i am guessing you are not aware that "Atkins Diet" typically means "high protein/low carb" - and no, you can't do it as a vegetarian no matter what babble is about to follow this post. besides, you need a lot of fat for ketogenic diets to work well.
although this is a special type of ketoginic diets where he is cycling carbs into his diet, one day a week - for body building/fat loss purpose. its good info in that it explains how ketogenic diets work and after reading it, you should be able to understand why without fat/meat, you are not going to put your body into ketosis (fat burning state)
http://low-carb.org/lylemcd/cyclic1.htm