First off, let me mention that real ninja back in the day did not do much in the way of acrobatic stuff. The most you would see would be forms of pole vaulting with a spear and ukemi (rolls and break falls). With that out of the way, some schools of ninjutsu teach running up vertical or close to vertical objects, primarily in the form of trees, and sometimes in the form of walls (although with Japanese castles, there wasn't much wall to run up). Ninpo Taijutsu, led by Dr. Masaaki Hatsumi recommends starting with a 12 foot long board that is somewhat slender and propping it up at a 45degree angle, and practicing running up it in a single sprint. After you get good at that, you increase the angle to something like 60 degrees, then 75 degrees, then 85, and finally 90 degrees. At this point you can then practice actually running up trees and walls. It is about keeping a good flow of energy and trying to do it in one fluid motion so to say. Some recommend taking large steps in your approach (like in Parkour), but in most ninjutsu you would take a series of quick, short steps.
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