The Atzema spiral, also known as the Pritch-Atzema spiral, is the curve whose catacaustic for a radiant point at the origin is a circle, as illustrated above.

It has parametric equations

where , which generates a circle of radius .

The sequence of rays generating the circle catacaustic as is varied from to is shown above.

More things to try:

Weisstein, Eric W. "Atzema Spiral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AtzemaSpiral.html