The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire $4\times4$ grid is covered by the star?
[asy]path x = (0,1)--(1,2)--(2,2)--(1,1)--cycle;
path y = reflect((0,0),(4,4)) * x;
path z = (1,0)--(2,1)--(3,0)--(3,1)--(2,2)--(1,1);
fill(x, gray(0.6));
fill(rotate(90, (2,2)) * x, gray(0.6));
fill(rotate(180, (2,2)) * x, gray(0.6));
fill(rotate(270, (2,2)) * x, gray(0.6));
fill(y, gray(0.8));
fill(rotate(90, (2,2)) * y, gray(0.8));
fill(rotate(180, (2,2)) * y, gray(0.8));
fill(rotate(270, (2,2)) * y, gray(0.8));
draw(z);
draw(rotate(90, (2,2)) * z);
draw(rotate(180, (2,2)) * z);
draw(rotate(270, (2,2)) * z);
add(grid(4,4));[/asy]