Touch is used by humans to estimate object shape using the contour following exploratory procedure. Here we demonstrate autonomous robotic contour following with a biomimetic tactile fingertip, the TacTip, using an active touch method previously developed for different types of touch sensors. We use Bayesian sequential analysis for perception and implement an active control strategy to follow an object contour. The technique is tested on a 110mm diameter circle and yields results comparable with those previously achieved on different sensors. We intend to extend the work onto a different robot platform with improved trajectory control to improve robustness, speed and match with human performance.