Writing quality content daily and never giving up. 4,000 a day is not much when you think about it. I know some websites get 10x that amount.
which statistics service are you using. Does that service has restrictions on how many visits per day it will record?
New content every day (if possible), new pictures, auto submission to Twitter, Facebook, Technorati and on any possible site. Social bookmarking, directories, blog directories, feed submission....
Mine also got visits around that line but it's depending on the recent trends in my niche. In some time, I got over 200 visits from search engines.