  A limitation to molecular implementations of tile-based self-assembly systems
is the high rate of mismatch errors which has been observed to be between 1%
and 10%. Controlling the physical conditions of the system to reduce this
intrinsic error rate $\epsilon$ prohibitively slows the growth rate of the
system. This has motivated the development of techniques to redundantly encode
information in the tiles of a system in such a way that the rate of mismatch
errors in the final assembly is reduced even without a reduction in $\epsilon$.
Winfree and Bekbolatov, and Chen and Goel, introduced such error-resilient
systems that reduce the mismatch error rate to $\epsilon^k$ by replacing each
tile in an error-prone system with a $k \times k$ block of tiles in the
error-resilient system, but this increases the number of tile types used by a
factor of $k^2$, and the scale of the pattern produced by a factor of $k$.
Reif, Sahu and Yin, and Sahu and Reif, introduced compact error-resilient
systems for the self-assembly of Boolean arrays that reduce the mismatch error
rate to $\epsilon^2$ without increasing the scale of the pattern produced. In
this paper, we give a technique to design compact error-resilient systems for
the self-assembly of the recursively defined patterns introduced by Kautz and
Lathrop. We show that our compact error-resilient systems reduce the mismatch
error rate to $\epsilon^2$ by using the independent error model introduced by
Sahu and Reif. Surprisingly, our error-resilient systems use the same number of
tile types as the error-prone system from which they are constructed.
