The equation for a simple spiral in polar coordinates (r = radius, t = angle) is about as simple as you can get:

r = t

CRT screens operate on cartesian coordinates, of course. These are defined by:

x = r (cos t)

y = r (sin t)

so the equation of a spiral in cartesian is:

x = t (cos t)

y = t (sin t)

Looped,
Code:

for (t = 0; t < 6.28 * 5; t += 0.1}
{
x = t * cos(t);
y = t * sin(t);
putpixel(x,y);
}

Play around with that to get a more general spiral (with the desired number of rings, and so on.) The general spiral equation is:

r = A + Bt

where A and B are constants. Just plug this into the polar to cartesion formula and vary the upper limit of the loop to get any spiral you want.

Edit: The for loop increment should be less than one.