sqrt(7) (Blue) and sqrt(11) (red).

Do they start at the same point, heading in the same direction?

same point (0,0) and same rotational direction, yes. Only the angle is different.

you may be able to spot a small black circle in the top right area where red and black spirals are close to each other. That's approx. where the start is. It's the origin but the first line segment doesn't get plotted, so it appears to be in the wrong place...

red and blue spirals...