The following chemicals are used as flocculants:[Wikipedia: Flocculation
http://en.wikipedia.org/wiki/Flocculation ]. I know about the chemicals, I don't know about the "natural" products listed.
alum
aluminium chlorohydrate
aluminium sulfate
calcium oxide
calcium hydroxide
iron(III) chloride
iron(II) sulfate
polyacrylamide
polyDADMAC
sodium aluminate
sodium silicate
The following natural products are used as flocculants:[
http://en.wikipedia.org/wiki/Flocculation]
Chitosan
Moringa oleifera seeds
Papain
A species of Strychnos (seeds)
Isinglass
In any case, a filter follows flocculation. Swimming pools need periodic treatment with a flocculant, and the filters need to be cleaned frequently after being treated with these.
I've done water systems in third world countries, and generally skip flocculation because it generally doesn't make people sick, it is usually just an appearance thing. Chlorination after filtering takes care of any bio-actives.
Sorry, too much chemical information again.