These Are Mathematical Sets

The following images look like animals, but they are not drawings. These are actually connected subsets of the plane. I have defined these sets by some families of circles which are related to trigonometric functions. In addition to the images in this post, you can see some images made by drawing line segments: A Bird In Flight, Fish, Boat.

Ant

This image shows the union of all circles of the form

(x-A(t))2+(y-B(t))2=(R(t))2,

for 0 < t ≤ π, where

A(t)=(cos(7t))9(cos(21t))10(cos(70t))8,

B(t)=cos(2t)+(cos(80t))2(cos(10t)cos(t))10+(1/3)(sin(420t))4-(2/3)(sin(t)sin(5t))10,

R(t)=(1/150)+(1/30)(sin(840t))2+(1/3)(sin(7t))8.

Spider

This image shows the union of all circles of the form

(x-A(t))2+(y-B(t))2=(R(t))2,

for 0 < t ≤ π, where

A(t)=(cos(7t))9(cos(21t))10(cos(70t))8(1+(1/3)(sin(5t))2),

B(t)=(1/4)cos(2t)+(cos(210t))3(cos(7t)cos(21t))10cos((8/5)t+(π/5))-(1/2)(sin(t)sin(5t))10,

R(t)=(1/32)+(1/6)(sin(7t))4+(1/6)(sin(t))8(sin(5t)sin(15t))10-(1/40)(cos(1260t))6.

Millipede

This image shows the union of all circles of the form

(x-A(t))2+(y-B(t))2=(R(t))2,

for 0 < t ≤ π, where

A(t)=cos(2t)+(1/17)(sin(906t))2+(1/6)(cos(t)cos(6t)cos(18t))14(cos(81t))10,

B(t)=(1/10)(cos(3t))2+(1/18)(2+(sin(2t))2)(cos(151t))9,

R(t)=(1/300)+(4/185)(sin(151t))10(3+2(sin(2t))2).