Exposure to nature has been shown to have psychological benefits, such as reducing mental fatigue and stress by restoring capacity in directed attention. Moreover, these effects have been found to extend to purposefully designed, virtual representations of nature. Several constructs have been proposed that underlie beneficial characteristics of nature but these constructs have been found difficult to quantify and reproduce consistently. This has made it challenging to create optimized restorative virtual nature environments. Here we present two studies to investigate the role of a more quantifiable parameter - fractals - in the restorative effects of virtual nature. Basic nature scenes featuring trees were generated based on fractal geometry. Results from both an online study including 2D images and a lab study featuring immersive VR showed a small but consistent preference for images with a fractal dimension of 2.3. Results from psychophysiological measurements in the lab study did not show clear effects of the nature scenes on recovery from stress. We discuss the implications of these findings in the light of research towards restoration and give directions for future research.