I am still trying to understand this issue, apologies for my lack of comprehension.

So just to clarify, there is nothing wrong in changing your body in the shape of getting a tattoo?

A follow up question about damage and purposeful loss of function – what about matam. There are a lot of practices around the world where people injure themselves, bleed, use chains etc. So is that type of matam declared haram by the marja’s?

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Yes, it is not prohibited to get a tattoo per se.
The rulings of the jurist vary when it comes to matam, some say it is allowed and some say no. Sayyid Sistani has not ruled on it. You should follow your marj’a.

I imagine if matam were to cause severe harm, that was irreparable, then it might become haram