The previous visualization attempts were certainly useful and provided interesting insights into possible solution approaches. It looked like this-
The next step was to improve the visualization in two ways.
First, to increase the relative size of each cell. In the earlier mappings each cell was represented by a single data point. This appeared in the charts as a pointed peak or valley. This iteration, I've expanded the matrix so that each cell in the physical matrix is represented by an array of four cells, each containing an integer representing the physical cell's path distance from the finish cell(s) in the center of the maze.
Second, the 'floating' appearance of the chart maze bothered visually. I found that my eye was frequently being drawn to the space under the maze rather than paying attention to its surface. To minimize this problem I added a boundary set of zero valued cells around the maze perimeter. When charted this pulls the edge of the maze down to zero creating a set of virtual edges.
This approach provides a lot more detail. For example, looking at exactly the same maze as before-
Now we can see detail in the run from the bottom edge to the final center cells that didn't appear before. It's also much easier to follow the maze path through the maze.
Sidebar: At some point it would be interesting to dramatically increase the number of Excel cells that map to each cell in the physical maze. An initial idea would be to have a 6x6 or 8x8 array where the perimeter of each array is set to an arbitrary percentage of the physical maze cell value - say 85%. Constructing it would be time consuming, but it might be worth it.
Rotating the chart we can examine detail and see relationships that would be difficult to discover just looking at the raw data-
I mentioned before that the first maze was actually used in a US micromouse competition back in the 1980's. I like it because of its simplicity. But as technology has advanced, and mouse designers get more and more creative, the competition organiziers have been forced to build more complexity and challenge into the mazes. I suspect, though I have no way to know, that they actually get a real kick out of designing mazes with features that will trip up even the most advanced mouse.
Here's a more recent competition maze analyzed in the same fashion as before:
This is a maze worthy of the name. Any mouse that can successfully map and optimize this one is definitely worthy of a metal. It includes features (hazards) like-
- Totally closed cells - there is no path for the mouse to enter the cells shown in purple
- The optimum path meanders all over the maze before finally making it's way to the center.
- There are numerous dead-end paths, and most of them result in eating a lot of the mouse's time
- Quite a few diagonal paths - if a mouse can travel on a diagonal without bumping into the walls it can gain quite a bit of time
The beginning cells in the maze look like this-
Comparing this part of the maze with the path visualization it became apparent that there may be significant opportunities to implement some sort of paring algorithm. For example, even before the mouse starts it's exploration of the maze it already knows that the final cells will be in the exact center of the maze. Therefore, any contiguous wall patterns that connect to the center four cells are going to define territory and may eliminate the need for further searching in some sections of the maze. In this example, the highlighted walls in the chart below may provide very useful information to accelerate the search.