This paisley is constructed from a semicircle for the head and two simple spiral segments for the boundaries of the tail. It is defined by

θ_{1}

θ_{2}

r_{major}

and

r_{minor}

r_{major}

is the radius of the circle that the spine of the paisley is on.

r_{minor}

is the radius of the semicircle defining the head.

(r_{major}, θ_{1})

is the coordinate of the tail of the paisley.

(r_{major}, θ_{2})

is the coordinate of the center of the semicircle head of the paisley.

Unfortunately the junction between the semicircle and the spiral segments are sharp.

While there is certainly a circle for a given radius which can be tangent to both of those spirals, At this stage I am too lazy to do the math necessary to calculate it.