That is a remarkable washing machine. There is no temperature adjustment or control of the spin speed so I guess this is an academic exercise. And what is "fuzzy" material ?
Anyway, assuming you are not able to make direct electrical connections to the machine, you'll have to use detectors as already mentioned to see what the current state is (maybe photo transistors or photoelectric cell etc.) and a set of solenoids to press the buttons to change the program.
To determine if it a led is blinking, the program has to identify a significant change in the light level and set a timer. If the next significant change in the light level is within a certain time period, then the program concludes the light is in a blinking state. You'll have to experiment to exclude the effects of ambient light.