A Butterfly (Just Using Graphs)

Hi today I have made a butterfly just using graphs First have a look at that then I will explain to you step by step

First you need something which will give you the out put of the graph.

Here I'm using GeoGebra

Wings are made up of  symmetrical functions

These are:

1.y=x^7 and y=x^(1/7)

2.y=-x^7 and y=-x^(1/7)

domain: -1<x<1

Head is made up of a circle centered at (0,1)

and radius is 1/8

Actually instead of x^2+(y-1)^2=1/8 I put x^2+(y-1)^2≤ 1/8

it indicates the area under the circle.

Similarly, the body of the butterfly is made up of ellipse 

x^2+(y^2)/8≤1/16

Finally the strips on the wing is of x=y and x=-y which {domain: -1<x<-0.25,0.25<x<1}