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A '''recurrence''' is a time the trajectory returns to a ___location it has visited before. The recurrence plot depicts the collection of pairs of times at which the trajectory is at the same place, i.e. the set of <math>(i,j)</math> with <math>\vec{x}(i) = \vec{x}(j)</math>. This can show many things: for instance, if the trajectory is strictly periodic with period <math>T</math>, then all such pairs of times will be separated by a multiple of <math>T</math> and visible as diagonal lines. To make the plot, continuous time and continuous phase space are discretized, taking e.g. <math>\vec{x}(i)</math> as the ___location of the trajectory at time <math>i \tau</math> and counting as a recurrence any time the trajectory gets sufficiently close (say, within ε) to a point it has been previously. Concretely then, recurrence/non-recurrence can be recorded by the binary function
:<math>R(i,j) = \begin{cases} 1
and the recurrence plot puts a (black) point at coordinates <math>(i,j)</math> if <math>R(i,j)=1</math>.
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