The disposition of the points of an imaginary circling measure,
on one of the two zerostepping conics,
is graphed versus transform step, below.

The yellow graphlines are obtained from a special case of transformation of a line into itself, namely, the “SRM”, the one having the invariant double points lying degenerately together, and at infinity. See the white points and lines. So the graphlines are constructed from first principles, and are exact—not measuredout, and inexact.

If you drag either of the directrices, D1 or D2, on the conic round the conic in either sense,
you will see the measure either expand or collapse, depending.
If it expands, you will observe that the measure at some stage overlaps itself.
In other words, as we have already seen, this measure cycles,
with a finite number of steps per cycle.
You will see that the overlay can, but need not be, “exact”,
meaning that the points of a given cycle can, but need not,
exactly fall on the corresponding points of previous or subsequent cycles.
If the overlay is exact, then the
whole measure, though repeating,
will appear to be stationary,
like a standing wave.
If the overlay is not exact, then points of a given cycle
must fall alongside corresponding points of the preceding (or of the subsequent) cycle,
and exactly this same shift of all the points
must occur per cycle, cumulatively—
so the entire measure
will show a phaseshift:
it will seem to precess,
like a travelling wave.
The graph of the disposition untangles this overlaying behaviour
by setting the repeating cycles out, side by side.
This measure cycles forever,
locally ^{*} only (i.e., without cycling through ∞)
on localised, circular or elliptical conics,
but, rather like tan θ,
both
locally and through ∞ on the straight line,
and the other, nonlocalised, noncircular, nonelliptical conics.
The Measure on one of the two singlestepping conics
is graphed below, versus transform step,
to display the wavelike, oscillatory character
of an imaginary cycling measure.
This graph of a measure and of a wave in motion is actually equivalent to the cycling of an inexact measure. Corresponding points of cycles would move along, and round in exactly the manner seen here. But you are required to imagine all the points of the measure That is to say, a shift of any one point It is indeed very like the propagation of a pulse The push clearly circulates, If the whole ring is to move, it cannot be perfecly elastic: it should have hysteresis, in which displacements are not fully recovered. 