Seeing Quantum Fractals

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Science  05 Feb 2010:
Vol. 327, Issue 5966, pp. 652-653
DOI: 10.1126/science.1186118

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If you have been fortunate enough to have been on a flight that lands near a beautiful sunny coastline, you will no doubt have taken in the scenery on the way down, and perhaps even marveled at the winding of the shore into the horizon. What you may not have realized is that the coastline is actually a fractal—an object that appears the same at all length scales (perhaps only statistically). Fractals actually abound in nature: Galaxies, clouds, mountains, trees, and broccoli are all familiar examples. But fractals can occur in the quantum realm as well, even though they have never been observed there, until, perhaps, now. On page 665 of this issue, Richardella et al. (1) report direct measurements of quantum mechanical electron waves that indicate that they may also possess a fractal nature.