6 weeks old cigarette burn is changing color from red to purple.is that normal, will it ever heal.i treated it well when i got burn with antibacterial?

Scar: It sounds like if the injury is 6 weeks old that what you are noticing now is the scar tissue forming. It will likely continue to fade a bit; however, the area may always have a scar. I'd advise protecting the area from the sun and moisturizing well with mederma or vitamin E

Cigarette burn: Burns take a while to heal depending on how deep, how wide. Color change occurs. You should seek medical attention for follow up and seek attention immediately if black (sign of necrosis, cell death), surrounding redness, swelling ,tenderness pus, pain,.Even with antibacterial you can get infected.