ABACABA pattern

Generating the pattern

In order to generate the next sequence, first take the previous pattern, add the next letter from the alphabet, and then repeat the previous pattern. The first few steps are listed here.

ABACABA is a "quickly growing word", often described as chiastic or "symmetrically organized around a central axis" (see: Chiastic structure and Χ). The number of members in each iteration is a(n) = 2ⁿ − 1, the Mersenne numbers ((sequence A000225 in the OEIS)). Replacing each letter with their respective numbers yields the ruler function.