In fanworks, Ran is sometimes shown as yelling "CHEN!" whenever Chen does something wrong. Now, she's more popularly known as "CHEEEEEEEEEN!"
Another popular meme regarding Chen is 「藍さまホイホイ」 or "Ran-sama hoihoi."
Yet another meme featuring Chen is "Honk Honk Chen". A comic strip make by 'bkub', showing Chen riding a bicycle, stopping in the road because Suika Ibuki is laying there drunk, and Chen honking the bicycle horn. This comic was translated to English and posted on 4chan. Soon, people began rearranging the panels to create new stories from it, editing panels, and the like.
Rin, being the only other cat character in the series, is often depicted in fanart fighting with Chen.
Some fans think Chen is around 100 years old, due to Chen with two tails. However, Chen is a Nekomata, and Ran is a Kitsune.
She is also shown being chased by Momiji or chasing Nazrin.