One potential negative impact on the quality of life of a spinal cord injured person is the loss of the ability to control devices in their immediate environment. Consequently, research and development has been conducted on technology designed to restore some measure of independence by providing means of control over these devices. A previous assistive device using changes in brain signals from eye closure as its switching system was created. Brain signals were processed using spectral analysis and although this was a successful technique, there were limitations that resulted in higher than desired switching errors. This paper presents results of an alternative method for processing brain signals as the basis for switching, called fractal dimension. In comparison to the spectral technique, the fractal dimension technique was successful in reducing the number of false positive and false negative errors. Additionally, it eliminated the need for a baseline setup for this system. This suggests that fractal dimension is a potentially viable method for analysing brain signals for use in assistive control systems.