wip tileset explainer

content/interference-fixes.typ

@@ -1,4 +1,4 @@
-#import "/lib.typ": todo
+#import "/lib.typ": example, todo
 
 = Preventing Interference <timing>
 
@@ -13,21 +13,99 @@ us to spawn transmission entities in that window.
 The fundamental principle here is to use tile-tick priority (TTP) to set a global order. See
 Charlie's great video on TTP for details. #todo[link video]
 
-The core principal is that repeaters have higher priority than other components. For example, if a
-repeater and comparator are scheduled to activate in the same tick, the repeater always (with one
-exception, if the comparator faces into a diode and the repeater does not) activates before the
-comparator does. By choosing a regular building pattern, we can avoid this exception entirely.
+#todo[fix tileset naming. the tileset is the *structure*. the particular sequence is just one instance of that tileset]
 
-// Among repeaters, they activate in the order in which they were scheduled. And among comparators,
-// they activate in the order in which they are scheduled. But every repeater activates before any
-// comparator (aside from that one exception). This gives us a *stable sort* which we can use to
-// globally define update order with arbitrary precision.
+A *tileset* is a sequence of redstone components which all update in the tile tick phase. Components
+later in the sequence have greater significance. To make the significance match our left-to-right
+reading convention, we diagram them so the signal flows right-to-left. For example:
+
+#todo[screenshot of the same arbitrary tileset]
+
+```
+cmp 1rep 2rep obs 1rep
+<---------------------
+```
+
+This section will cover how to read and construct tilesets that enforce a *global* ordering for
+wireless redstone.
+
+=== The Tile Tick Priority Queue
+
+The game schedules tile updates through a priority queue; different components have different
+priority, so each stage of the tileset iteratively refines the global order. Across the full
+tileset, we can enforce an arbitrary global ordering.
+
+#todo[the priority table
+
+  call out here that basic comparators and all other components, so from here on out we're just
+  going to use comparators for simplicity.
+]
+
+Components with different priority always update in priority order, but components with equal
+priority update in scheduled order.
+
+#todo[rephrase or remove
+
+  The core principal is that repeaters have higher priority than other components. For example, if a
+  repeater and comparator are scheduled to activate in the same tick, the repeater always (with one
+  exception, if the comparator faces into a diode and the repeater does not) activates before the
+  comparator does. By choosing a regular building pattern, we can avoid this exception entirely.
+
+  // Among repeaters, they activate in the order in which they were scheduled. And among
+  // comparators, they activate in the order in which they are scheduled. But every repeater
+  // activates before any comparator (aside from that one exception). This gives us a *stable sort*
+  // which we can use to globally define update order with arbitrary precision.
+
+]
+
+#example[
+  #todo[this explanation is so janky]
+
+  Say these three tilesets are started in the same gametick, `t=0`.
+
+  ```
+    <------
+  1 rep cmp  ab
+  2 cmp rep  cd
+  3 2rep     e
+    <------
+  ```
+
+  Once `b`, `d`, and `e` are scheduled, the priority queue looks like this:
+
+  ```
+  t=2 [d] [b]
+  t=4 [e]
+  ```
+
+  Now at `t=2`, we process the queue in order.
+
+  - `d` activates and schedules `c`.
+  - `b` activates and schedules `a`.
+
+  ```
+  t=4 [e a] [c]
+  ```
+
+  Now at `t=4`, the end of the tileset, the lanes will always update in order `3 1 2`
+
+]
+
+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
+
+#todo[describe the mixed delay permutation tilesets and the alphabetization procedure]
 
 === Binary
 
-The simplest tilesets are made entirely of comparators and 2gt repeaters. Repeaters activate before
-comparators, so if we think of it like sorting words alphabetically, we can identify repeaters with
-"A" and comparators with "B".
+The simplest tilesets are made entirely of comparators and 2gt repeaters (alternatively: observers
+and 2gt repeaters). Repeaters activate before comparators, so if we think of it like sorting words
+alphabetically, we can identify repeaters with "A" and comparators with "B".
 
 So, suppose we have a "binary tileset" that is 2gt long. There are two options, A and B. If we
 alphabetize these, we see the A (repeater) always executes before the B (comparator). With such a
@@ -96,7 +174,7 @@ cmp rep rep cmp cmp rep rep
 
 === Lexicographic
 
-=== Mixed Priority Jamming
+=== Jamming
 
 == Block Event Delay