The dyadic transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation)
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.
The dyadic transformation provides an example of how a simple 1-dimensional map can give rise to chaos.
Read more about Dyadic Transformation: Relation To Tent Map and Logistic Map, Periodicity and Non-periodicity, Solvability, Rate of Information Loss and Sensitive Dependence On Initial Conditions