Just read this, not sure how true it is but thought it was interesting...
"The first Red stripe represented Texaco, the famous American oil retail brand, who had partnered with BMW during the early days of M racing. Blue represented BMW and Bavarian region. The purple was used to represent the partnership and to allow for a nice transition between the two colors, blending as some may call it.
Once the BMW/Texaco partnership ended, BMW had to buyout Texaco for the rights to the red."
"The first Red stripe represented Texaco, the famous American oil retail brand, who had partnered with BMW during the early days of M racing. Blue represented BMW and Bavarian region. The purple was used to represent the partnership and to allow for a nice transition between the two colors, blending as some may call it.
Once the BMW/Texaco partnership ended, BMW had to buyout Texaco for the rights to the red."