construct this pattern:

> restart;

> x:=cos(t);

> y:=sin(t);

> m:=[x+t*sin(s),y+t*cos(s),s=-Pi..Pi];

> t:=k*Pi/50;

> w:=evalf(m);

> plot([w$k=1..100],color=blue,scaling=constrained,axes=none);

>