Magic is primarily about problem solving. A magician or their team has two goals to accomplish: first, they want to make improbable events happen; and second, they want to make those improbable events perceived as totally impossible. And they want to achieve the two goals simultaneously. This is when computational thinking kicks in and plays a role in helping them to organize and visualize a routine.
When a young magician practices in front of a computer by watching a video clip, they usually start with picturing the routine and proceed with manipulating props, such as cards and coins. In other words, they're utilizing their mental tools and physical tools. What they might have skipped is going through a graphic tool, something like a note sheet or, with someone else's assistance, a worksheet.
So I started with a traditional flow chart, split it into left and right halves, and applied some pattern recognition tools into it to arrive at the system below. Check out Darwin Ortiz's book on theorizing magic, Designing Miracles, for the ideas of outer reality and inner reality as well as other interesting concepts which have been integrated into my system; and you can probably add more useful concepts to my chart. This flow chart helps us to grasp the structure and logical flow of the routine and to compare the point of view of the audience and that of the magician. It allows us to picture the relationship among time flow, realities and pairs, sequences or groups of moves.
Now check out my sample notes: