true
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t 4
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p 0 0 0 powered=false
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p 1 0 0 powered=true
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t 6
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p 1 0 0 powered=false
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t 8
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p 2 0 0 powered=true
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t 10
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p 3 0 0 powered=true
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t 12
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p 2 0 0 powered=false
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p 4 0 0 powered=true
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t 14
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p 3 0 0 powered=false
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t 16
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p 4 0 0 powered=false
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t 20
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p 0 0 0
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```
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== The Scheduled Tick Priority Queue
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There are two aspects that affect a scheduled tick's placement in the queue: its _priority_ and its
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_delay_. Scheduled ticks with higher (more negative) priority update first in a given game tick.
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Scheduled ticks with equal priority update in the order they were scheduled.
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See @block-priority for a list of priorities. The most important point is that repeaters have higher
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priority than other components.
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== Binary Tilesets
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The simplest (and generally most useful) tilesets use only two priorities. This allows us to
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identify each tile sequence with a binary value and easily read the update order and carve up the
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the full tile set for different systems. Typically we use comparators (or observers) and 2gt
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repeaters.
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We identify the higher priority (repeater) with `0`, since it sorts/updates earlier, and identify
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the lower priority (observer/comparator) with `1`. Then we can read off the elements of the tile
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sequence to form a binary number.
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Components that activate later in the sequence have a stronger effect on the order, so to match our
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left-to-right reading convention, we diagram tile sequences so the signal flows right-to-left.
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Consider this 4gt tileset.
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#show raw.where(lang: "mc-diorama"): it => diorama(
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autoplay: true,
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loop: true,
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theta: 90,
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phi: 90,
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speed: 0.33,
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radius: 8,
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orbit: false,
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it.text,
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)
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```mc-diorama
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p 0 -1 0 smooth_stone_slab type=top
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p 1 -1 0 smooth_stone_slab type=top
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p 2 -1 0 smooth_stone_slab type=top
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p 3 -1 0 smooth_stone_slab type=top
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p 4 -1 0 smooth_stone_slab type=top
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p 5 -1 0 smooth_stone_slab type=top
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p 6 -1 0 smooth_stone_slab type=top
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p 7 -1 0 smooth_stone_slab type=top
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p 0 0 0 redstone_wire east=side west=none south=side power=0
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p 1 0 0 redstone_wire east=side west=side south=side power=0
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p 2 0 0 redstone_wire east=side west=side south=side power=0
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p 3 0 0 redstone_wire east=side west=side south=side power=0
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p 4 0 0 redstone_wire east=side west=side south=side power=0
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p 5 0 0 redstone_wire east=side west=side south=side power=0
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p 6 0 0 redstone_wire east=side west=side south=side power=0
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p 7 0 0 redstone_wire east=none west=side south=side power=0
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p 0 0 1 repeater facing=north delay=1 powered=false locked=false
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p 1 0 1 comparator facing=north mode=compare powered=false
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p 2 0 1 repeater facing=north delay=1 powered=false locked=false
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p 3 0 1 comparator facing=north mode=compare powered=false
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p 4 0 1 repeater facing=north delay=1 powered=false locked=false
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p 5 0 1 comparator facing=north mode=compare powered=false
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p 6 0 1 repeater facing=north delay=1 powered=false locked=false
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p 7 0 1 comparator facing=north mode=compare powered=false
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p 0 0 2 repeater facing=north delay=1 powered=false locked=false
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p 1 0 2 repeater facing=north delay=1 powered=false locked=false
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p 2 0 2 comparator facing=north mode=compare powered=false
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p 3 0 2 comparator facing=north mode=compare powered=false
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p 4 0 2 repeater facing=north delay=1 powered=false locked=false
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p 5 0 2 repeater facing=north delay=1 powered=false locked=false
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p 6 0 2 comparator facing=north mode=compare powered=false
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p 7 0 2 comparator facing=north mode=compare powered=false
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p 0 0 3 repeater facing=north delay=1 powered=false locked=false
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p 1 0 3 repeater facing=north delay=1 powered=false locked=false
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p 2 0 3 repeater facing=north delay=1 powered=false locked=false
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p 3 0 3 repeater facing=north delay=1 powered=false locked=false
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p 4 0 3 comparator facing=north mode=compare powered=false
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p 5 0 3 comparator facing=north mode=compare powered=false
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p 6 0 3 comparator facing=north mode=compare powered=false
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p 7 0 3 comparator facing=north mode=compare powered=false
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t 0
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p 0 0 0 power=15
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p 1 0 0 power=15
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p 2 0 0 power=15
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p 3 0 0 power=15
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p 4 0 0 power=15
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p 5 0 0 power=15
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p 6 0 0 power=15
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p 7 0 0 power=15
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t 1
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p 0 0 1 powered=true
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p 2 0 1 powered=true
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p 4 0 1 powered=true
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p 6 0 1 powered=true
