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:<math>\qquad x_{n+1} = r x_n (1-x_n) </math>
In this case, the value of {{math|''x''}} is chaotic when {{math|''r''}} >~ 3.57... and rapidly switches between different patterns in the value of {{math|''x''}} as one iterates the value of {{math|''n''}}. A simple threshold controller can control or direct the chaotic map or system to produce one of many patterns. The controller basically sets a threshold on the map such that if the iteration ("chaotic update") of the map takes on a value of {{math|''x''}} that lies above a given threshold value, {{math|''x''}}*,then the output corresponds to a 1, otherwise it corresponds to a 0. One can then reverse engineer the chaotic map to establish a lookup table of thresholds that robustly produce any of the logic gate operations <ref>Sudeshna Sinha and William L. Ditto, "Dynamics Based Computation", Physical Review Letters, vol. 81 (1998) pp. 2156-2159</ref><ref>Sudeshna Sinha and William L. Ditto, "Computing with Distributed Chaos", Physical Review E, vol. 60 (1999) pp. 363-377. </ref> <ref>Toshinori Munakata, Sudeshna Sinha and William L. Ditto, "Chaos Computing: Implementation of Fundamental Logical and Arithmetic Operations and Memory by Chaotic Elements", IEEE Transactions on Circuits and Systems, vol. 49 (2002) pp. 1629-1633. <\ref>. Since the system is chaotic, we can then switch between various gates ("patterns") exponentially fast.
== ChaoGate ==
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