These Are Mathematical Sets

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

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))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).

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