A method is described for mapping the perimeter of shapes as a sequence of connected X & Y coordinates. It operates by tracking, in tandem, along a dilated outline of the shape and the true outline, maintaining contact between both tracks. This combination permits the complete mapping of binary shapes regardless of their complexity. The resulting sequence of X & Y coordinates form an 8-connected map of the outline, which can then be used to obtain fractal dimensions using structured walks. The method requires a digitised image that has been converted into a binary form and the ability to read the values of individual pixels from the digitised binary image. In addition a number of approaches for increasing the efficiency of the twin tracking algorithm are outlined. Obtaining fractal dimensions from a structured walk based on a fully mapped perimeter increases the accuracy of the measured fractal dimensions, extends the range of step sizes over which measurements can be made and permits a highly detailed examination of the perimeter.