We examine the presence of multifractal properties in the spatial structure of observed IPv4 addresses in measured Internet traffic. A collection of traffic samples from a variety of network settings are assembled and their spatial structures evaluated for multifractal properties using the method of moments approach. We show that all collected traces have properties consistent with multifractal scaling, but that the scaling behaviors vary by trace. We propose mechanisms which may give rise to these behaviors, and then discuss a number of ways by which our empirical finding concerning the spatial structure of observed IP addresses in measured network traffic can be utilized in practice, including its use in modern dataplane network monitor settings, both as a metric to monitor and as a means to increase hardware utilization efficiency.