A central question in neuroscience is how the brain represents and processes information to guide behavior. The principles that organize brain computations are not fully known, and could include scale-free, or fractal patterns of neuronal activity. Scale-free brain activity may be a natural consequence of the relatively small subsets of neuronal populations that respond to task features, i.e., sparse coding. The size of the active subsets constrains the possible sequences of inter-spike intervals (ISI), and selecting from this limited set may produce firing patterns across wide-ranging timescales that form fractal spiking patterns. To investigate the extent to which fractal spiking patterns corresponded with task features, we analyzed ISIs in simultaneously recorded populations of CA1 and medial prefrontal cortical (mPFC) neurons in rats performing a spatial memory task that required both structures. CA1 and mPFC ISI sequences formed fractal patterns that predicted memory performance. CA1 pattern duration, but not length or content, varied with learning speed and memory performance whereas mPFC patterns did not. The most common CA1 and mPFC patterns corresponded with each region's cognitive function: CA1 patterns encoded behavioral episodes which linked the start, choice, and goal of paths through the maze whereas mPFC patterns encoded behavioral "rules" which guided goal selection. mPFC patterns predicted changing CA1 spike patterns only as animals learned new rules. Together, the results suggest that CA1 and mPFC population activity may predict choice outcomes by using fractal ISI patterns to compute task features.