Construct this pattern

> restart:

> x:=cos(t);

> y:=sin(t);

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

> t:=n*Pi/20;

> w:=evalf(m):

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

maple