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Published online by Cambridge University Press: 09 September 2016
Let $\{f_{n}\}_{n\geq 1}$ be an infinite iterated function system on $[0,1]$ and let $\unicode[STIX]{x1D6EC}$ be its attractor. Then, for any $x\in \unicode[STIX]{x1D6EC}$, it corresponds to a sequence of integers $\{a_{n}(x)\}_{n\geq 1}$, called the digit sequence of $x$, in the sense that
This work was supported by the Fundamental Research Funds for the Central University (Grant No. 2662015QC001) and NSFC (Grant Nos. 11426111 and 11501168).