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The chances of two people independently browsing to the same location will approach 0 as zoom depth increases.  The set of visited locations is very sparse.

With Newton-Raphson zooming, even the zoom path may be very sparse.

You need to decide what iteration data to store.  Better make it extensible.  It won't compress well. One of my renderers outputs 16 bytes per pixel, and even that is a small subset of possible data for colouring.  That makes a HD image 32MB big.  Better make the clients be able to request different "planes" of iteration data separately to avoid useless data transfers.

Personally, I thought about this stuff quite a lot in the past. Now I think it's not worth it really.

It'd probably be nice however to write just a mapping site where users can add links to images and/or videos (hosted on Deviant Art or Youtube or wherever) by location, perhaps with facility to upload parameter files (either marked public under a CC license, or private with only the location information being used - not any colouring etc).  As with any site with "user generated content", there may need to be protections against automated spamming and potentially human moderation for inappropriate content being added.