Board Thread:Theories and Speculation/@comment-35448581-20160502192848/@comment-734582-20160506174421

Ravenlot 27 wrote: However, there's still the question why Hamura's Byakugan remained unchanged among all his descendants, while Hagoromo's Rinnegan was split into 2 different powers and continued to change it's form between his descendants. Because the Sharingan's power resides in the brain (see Tobirama's explanation of the Sharingan) and so it becomes personalized.

Furthermore, the Rinnegan's paths are very much physical powers (and hinted at as such since Hagoromo has Six Paths Yang power), and in a sense the Rinnegan is merely an indicator Six Paths power is present (In addition to it's actual Dojutsu powers, like easily decoding any jutsu).

As to Otsutsuki, i think it's indeed the case: the Byakugan is a physical eye (it's different even in basic form) and the Sharingan is a manifestation of the mind's eye (indistinguishable when retracted). The Rinne Sharingan being a Third eye or "mind's eye" definitely suggest this.

This is probably why it's different. Also, note that the Rinnegan is a physical eye whereas the Tenseigan is awoken and fades like a Sharingan.

My guess is that Sharingan + Six Paths Yin power = Rinne Sharingan. Sharingan + Six Paths Yang power (e.g. Hagoromo) = Rinnegan. Six Paths Yin power + Byakugan= Tenseigan. Six Paths Yang Power + byakugan = unknown. Kaguya has no Tenseigan because her Six Paths Yin power manifests in her Sharingan and her Yang probably in her body (e.g. total control over her body, like her hair).

I believe that Hamura's power was split differently (Dojutsu + body power) unlike Hagoromo's kids (One body, the other Dojutsu)