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t 2
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p 1 0 1 powered=true
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p 3 0 1 powered=true
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p 5 0 1 powered=true
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p 7 0 1 powered=true
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t 3
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p 0 0 0 power=0
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p 1 0 0 power=0
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p 2 0 0 power=0
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p 3 0 0 power=0
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p 4 0 0 power=0
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p 5 0 0 power=0
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p 6 0 0 power=0
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p 7 0 0 power=0
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t 4
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p 0 0 2 powered=true
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p 4 0 2 powered=true
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t 5
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p 1 0 2 powered=true
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p 5 0 2 powered=true
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t 6
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p 2 0 2 powered=true
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p 6 0 2 powered=true
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t 7
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p 3 0 2 powered=true
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p 7 0 2 powered=true
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t 8
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p 0 0 1 powered=false
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p 2 0 1 powered=false
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p 4 0 1 powered=false
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p 6 0 1 powered=false
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t 9
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p 0 0 3 powered=true
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t 10
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p 1 0 3 powered=true
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t 11
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p 2 0 3 powered=true
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t 12
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p 3 0 3 powered=true
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t 13
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p 1 0 1 powered=false
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p 3 0 1 powered=false
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p 5 0 1 powered=false
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p 7 0 1 powered=false
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t 14
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p 4 0 3 powered=true
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t 15
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p 5 0 3 powered=true
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t 16
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p 6 0 3 powered=true
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t 17
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p 7 0 3 powered=true
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t 18
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p 0 0 2 powered=false
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p 4 0 2 powered=false
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t 19
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p 1 0 2 powered=false
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p 5 0 2 powered=false
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t 20
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p 2 0 2 powered=false
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p 6 0 2 powered=false
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t 21
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p 3 0 2 powered=false
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p 7 0 2 powered=false
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t 22
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p 0 0 3 powered=false
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t 23
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p 1 0 3 powered=false
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t 24
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p 2 0 3 powered=false
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t 25
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p 3 0 3 powered=false
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t 26
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p 4 0 3 powered=false
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t 27
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p 5 0 3 powered=false
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t 28
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p 6 0 3 powered=false
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t 29
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p 7 0 3 powered=false
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t 30
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p 0 0 0
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```
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We can express the same tileset numerically like so:
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```
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000 = 0
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001 = 1
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010 = 2
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011 = 3
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100 = 4
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101 = 5
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110 = 6
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111 = 7
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```
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Using the same pattern, we can generate a tile sequence for an arbitrary value of arbitrary
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bit-length. For example, the 8-bit tileset for `150` is:
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10010110
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#show raw.where(lang: "mc-diorama"): it => diorama(
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theta: 90,
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phi: 90,
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speed: 0.33,
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radius: 5,
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orbit: false,
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it.text,
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)
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```mc-diorama
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p 0 -1 0 smooth_stone_slab type=top
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p 0 -1 1 smooth_stone_slab type=top
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p 0 -1 2 smooth_stone_slab type=top
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p 0 -1 3 smooth_stone_slab type=top
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p 0 -1 4 smooth_stone_slab type=top
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p 0 -1 5 smooth_stone_slab type=top
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p 0 -1 6 smooth_stone_slab type=top
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p 0 -1 7 smooth_stone_slab type=top
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p 0 0 0 repeater facing=north powered=false locked=false delay=1
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p 0 0 1 comparator facing=north powered=false mode=compare
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p 0 0 2 comparator facing=north powered=false mode=compare
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p 0 0 3 repeater facing=north powered=false locked=false delay=1
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p 0 0 4 comparator facing=north powered=false mode=compare
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p 0 0 5 repeater facing=north powered=false locked=false delay=1
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p 0 0 6 repeater facing=north powered=false locked=false delay=1
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p 0 0 7 comparator facing=north powered=false mode=compare
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```
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To break this down: the bottom two (AA, AB) end in repeaters, so they must come first. Among those,
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(AA) comes first. Among the top two (BA, BB), (BA) comes first. It's standard alphabetizing. Just as
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the order of the alphabet creates an ordering over all words, the ordering of the comparator and
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repeater creates an ordering of all tilesets.
