Re: Le Sax Technical Fun Stuff...
Saxophone2001 is right. It will take patience and practice but humming in the back of the throat while you play is traditionally how it is done. When you hum you want to change the pitch around until you get the type of growl you're looking for. Eventually you will get to where you can remember pitches and won't have to search, so, in effect, you could play slews of licks all in a gravely growl.
All I have to say about improvising is start with the basic chord progressions that Saxophone 2001 metioned. Also, try to take the scales that fit those chords and manipulate them into different patterns. For example, instead of 1-3-5-b7 you could play b7-5-3-1 or even further with 1-5-3-b7, b7-3-5-1, and so on and so on. Just try to practice as many different patterns as you feel comfortable with and in addition to giving you material it will also increase your fluidity on the scales.
Also, with the basics in mind, you could jazz it up a little with different rhythms such as triplets, sixteenth notes, and so on. A good website that gives lessons on improv. is www.petethomas.co.uk This site accepts donations but I am ashamed at myself because I've never donated=( Donations are not required. This site has techniques also, it just takes a little patience to find everything.
Good luck in your future efforts and I hope your improv. skills improve.
Dark Eyes (unloved thesis)