Square wave on attiny

I need some help here. I am a noob when it comes to programming, the craziest stuff I have made just consists of flashing leds or RGB leds flowing through their colors.

So my project: I have some led strips that I am going to power with an N channel mosfet. I would like there to be two switches - a momentary switch to turn the leds on and another momentary switch that would change the duty cycle of a square wave to adjust brightness. For example turning on the circuit the leds would be lit at 25% brightness, pressing the button bumps up the brightness to 50% then 75% then 100% (or as close to 100% as possible) and then back down to 25 percent. Also I could care less about the frequency of the wave as long as there is no flickering to be seen by the human eye.

Is this even possible with an Attiny45 or 85? Is there a better micro controller or timer i should use? I would like the circuit to be as small as possible.

Also link me to any write-ups I should read to learn more about this!

Thanks everyone!

Yes this is possible using the tiny85 as the Arduino core supports up to 3 analogue outputs.

Riva:
Yes this is possible using the tiny85 as the Arduino core supports up to 3 analogue outputs.

Thanks a lot for the answer, it's good to know I can complete my project with everything I need sitting here in front of me. Now! - On to a lot of research