CAD tip # 13960:

The Cartesian definition of the drawing function is in this case:

X = +a √φ cos(φ)
Y = +a √φ sin(φ)

X = -a √φ cos(φ)
Y = -a √φ sin(φ)

So in the LISP notation for 2DPlot:

(defun fXYfermat (f)
 (list
  (* fCa (sqrt f)(cos f))
  (* fCa (sqrt f)(sin f))
 )
)

In the 2DPlot app, this curve has the internal preset of 13.

After capping both ends of the spiral branches and hatching the areas you can (by looking in the hatch properties) verify one of the properties of Fermat's spirals - divides the plane into two connected regions with the same area. Or that the area between any two consecutive full turns around the spiral is invariant.