The more we know about ourselves, both good and bad, the more comfortable we feel. This is because the unknown almost always makes us feel nervous. One of the important tasks for an adolescent to learn is self-awareness. Of course, this also applies to all ages. But specifically, the adolescent years are designed to help young people figure out who they are becoming.
By the time a teen graduates from high school, they should have a basic understanding of how they behave in various situations. Such as who they connect with, what they believe in, what values they have, what they feel indifferent about, what passions they have, what motivates them, what they avoid, what challenges them, if they even like to be challenged, what relationships mean to them and so on.
The teen years appear chaotic to some adults because the teens are often orienting themselves to answer these questions...even if they are not consciously doing it. It is almost like trying to pick out your "perfect horse" in a field of 10,000 horses.
So, the good news is, that the purple hair probably is just a phase, or a way of sampling the world. In general, the more these young people practice learning about themselves, the more they will know how to move forward in a direction they want to go. They will be more likely to be confident adults and comfortable with how to approach the world. These are the kind of adults we want to have our children grow up to be.
By the way, the sampling of the world continues into adulthood. The more we are able to look at ourselves, the more proficient we get at orienting. So, it is never too late!