Reading Orders

Each eye has one of 5 possible positions: center, up, right, down, left. From reverse engineering the code, this is the order that they are stored in, clockwise starting at the center. If you denote each position as a base-5 value 0, 1, 2, 3, or 4, you can read each trigram as a single base-5 number, but there are many possible ways to do this, depending on the order that you read the eyes. The alternating nature of the triangles also complicates things a bit.

However, one particular choice of reading order can be distinguished by the fact that it has 83 unique values, covering the range of 0-82 with no gaps and fairly even distribution, and both even and odd position trigrams (both directions of triangles) cover the same range of 83 values. This order is also fairly natural, reading the eyes within the triangle in a clockwise order starting at the top-left (or from the bottom-right for the upside-down triangles).

Other reading orders can show different ranges of values depending on the direction of the triangle, or cover non-contiguous ranges, but the fact that there are only 83 unique trigrams is an invariant, and every reading order is technically a substitution of every other, on the set of even and odd position trigrams. In any case, if you want to assign a label/index to each unique trigram, the 0-82 range seems ideal for this. We have not found any evidence either way yet that the particular values matter, they might as well just be labels, so you might as well use the reading order which gives them indexed values. But the 0-82 unbroken range would be highly unlikely to happen by chance, so it's generally assumed to be correct.