two tiles) and a three-tile relation (transforms three tiles per transition
simultaneously). In order to generate transition relations, we iterate through
a screen and for each tile we check neighbouring space with the purpose of
-generating only the relevant relations. For example, if we concider a tile in
+generating only the relevant relations. For example, if we consider a tile in
the top-left corner, there is no need to generate one or two-tiled transition
relations which can transform tiles to the left or to the right of that given
tile. For each possible direction of agent movement, we define a $\delta$ and a
$\gamma$ variables which represent the change in coordinate values respectively
-for the next position and the position next to the next postition.
+for the next position and the position next to the next position.
$$\delta_{(x,y)}(m)=\begin{cases}
(x-1, y) & \text{if } m = left\\
(x+1, y) & \text{if } m = right\\