Here is how I created the background to the Marvin the Martian nails. I largely followed CutePolish from YouTube's tutorial here.
Lightly sponge on some white in random shapes & directions. Sinful Colors Snow Me White
Sponge some yellow to the centers. Barielle Lemondrops.
Sponge on some pink around the edges. China Glaze Dance Baby mixed with a little bit of Orly Terra Mauve.
Sponge some dark blue polish around the edges to fade it into the black. Barielle Berry Blue.
Add some tiny white dots of polish either with a toothpick or paintbrush.
Add a coat of tiny glitter polish. China Glaze Fairy Dust. Seal with topcoat!