The default answer most people would give is purples, since those shades do tend to work really well with greens.
The colors in the purple side that I have been loving lately are Grifter from my ammo pallet, Last Call (a little more on the pink side sometimes I use it paired with Grifter. It works much better than you'd think), AC/DC and then Bordello (yes I know that is a soft pink) from the feminine pallet. I have used these shades in different combinations with stunning results each time. So far my favorite purple liner is Desperation though I am also very fond of Psychedelic Sister for the brightness and Ether for the softer grey with purple glitter. If you love shimmer and glitter and shine as much as I do take a look at Intergalactic from the new Moondust shadows. I have that as well and love it. It's a very versatile shadow that I use both alone wet and dry and then dry as a wash over my shadow look of the day to add some eye popping color and of course glitter!
Don't let the "purple for green eyes" get you stuck on just those shades though. Today for example I wore a base of Shattered with a touch of Sin on the outer corners to warm it slightly, Polyester Bride in the inner corner and tear duct and very carefully and lightly applied Oil slick to my crease to darken and define it a little, blended the crease out with a little W.O.S from the naked basics and highlighted the brow with Venus from the same pallet. I used Gunmetal (used dry) as a liner just along my upper lash line for a little definition and finally the 24-7 liner in Cuff alone the bottom waterline. It looked absolutely phenomenal.
This has already turned into a longer answer than I intended. I'll cut it short and list the other shades I've used that have been amazing.
Hijack (deep teal), Deep End (a brighter teal), Lost (deep brown toned bronze), Chopper (lighter reddish bronze), Smog ( a medium bronze) Maui Wowie (Gold) and anything in the Naked Basics.
Another very much loved investment was another of the Moondust shadows Space Cowboy. It adds some gorgeous shimmer when used as a wash without significantly altering the colors of your shadows and looks amazing when used wet for added drama and a cat eye liner. I've only done black so far but I suspect it'd look great with demolition or even one of the brighter liners. Intergalactic also looks amazing wet with a black cat eye.
I hope this gives you some ideas and some different shades to experiment with!
2 years, 11 months ago