Okay, here's a suggestion for how to resolve this:
A gel mother that is not on gel is not considered to be connected to anything. When gel grows, such an isolated mother creates gel on the square it's on, and on each of the eight surrounding squares.
A gel mother that is on gel is considered to be connected to each of the four orthogonally adjacent squares (if any of those squares contain gel). It is not directly connected to the four diagonally adjacent squares. For example, consider this configuration:
GG..
GG..
.M..
..GG
..GG
Here, the mother is connected to the upper gel blob, but not to the lower one. To make the connection clear, the square just above the mother should be drawn as an east edge, instead of as a southeast corner.
The motivation for these rules is that they're easy to display. A mother that is not on gel
looks isolated, and cannot be depicted as being connected to adjacent squares of gel. On the other hand, a mother on gel often looks like it should be connected to the orthogonally adjacent squares -- for example, in the picture Mazer provided. Note that it'll look sort-of connected even if the tile below the mother is redrawn as a north edge.
In the case where a mother is orthogonally adjacent to a corner square (under the current graphics rules) it doesn't really look connected, although the gel pieces do touch at a point. You could decide that it's not connected in this case. However, I think this is a needless complication, especially since it's easy to redraw the corner as an edge square, thus making the connection clear.
Finally, there's the diagonally adjacent squares. In most cases, the mother will be connected to these through an orthogonally adjacent square. The only exception is this situation:
M.
.G
Here, the gel square must be either a northwest corner, which doesn't look connected, or a mother on gel, in which case it doesn't matter whether the squares are connected. Hence, the rule should be that the mother isn't connected to this square. Note that even if the northwest corner is redrawn as an interior gel tile, it doesn't really look connected to the mother, since the squares only touch at a single point.
One thing regarding cuttability needs to be mentioned. Under this suggestion, you can have a situation like this:
MGG
.GG
Here, the gel square next to the mother is depicted as a north edge, but it looks like an inner corner to the southwest. It's not immediately clear whether this square should be cuttable. My suggestion is that it should not be -- for simplicity, squares drawn as edges or corners are not cuttable, but all others are.
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