diff --git a/content/tilesets.typ b/content/tilesets.typ index 9685c1a0..504c4f94 100644 --- a/content/tilesets.typ +++ b/content/tilesets.typ @@ -292,56 +292,10 @@ p 0 0 6 repeater facing=north powered=false locked=false delay=1 p 0 0 7 comparator facing=north powered=false mode=compare ``` -To break this down: the bottom two (AA, AB) end in repeaters, so they must come first. Among those, -(AA) comes first. Among the top two (BA, BB), (BA) comes first. It's standard alphabetizing. Just as -the order of the alphabet creates an ordering over all words, the ordering of the comparator and -repeater creates an ordering of all tilesets. - -The 6gt tileset. There are now eight options. - -``` -<--------- -... -``` - -As the tilesets get larger, it's less useful to lay out the entire tileset and more useful to find -the next and previous lanes. - -For example, take this 7-diode tileset. - -``` -cmp rep rep cmp rep cmp cmp -<-------------------------- - B A A B A B B -``` - -We can easily find the next lane by thinking of this not as a *word* but as a *number*. We have two -options, and one is greater than the other. - -``` -cmp rep rep cmp rep cmp cmp -<-------------------------- - B A A B A B B - 1 0 0 1 0 1 1 -``` - -We can think of this tileset as a 7-bit binary number, in this case the value 75. We can find the -next lane by simply incrementing by one. - -``` - 1 0 0 1 0 1 1 (75) - + 1 - 1 0 0 1 1 0 0 (76) -<-------------------------- -cmp rep rep cmp cmp rep rep -``` - - -// So the full picture involves arbitrary components and priorities. As long as all the tilesets -// have -// the same total delay and end at the same time, we can determine a global ordering. However the -// general picture is hard to reason about, we basically have to simulate the priority queue to make -// predictions. If we restrict the design of the tilesets a bit, there are two simplifications we could +So the full picture involves arbitrary components and priorities. As long as all the tilesets have +the same total delay and end at the same time, we can determine a global ordering. However the +general picture is hard to reason about, we basically have to simulate the priority queue to make +predictions. If we restrict the design of the tilesets a bit, there are two simplifications we could take to make things easier to reason about. == Permutation Tilesets