Animals often forage via Levy walks stochastic trajectories with heavy tailed step lengths optimized for sparse resource environments. We show that human visual gaze follows similar dynamics when scanning images. While traditional models emphasize image based saliency, the underlying spatiotemporal statistics of eye movements remain underexplored. Understanding these dynamics has broad applications in attention modeling and vision-based interfaces. In this study, we conducted a large scale human subject experiment involving 40 participants viewing 50 diverse images under unconstrained conditions, recording over 4 million gaze points using a high speed eye tracker. Analysis of these data shows that the gaze trajectory of the human eye also follows a Levy walk akin to animal foraging. This suggests that the human eye forages for visual information in an optimally efficient manner. Further, we trained a convolutional neural network (CNN) to predict fixation heatmaps from image input alone. The model accurately reproduced salient fixation regions across novel images, demonstrating that key components of gaze behavior are learnable from visual structure alone. Our findings present new evidence that human visual exploration obeys statistical laws analogous to natural foraging and open avenues for modeling gaze through generative and predictive frameworks.