One well-known symbol of the philosophy of duality known as yin and yang is the taijitu.



Task

   Create a function that, given a parameter representing size, generates such a symbol scaled to the requested size.
   Generate and display the symbol for two different (small) sizes.


<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" 
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns="http://www.w3.org/2000/svg" version="1.1"
    xmlns:xlink="http://www.w3.org/1999/xlink"
    width="600" height="600">
 
<!-- We create the symbol in the rectangle from (0, 0) to (1, 1)
and then translate it so it's centered on the origin. -->
<symbol id="yinyang">
  <g transform="translate(-0.5, -0.5)">
    <!-- A white circle, for the bulk of the left-hand part -->
    <circle cx="0.5" cy="0.5" r="0.5" fill="white"/>
    <!-- A black semicircle, for the bulk of the right-hand part -->
    <path d="M 0.5,0 A 0.5,0.5 0 0,1 0.5,1 z" fill="black"/>
    <!-- Circles to extend each part -->
    <circle cx="0.5" cy="0.25" r="0.25" fill="white"/>
    <circle cx="0.5" cy="0.75" r="0.25" fill="black"/>
    <!-- The spots -->
    <circle cx="0.5" cy="0.25" r="0.1" fill="black"/>
    <circle cx="0.5" cy="0.75" r="0.1" fill="white"/>
    <!-- An outline for the whole shape -->
    <circle cx="0.5" cy="0.5" r="0.5" fill="none"
      stroke="gray" stroke-width=".01"/>
  </g>
</symbol>
 
<use xlink:href="#yinyang"
  transform="translate(125, 125) scale(200, 200)"/>
 
<use xlink:href="#yinyang"
  transform="translate(375, 375) scale(400, 400)"/>
 
</svg>