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


2015-11-18-1447856495-9994392-Ant.jpg
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


2015-11-19-1447923118-6325761-Spider.jpg
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


2015-11-20-1448037505-566228-Millipede.jpg
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).