Around −1

The gold curve is the loop's answer to sine waves, for ω from 0 to infinity: a point's distance from the centre is how much the answer is magnified, and the angle it has turned from due right is how far the answer lags, a full turn being one cycle; the faint curve is its mirror image. With no delay, drag K up: the whole curve grows and −1 stays put. Below K = 8 neither the curve nor its mirror goes round −1; past 8 they wind round it twice, and the response with feedback, top right, swings ever wider. Without feedback the loop is stable, so the count of turns is all it takes. Now set K back to 2 and drag the delay τ: the gain at every frequency stays the same, and the curve only turns further and further, twisting into a spiral. Where it crosses the ice-blue circle the gain is exactly 1, and the coral arc from there round to −1 is the margin; the bottom-right corner measures it on the curve and works it out again from a formula. The longer the delay, the less margin, and the longer the swings take to die away; at a delay of about 1.54 the margin is used up and they never stop, and beyond that they grow. With K at 1 or below the curve never leaves the circle, and no delay can upset the loop.