Eye gaze tracking has traditionally employed a camera to capture a participant's eye movements and characterise their visual fixations. However, gaze pattern recognition is still challenging. This is due to both gaze point sparsity, and a seemingly random approach participants take to viewing unfamiliar stimuli without a set task. Our paper proposes a method for integrating eye gaze into machine learning by converting a fixation’s two dimensional (x, y) coordinate into a one dimensional Hilbert curve distance metric, making it well suited for implementation into machine learning. We will compare this approach to a traditional grid-based string substitution technique, with an example implementation demonstrated in a Support Vector Machine and Convolutional Neural Network. Finally, a comparison will be made to examine what method performs better. Results have shown that this method can be both useful to dynamically quantise scanpaths for tuning statistical significance in large datasets, and to investigate the nuances of similarity found in shared bottom-up processing when participants observe unfamiliar stimuli in a free viewing experiment. Real world applications can include expertise-related eye gaze prediction, medical screening, and image saliency identification.