Principles of Escape Tile Design
             or
  The Laws of Escape Physics


This document is intended as a sort of self-narrative on the
principles of Escape. Since it's just a computer program, that is of
course silly; the C++ source file move.h "defines" the physics of the
universe. However, the interaction between features of the game
(which, on their own, are simple) leads to some subtle effects worth
thinking about clearly. The idea here is to lay out abstract
"principles" that can be used as guidelines when deciding between
several different possibilities. Designing around such principles has
the benefit that the player can use them to intuit game semantics; a
knowledge of "why" helps him deduce "what" without reading the code.
This can be the case even if he doesn't know the principles directly.

However, we must recognize that the Escape semantics are inevitably
complex and filled with opportunities for hidden information. Although
it's desirable to reduce complexity and hidden information, this may
not always be possible. Therefore, the burden remains squarely with
the puzzle author to compose levels that are scrutable.


The Laws of Escape Physics are listed in order of decreasing
importance. If behavior 'B' is implied by later rules but 'A' by
earlier rules, then behavior 'A' must hold.

1. Finitism

  Every Escape move terminates in finite time.


2. Determinism

  The Escape physics must be deterministic. Executing the same move
  in the same state multiple times must yield the same result.


3. Discreteness

  All action takes place on a discrete grid, in discrete time steps.


4. Conservation of Matter

  With the exception of explicit destruction (zapping blocks by
  electricity; pushing grey into holes; breakable blocks; bombs),
  Escape "matter" is conserved. In particular, there should be no
  mechanism that creates blocks out of nothing. (A "bug" in DOS Escape
  allowed this, because a certain combination of panels would both
  push a block onto another square and move it into the bizarro world,
  where it would be safe from being erased.)

  That means, for instance, that no panel interaction should increase
  or decrease the total number of blocks (of any type) in the world
  (including, of course, the bizarro world).


5. End-of-Turn Metaphysics

  Metaphysical events, such as the player dying or "escaping" the level,
  occur only at the end of the turn. A turn is made up of the individual
  motions of each entity.


6. Forward-Independence of Motion

  Each turn is composed of one or more motions. The player makes
  exactly one motion, and each bot makes one or zero motions. The
  player's motion happens first, followed by each bot's motion, in
  order of bot number. Because these motions happen sequentially, each
  motion acts on the board in the state that it was in at the
  end of the last motion. There is no "forward dependence" (changing
  one's move based on what will happen in a later motion) and no chance
  to retry an unsuccessful motion after a later entity has moved.

  However, bots do affect each other in various ways: destroying each
  other, pushing, etc.


7. Panels are Triggered by Edge-Effects

  Panels are not triggered by the presence of objects atop them.
  Panels are also stateless: there is no 'on' or 'off' position.
  Rather, panels are triggered by the "edge effect" of a block or
  entity moving atop them. Panels are triggered at the end of each
  motion. Because these happen all at once, triggering a panel twice
  in one motion is the same as not triggering it at all (so sometimes
  the game indeed represents this as zero triggers). However, two
  triggers in the same *turn* cannot necessarily be cancelled, since
  there may be intervening motions that depend on the panel's effects.

  This edge-effect behavior also implies that there are no transitive
  effects of panels, since triggered panels only cause swaps, not
  block/entity motion. Observe the non-obvious fact that this would
  not hold if we gave a stateful semantics to panels based on the
  presence of a block or entity: Imagine a sequence of panels 0..n,
  where panel i targets the location of panel i + 1. Each panel
  location is currently occupied by a robot, with panel 0 being
  unoccupied and adjacent to the player. When the player steps on
  panel 0, the panel at location 1 flips into the bizarro world. Since
  it no longer has an entity atop it, this triggers it and flips the
  panel at location 2 into the bizarro world, etc.. If panel n targets
  back to panel 0, this causes the chain reaction to in fact form an
  infinite cycle.

  (This cyclic problem is exhibited even in the simplified case of a
   panel that targets itself, so this is not even dependent on bots.)

  (Also, an instance of panel abuse can be achieved with only gold
   blocks, by causing a panel that the player is standing on to appear
   or disappear. That panel can be arbitrarily far away.)


8. The Entity Exclusion Principle

  Two entities may not (sustainably) share the same location on the
  grid.

  This implies the following (perhaps strange) behavior. If a bot is
  on a panel, and a Dalek walks onto that bot, then the panel triggers
  once (from the edge effect of the Dalek walking onto it). Since the
  Dalek and the other bot become one broken bot, this edge effect is
  "unpaired."