DnD 4 Countdown 24 - Don't be such a square

One of the changes in DnD4 vs. earlier editions is the simplification of diagonal movement. It's a subtle but interesting change. Earlier when you moved diagonally, you counted 3 squares for every 2 squares you moved. If you wanted to move 5 squares diagonally you counted [1] [2,3] [4] [5,6] [7] (each bracket representing a square), so it took 7 steps to move 5 squares.

In the next edition it is a straight 1:1 relationship. For each square it's one step.

With this in mind, why not abandon the square maps altogether? There are two other ways to do things, both which are actually more suited to the 1:1 relationship.

Hexagonal maps

During the 90s, my big go-to-game was Gurps, which used maps with hexagons. I can't see any problems with using hexagon maps in DnD4 at all. The hexagons allow for more freedom of movement and it's easier to visualise blast areas and cones (for instance). I definately get a more "organic" feel from the map when I'm using hexagons instead of squares.

I can only see two drawbacks of it, neither which I consider being a major problem. The first one is that you can only group up 6 against one opponent (since a hexagon always has six neighbours, instead of 8).
The second is that it can be a bit more cumbersome making maps with straight lines (corridors, halls etc).

No grid at all

Another option is to use no grid at all. Many wargames use this, so it's a tried method. It's a bit more loose than using a grid, but it should still be manageable. What you need is a piece of string for measuring distance travelled. If you wan't to move from point a to point b, you measure how long you can move on the string, and then place the string between A and B to see if you can get there.

Blasts and cones don't have to fit into a grid, but instead you just use circular or conic templates. ZoC are measured with a 1" marker or similar.

There might be a bit more decisions to be made with this method, but I believe it's perfectly usable.