The first time we see the purple cat is Girl Meets Creativity. We know that purple is Riley's color, and the cat shows up during episodes that involve Maya and art.
So what is the purple cat? And why does the art teacher say that Riley has painted the perfect purple cat at the end of Girl Meets Upstate?
I have a theory.
Purple is Riley's color, but the cat itself represents Maya. The purple cat stands for Riley's influence on Maya, but it's a little more than that. It's also the identity that Riley sees for Maya. Riley and Maya begin the show believing that Riley is day and Maya is night.
Over the course of season 2, Maya develops different character traits. She has been influenced by Riley, but she also has made her own decision about hope and happiness.
We know that Maya is an over the top and angry character at the beginning of season 1, and we watch her grow in season 2. Riley sees things very differently, which is why she thinks that Maya is gone in Girl Meets Triangle.
Riley sees the world in black and white. Right and wrong are very clear to her, but she is also raised with the idea that she has to be happy all the time. This comes out in Girl Meets Yearbook. Riley decides to go in the opposite direction with her alias Morotia M Black.
This is the first obvious clue that the writers give you on what Riley believes her identity to be. Maya is also thrown when Riley is, and she tries to be her as well:
But Maya quickly reverts back because she discovers a secret about Riley, and she knows who she is. She accepts her flaws through season 2, and she even deals with her anger. So, Maya changes, but Riley doesn't see it that way.
Riley is very insecure, and this comes up in several episodes. She has viewed herself to be the sun, always bright and happy, and she doesn't register negative emotions or accept them. Instead, she has an escapist approach. Instead of admiting that she's wrong, Riley has this habit of "fixing" everyone around her. We see this in several episodes, but it is most obvious (and represented through paint) in Girl Meets Maya's mother.
When Riley decides to "fix" Maya's life, they have a paint fight. We see another fight like this in Girl Meets Upstate. And this is where the dialogue in Girl Meets Triangle comes to play.
There are two obstacles that stand in Riley's way from progressing the way Maya has: her view of herself, and her ability to face reality.
This show is called Girl Meets World after all.
So both paintings in Girl Meets Triangle are representative of the way each girl views the world.
But this was not done intentionally. Because Riley believes that she is doing the best thing she possibly can for her friend. Her influence is mirrored in Girl Meets Upstate by the influence that Cory has on Shawn.
Shawn repeatedly states that Cory has influenced him, and now that Riley believes Maya lost herself, Shawn believes that he has lost himself as well. But there is a difference between the influence that Cory has on Shawn, and the influence that Riley has on Maya.
Shawn says, "All my life I chased after Cory and Topanga, and what they had. But I don't want that anymore. I want what I'm supposed to have."
Shawn makes the decision himself, but Maya has still allowed Riley's influence to dictate her life. This is understandable because Riley and Maya are still teenagers. Riley has a lot of growing to do, but Maya has grown. In order to make Riley and Maya stay on the same page, Maya has to step back.
There's one more purple cat that appears in Girl Meets Legacy:
This purple cat is clear and everything is swirling around it. We know that the swirls represent when "the world swirls you all up"
This picture is the exact opposite of Maya's painting:
Maya is seeing the world differently from Riley, and her identity has been changed by her growth. Her purple cat represents that the world is swirling around, blurring her vision and she doesn't know what to do.
Riley, with the best intentions, is trying to simplify this process, and keep everything the same. Her growth is going to be letting go of her expectations of the world and accepting it for what it really is. Until Riley and Maya accept that they are different, and they will not always agree, neither will be able to grow at this point. Lucas is a big part of that, but it was clear from the pilot that the girls are trying to keep everything the same while the world changes around them.
But Maya's step back isn't necessarily a bad thing.
We'll see how this plays out in Girl Meets True Maya.
From the promo, Maya's rebellion is similar to Riley's. She goes too far and has to find balance between the dark and light aspects of her personality.