An octonacci (Pell) chain is a quasiperiodic sequence obtained by applying the two-letter substitution rule , recursively to the initial word ; in the limit this gives a semi-infinite aperiodic sequence . The term octonacci comes from the similarity to the Fibonacci substitution rule , , for which the resulting self-similar semi-infinite aperiodic sequence is . For an infinitely long Fibonacci chain, the limit of the ratio of the frequencies of the two letters and is the golden ratio ; for the octonacci chain, the limit of the ratio is the silver ratio ().

In this Demonstration, the two letters and in the octonacci (Fibonacci) word sequence are graphically represented by a long and short spacing on the grid axes ( and ). The "nesting index " control lets you generate octonacci (Fibonacci) word sequences of different lengths, and you can see product grids of different complexity with the "add grid product lines" checkbox control (only for octonacci enabled, since for Fibonacci the superposition is complete). By changing the "long to short ratio " slider you can also investigate the transition between periodic and quasiperiodic order .