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The dyadic transformation is the mapping
∞ {\displaystyle ^{\infty }} is the set of sequences from {\displaystyle } ] produced by the rule
Equivalently, the dyadic transformation can also be defined as the iterated function map of the piecewise linear function
The name bit shift map arises because, if the value of an iterate is written in binary notation, the next iterate is obtained by shifting the binary point one bit to the right, and if the bit to the left of the new binary point is a "one", replacing it with a zero.
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