  Initiated by Mizutani and Ito's work in 1987, Kawamura and Allen recently
showed that certain self-similar sets generalized by two similar contractions
have a natural complex power series representation, which is parametrized by
past-dependent revolving sequences.
  In this paper, we generalize the work of Kawamura and Allen to include a
wider collection of self-similar sets. We show that certain self-similar sets
consisting of more than two similar contractions also have a natural complex
power series representation, which is parametrized by {\it $\Delta$-revolving
sequences}. This result applies to several other famous self-similar sets such
as the Heighway dragon, Twindragon, and Fudgeflake.
