#JavaScript (E6) + Html 173 176 193

Edit: big cut, thanks to William Barbosa

Edit: 3 bytes less, thanks to DocMax

173 bytes counting the function and the canvas element needed to show the output.

Test save as html file and open in FireFox.

JSFiddle

<canvas id=C>
<script>
F=(n,x,y,r,p)=>{
  for(t=C.getContext("2d"),C.width=C.height=600;n--;x-=(x-p[i])*r,y-=(y-p[i+1])*r)
    i=Math.random(t.fillRect(x,y,1,1))*p.length&~1      
}
F(100000, 300, 300, 0.66, [100,500, 500,100, 500,500, 100,100, 300,150, 150,300, 300,450, 450,300]) // Function call, not counted
</script>

JavaScript (E6) + Html 173 176 193

Edit: big cut, thanks to William Barbosa

Edit: 3 bytes less, thanks to DocMax

173 bytes counting the function and the canvas element needed to show the output.

Test save as html file and open in FireFox.

JSFiddle

<canvas id=C>
<script>
F=(n,x,y,r,p)=>{
  for(t=C.getContext("2d"),C.width=C.height=600;n--;x-=(x-p[i])*r,y-=(y-p[i+1])*r)
    i=Math.random(t.fillRect(x,y,1,1))*p.length&~1      
}
F(100000, 300, 300, 0.66, [100,500, 500,100, 500,500, 100,100, 300,150, 150,300, 300,450, 450,300]) // Function call, not counted
</script>

#JavaScript (E6) + Html 173 176 193

Edit: big cut, thanks to William Barbosa

Edit: 3 bytes less, thanks to DocMax

176 bytes counting the function and the canvas element needed to show the output.

Test save as html file and open in FireFox.

JSFiddle

<canvas id=C>
<script>
F=(n,x,y,r,p)=>{
  for(t=C.getContext("2d"),C.width=C.height=600;n--;x-=(x-p[i])*r,y-=(y-p[i+1])*r)
    i=Math.random(t.fillRect(x,y,1,1))*p.length&~1      
}
F(100000, 300, 300, 0.5, [100,450, 500,450, 100,100]) // Function call, not counted
</script>

#JavaScript (E6) + Html 173 176 193

Edit: big cut, thanks to William Barbosa

Edit: 3 bytes less, thanks to DocMax

173 bytes counting the function and the canvas element needed to show the output.

Test save as html file and open in FireFox.

JSFiddle

<canvas id=C>
<script>
F=(n,x,y,r,p)=>{
  for(t=C.getContext("2d"),C.width=C.height=600;n--;x-=(x-p[i])*r,y-=(y-p[i+1])*r)
    i=Math.random(t.fillRect(x,y,1,1))*p.length&~1      
}
F(100000, 300, 300, 0.66, [100,500, 500,100, 500,500, 100,100, 300,150, 150,300, 300,450, 450,300]) // Function call, not counted
</script>

#JavaScript (E6) + Html 176 193

Edit: big cut, thanks to William Barbosa

176 bytes counting the function and the canvas element needed to show the output.

Test save as html file and open in FireFox.

JSFiddle

<canvas id=C>
<script>
F=(n,x,y,r,p)=>{
  t=C.getContext("2d"),C.width=C.height=600;
  for(;n--;)
  t.fillRect(x,y,1,1),
  i=Math.random()*p.length&~1,
  x-=(x-p[i])*r,y-=(y-p[i+1])*r
}
F(100000, 300, 300, 0.5, [100,450, 500,450, 100,100]) // Function call, not counted
</script>

#JavaScript (E6) + Html 173 176 193

Edit: big cut, thanks to William Barbosa

Edit: 3 bytes less, thanks to DocMax

176 bytes counting the function and the canvas element needed to show the output.

Test save as html file and open in FireFox.

JSFiddle

<canvas id=C>
<script>
F=(n,x,y,r,p)=>{
  for(t=C.getContext("2d"),C.width=C.height=600;n--;x-=(x-p[i])*r,y-=(y-p[i+1])*r)
    i=Math.random(t.fillRect(x,y,1,1))*p.length&~1      
}
F(100000, 300, 300, 0.5, [100,450, 500,450, 100,100]) // Function call, not counted
</script>