Dear Friends, 

there is a particular breath work for cultivating endurance amongst the training manuals of Ninjas and proponents of the syncretic mountain asceticism, known as shugendō, which is called the "mountaineer's breath" (登山家の呼吸, tozan-ka no kokyū). It has an interesting paradiddle-like ratio of inhalation/exhalation that supposedly can extend one's ability to stealthily run across mountains at night, as long as the individual breathed in this complicated way while running... I've recently tried it...I guess, I need more practice.
Some stories say that a high-level ninjutsu-sha could run up to 200kms in a day! These extend into the stories of the "marathon monks" that, as part of their spiritual duty would run a marathon, everyday for days on end. Life without Netflix is unbounded with potential, it seems.

Anyways, the rhythmic pattern for this breath, is: 
1 round = 1-inhalation, 2-exhalations, 1-inhalation, 1-exhalation, 2-inhalations, 1-exhalation

I'm wondering if this is similar to any haṭha yogic prāṇāyāma? 

I'm not implying any causal link, necessarily. I leave that to others, who, in common parlance across various social media make consonant claims. Interestingly, a re-orientalized and imagined mythical Ninja culture is framed as being able to help reduce stress and tension, make people fitter, run for the train... and generally more able to endure more of life's problems, and, also have a transformative potential related to the twins of transglobal yoga's popularity: 1) accumulate power(s) and 2) achieve moral reformation. 

All the best,

パトリック　マッカートニー
Patrick McCartney, PhD
Research Affiliate - Organization for Identity and Cultural Development (OICD), Kyoto
Research Associate - Nanzan University Anthropological Institute, Nagoya, Japan
Visiting Fellow - South and South-east Asian Studies Department, Australian National University
Member - South Asia Research Institute (SARI), Australian National University

Skype / Zoom - psdmccartney
Phone + Whatsapp + Line:  +61410644259
Twitter - @psdmccartney @yogascapesinjap

bodhapūrvam calema ;-)