I typed out a big reply and my browser puked. I'll try again.
The only time calories are counted using Atkins if a person (such as I) turns out to be metabolically resistant and has to go on a special 1,000 calories a day "Fat Fast" for a few days to restart the fat-burning process, after which the dieter returns to regular Atkins. If using Atkins properly doesn't result in weight loss, he says you should look at quantities of food consumed (calories).
If Atkins defines and recommends anything concerning simple v. complex carbs, I missed it, and can't give an educated reply. He lists major foods by food groups in the back of his book and on his web site, showing the total carbs in each, and this information is what one uses to put together a balanced food selection each day. That's what I use to know how many carbs a day I can eat. (For me, that is < 20 a day.)
Snack foods like potato chips and oreos are definitely out. For life.
His web site,
http://www.atkinscenter.com, has loads of details on all this.
Atkins is also being attacked by leftist groups because it has developed into a very successful corporation.
The idea of a growing corporation influencing consumers against vegetarianism drives these people nuts.