N-Grams by Base

Each row of the diagrams above show the patterns that occur in the same number base, indicated by the number in the left-most diagram. This organization points out many regularities in the patterns. For instance, division by a number one less than the base yields single-digit repeating patterns (e.g., in base ten, 1/9 = 0.111…, 5/9 = 0.555…). There is also a strong regularity in the patterns on either side of the vertical center line for the odd-numbered bases. Looking more closely, the patterns equidistant from this center line nest with each other. To see this more clearly, see the diagram for Paired N-Grams.