There is a Photoshop hoax roaming the webs and the folks over at Snopes have debunked it thoroughly. The story states that fifteen purple ladybugs were found on a hawaiian beach. Although the story comes from a known hoax/satire site, many people don't understand that.
YES! They Do Exist!! These are purple ladybugs - the 15 spotted ladybug is found only in Hawaii. When young, it is grayish in color with 15 black spots on the body. As it grows old, the color of the body changes to dark purple and hence, the spots are not clearly visible. Isn't this the most beautiful thing you've seen all day! Share this beauty of nature with your friends!
Aparently, there are people out there that are all about the Legend of The Purple Ladybugs. The image below is from Snopes' research of said ladybug picture. It's clear that this is just a case of digital color shading.
It is true that ladybugs (or "ladybirds" in the UK) exhibit some color variations, as noted in a June 2015 study undertaken at the Universities of Exeter and Cambridge examining the relationship between ladybug signaling and their visual appearance to predatory birds, according to Snopes.