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Say one has two variables that change with time in a cyclical manner but instead of plotting time on the x-axis, one plots them directly —without applying a transform or any kind of manipulation. I know it is absolutely not brain surgery, but I once encountered a name for this and I cannot recall what it is. What is it called?

Matlab had an animated plot called a comet plot, but it wasn't that. It wasn't an arrow plot either (also that would be a quiver plot in my mind).

plot

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    $\begingroup$ Perhaps phase space? $\endgroup$
    – Sycorax ♦
    Commented May 29, 2022 at 15:00
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    $\begingroup$ I really like phase space plot, it is more informative than some person's name —which to be perfectly honest I dislike when trivial concepts bare someone's name. And given that no name has been suggested, I suspect I may have seen a special particular case. So @Sycorax would you mind copypasting your comment as is as an answer so I can accept it? Ta! $\endgroup$
    – Matteo Ferla
    Commented May 30, 2022 at 9:03

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A phase space is a space where all possible states of a time-varying system are represented. This matches your plot because all possible configurations of those 2 variables are represented on the plane of the graph.

The concept of "time" is only represented implicitly as the path between the observed data. This is clearer if we animate the plot so that the earliest data are plotted first, and then we add data sequentially during the animation.

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  • $\begingroup$ Although this might be a name for the space defined by the coordinates, it does not describe the plot, which leaves one thinking there must either be a better answer or no answer. $\endgroup$
    – whuber ♦
    Commented May 30, 2022 at 19:47
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    $\begingroup$ @whuber - apparently a "phase space plot" or "phase space trajectory plot" is a thing... stackoverflow.com/questions/30020351/matlab-phase-space-plot for example. $\endgroup$
    – jbowman
    Commented May 31, 2022 at 15:33
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    $\begingroup$ Connected scatterplot is a name I have seen used. Kind of related when people do traces in animated scatterplots ala Han's Rosling. $\endgroup$
    – Andy W
    Commented May 31, 2022 at 15:43
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    $\begingroup$ Also: mentions of phase plane, state space. trajectory, hysteresis, but clearly some of these terms are more general than others. There are examples with various more or less infamous curves in economics, e..g the Phillips curve. $\endgroup$
    – Nick Cox
    Commented May 31, 2022 at 15:57

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