The ATR-ADX stop is effectively a double adaptive stop that trails the price, by both adapting to the true range of the price, and the average directional change. When the stop is below the price (long trade) the value never decreases until the price intersects the stop, and it reverses to being above the price (short trade). When the stop is above the price it will never increase until it is intersected by the price. As the true range and change, the stop will move more quickly or more slowly.
Depicted are two instances of the Adaptive ATR Trend Indicator on the chart. One uses a constant 4.0 ATR multiplier (21-TR lookback for both) and the other switches between 4.0 ( Rising) and 1.5 ( Falling). This is to highlight the difference between using a constant ATR multiplier vs. using one that is adjusts based on the "trendiness" of the .