I'm too lazy to look it up on the datasheet right now to confirm, but I believe the ATTiny85 has only two hardware PWM pins. You can have as many software PWM pins as you like, though. An ATTiny85 should have no problem running two hardware + one software PWM pins.
Can it handle a software PWM while computing the change in output value from one color to next smoothly? My color changing idea was along this line:
randomize new red, green. and blue value
calculate difference between current value and new value to determine increment rate
increment current R, G, B PWM value once per second
when the current R, G, and B value reaches the target value, repeat for new value.
Obviously with 3 hardware PWM, I could use wait 1 second before changing value. But with software PWM, I can't do that since I'd need to continuously toggle the pin on and off at millisecond interval to simulate PWM.
What about Digispark?? https://www.kickstarter.com/projects/digistump/digispark-the-tiny-arduino-enabled-usb-dev-board suggests 3 hardware PWM and it has built in USB support. If the PWM pin isn't shared with those used for USB, I could tap into the laptop's web cam (which uses USB) and connect to that, allowing me to change (ie static color only or cycle between specific color for event or something) without having to open my laptop. I never used the built in web cam anyway (don't like the idea hacker could see me without my knowing so I unplugged it when I first got the laptop)