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The 6gt tileset. There are now eight options.
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```
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<---------
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...
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```
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As the tilesets get larger, it's less useful to lay out the entire tileset and more useful to find
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the next and previous lanes.
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For example, take this 7-diode tileset.
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```
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cmp rep rep cmp rep cmp cmp
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<--------------------------
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B A A B A B B
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```
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We can easily find the next lane by thinking of this not as a *word* but as a *number*. We have two
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options, and one is greater than the other.
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```
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cmp rep rep cmp rep cmp cmp
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<--------------------------
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B A A B A B B
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1 0 0 1 0 1 1
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```
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We can think of this tileset as a 7-bit binary number, in this case the value 75. We can find the
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next lane by simply incrementing by one.
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```
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1 0 0 1 0 1 1 (75)
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+ 1
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1 0 0 1 1 0 0 (76)
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<--------------------------
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cmp rep rep cmp cmp rep rep
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```
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// So the full picture involves arbitrary components and priorities. As long as all the tilesets
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// have
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// the same total delay and end at the same time, we can determine a global ordering. However the
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// general picture is hard to reason about, we basically have to simulate the priority queue to make
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// predictions. If we restrict the design of the tilesets a bit, there are two simplifications we could
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take to make things easier to reason about.
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== Permutation Tilesets
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#todo[describe the mixed delay permutation tilesets and the alphabetization procedure]
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== Lexicographic Tilesets
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== Jamming
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== Observer Bug <observer-bug>
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== Tables
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=== Block Tick Priorities <block-priority>
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#table(
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columns: 4,
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table.cell(rowspan: 3)[Repeater],
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[Facing diode (that is not facing it)],
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[`EXTREMELY_HIGH`],
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[-3],
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[Powering off],
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[`VERY_HIGH`],
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[-2],
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[Powering on],
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[`HIGH`],
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[-1],
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table.cell(rowspan: 2)[Comparator],
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[Facing diode (that is not facing it)],
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[`HIGH`],
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[-1],
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[Otherwise],
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[`NORMAL`],
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[0],
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table.cell(colspan: 2)[All other components],
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[`NORMAL`],
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[0],
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)
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=== Block Tick Delays <block-delay>
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#table(
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columns: 2,
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[Repeater], [2gt, 4gt, 6gt, 8gt],
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[Comparator], table.cell(rowspan: 4)[2gt],
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[Redstone Torch],
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[Falling Blocks],
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[Observer (see @observer-bug)],
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[Dispenser], table.cell(rowspan: 3)[4gt],
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[Dropper],
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[Redstone Lamp],
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[Iron Pressure Plate], table.cell(rowspan: 4)[10gt],
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[Gold Pressure Plate],
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[Tripwire Hook],
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[Tripwire],
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[Stone Button], table.cell(rowspan: 3)[20gt],
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[Stone Pressure Plate],
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[Detector Rail],
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[Wooden Button], table.cell(rowspan: 2)[30gt],
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[Wooden Pressure Plate],
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)
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=== Fluid Tick Delays <fluid-delay>
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#table(
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columns: 2,
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[Water], [5gt],
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[Nether Lava], [10gt],
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[Lava], [30gt],
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)
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