To pick a more useful example, the number 406 looks like this. So our example of 27 from earlier looks like this. The increasing number positions are arranged in a spiral.

The next difference is that Villein numbers aren't written out in columns like ours. For our example of 27 above, it can be read as 3 connections * 4^0 + 2 connections * 4^1 + 1 connection * 4^2. The same logic applies to larger numbers. Technically, this means the lines between dots could go in any direction, but the Villein standard uses specific connections. Just count the number of connections to the central dot and multiply like in the image below. While it looks confusing, the Villein system is actually quite simple. Villeins frustratingly don't use Arabic numerals like we do. This gets more complicated when there are multiple digits - any number greater than three - but the math stays the same. Therefore, you can write the number three as 3 x 4^0. In base 4, you just replace the exponents of 10 with exponents of four. Multiple digits use the same math and then get added together. This is called positional notation.īroken down this way, you can write the number 3 as 3 x 10^0. (Any number to the zeroth power is one.) The next digit to the left is 10 to the first power, followed by 10 to the second power, etc. This means that every digit, reading from right to left, represents a count of exponentially increasing factors of 10 starting on the right with 10^0.

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