We investigate the dynamic structure of human gaze and present an experimental study of the frequency components of the change in gaze position over time during free viewing of computer-generated fractal images. We show that changes in gaze position are scale-invariant in time with statistical properties that are characteristic of a random walk process. We quantify and track changes in the temporal structure using a well-defined scaling parameter called the Hurst exponent, H. We find H is robust regardless of the spatial complexity generated by the fractal images. In addition, we find the Hurst exponent is invariant across all participants, including those with distinct changes to higher order visual processes due to neural degeneration. The value we find for H of 0.57 shows that the gaze dynamics during free viewing of fractal images are consistent with a random walk process with persistent movements. Our research suggests the human visual system may have a common strategy that drives the dynamics of human gaze during exploration.

We propose a carbon-nanotube-based neural sensor designed to exploit the electrical sensitivity of an inhomogeneous fractal network of conducting channels. This network forms the active layer of a multi-electrode field effect transistor that in future applications will be gated by the electrical potential associated with neuronal signals. Using a combination of simulated and fabricated networks, we show that thin films of randomly-arranged carbon nanotubes (CNTs) self-assemble into a network featuring statistical fractal characteristics. The extent to which the network’s non-linear responses will generate a superior detection of the neuron’s signal is expected to depend on both the CNT electrical properties and the geometric properties of the assembled network. We therefore perform exploratory experiments that use metallic gates to mimic the potentials generated by neurons. We demonstrate that the fractal scaling properties of the network, along with their intrinsic asymmetry, generate electrical signatures that depend on the potential’s location. We discuss how these properties can be exploited for future neural sensors.