Past research has discovered fractal structure in eye movement variability and interpreted this result as having theoretical ramifications. No research has, however, investigated how properties of the eye-tracking instrument might affect the structure of measurement variability. The current experiment employed fractal and multifractal methods to investigate whether an eye-tracker produced intrinsic random variation and how features of the data recording procedure affected the structure measurement variability. The results of this experiment revealed that the structure of variation from a fake eye was indeed random and uncorrelated in contrast to the fractal structure from a fixated, real human eye. Moreover, the results demonstrated that data-averaging generally changes the structure of variation, introducing spurious structure into eye movement variability.