How does the self cleaning water cleaner work

Water cleaner?
Water filter?
Water softener?
I have a softener with a pre-filter that I suppose you could call self cleaning, because the softener tank uses no electricity, no salts, and never needs any maintenance. The filter just gets changed once a year or less, but even a little old lady can do that.
The 'softener' part works by crystallizing minerals rather than doing mineral ion exchange. They still exist, but don't harden in pipes or on pots and shower heads. The leave a soft white film that wipes right off.
They are expensive but worth it! Mine was $1200, by Pelican.