We take the regular grid and color it like a chessboard into white and black. Black sites get a rotor that alternates between East and West. White sites get a rotor that alternates between North and South.
The color scheme is as follows:
Unfilled = White
Next Goes Down = Blue
Next Goes Up = Green
Next Goes Left = Red
Next Goes Right = Black
So half the sites alternate between red and black, starting with red, while the other half alternate between blue and green, starting with blue. Note that there is no colormap that results in really bold colors, because every region is a blend of two colors, so bold colors like red are unattainable. You may enjoy downloading the file and looking at it with your favorite image viewer, which will let you zoom in so you can see the individual pixels quite clearly.
This picture took about 8 hours to make on an old 550MHz G4. Being formed from one million particles, it contains one million non-white pixels. Since I knew the circle would be so circular, I was able to pick an efficient size for the array, leaving just a one pixel wide empty margin on each side.
The "bmp" image file is over 700k, so it may take a while to download depending on your connection.
Next we have a black and white picture obtained by considering just one color of the checkerboard, and turning your head 45 degrees so that the resulting grid matches the screen pixel grid. The goal here is to create a two-color image, so unfortunately one of the rotor directions is the same color as the "not yet filled" color (white). We choose the color so that the first particle to arrive (which simply gets absorbed, rather than routed) also flips this color (in other words, sites which have absorbed but not yet routed are shown in black).
And here is the other half of the checkerboard. As can be seen in the color picture above (which is what these black and white images derive from), the two patterns are far from independent. Each of these black and white pictures is a 90k "bmp" file.
For a comparison of these with the traditional rotor router picture, see here.