JUDDD is a technique of calorie cycling. You can implement it on almost any plan. Basically you have one very low calorie day (almost a fast) followed by a day of big (but measured) eating. The calories can average out to whatever you choose.
For example if you are on a plan that calls for 1500 calories a day, you might eat 500 calories on a down day and then have 2500 on an up day. It allows you to keep your caloric average low and keeps your body from adjusting to your diet by constantly changing the caloric intake from one day to the next. You never go into starvation mode and you lose weight faster. That's the theory, at least.
You can plan for office parties or dinner with friends because the up day calories are pretty high. You just plan to have a down day afterward. The cycle is every other day, but sometimes you can shift your days around to accommodate your social/Holiday calendar.
There are other details such as resveratrol and carnitine supplementation, exact ratios of up-day to down-day calories (induction is 5:1). And that's JUDDD.
My plan calls for a lot less calories, so my down days are about 350 calories (prety much a fast) and my up days are about 1650 for an average of 1000 calories a day.
On Atkins (low-carb) induction you are limited in veggies and fruits because they are high in carbs. You are supposed to eat vegetables but you have to carefully measure them to make sure you stay within your carb limit. Once you are established and steadily losing 2 - 2.5 pounds a week you start to add non-starchy (mostly leafy & cruciferous) vegetables back in more and more until you find your tipping point (where you stall). Certain high carb veggies (tomatoes, carrots, winter squash) are quite limited until you reach your goal. Most fruit is allowed in limited quantities only in maintenance.