Uno can do that.
Need 11 current limit resistors.
LEDs & resistors herehttp://www.dipmicro.com/store/index.php?act=viewCat&catId=511
Pick resistor based on (5V - Vforward of LED)/.02 = resistance needed.
Browse Learning Section, or the Playground, for ShiftPWM, will let you fade up/down LED on any pin, and not just the 6 pins with hardware PWM.
9V battery only has 200-300mAH of power. Use 5AAs (7.5) into the barrel jack instead, for 2000-2500mAH of power. Add a 6th if you want, will just into heating up the 5V regulator tho.
11 LEDs drawing 20mA = ~220maH by themselves when all are on.
Thanks for the great info. Am I correct in assuming that your calculation is based on dividing the voltage I need to dissipate by the max current draw of the LED, corrected for units of scale? Is there a good explanation of reverse voltage somewhere that someone can point me to? Also what would happen if an LED had a working voltage of say 3.5v at 40 mA? The I/O pin on the board cannot output more than 40 and due to the losses associated with switching electronics I'd assume it would actually be a tiny bit less than 40 mA.
I accomplished exactly what I wanted to do without needing PWM at all. I've spent an abnormal amount of time working this project and relearning C after 15 years of booze erased all the time I spent in computer science in high school.