## These Are Mathematical Sets

The following images look like animals, but they are not drawings. These are actually

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))^{10}cos((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}).

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