I am not a battery expert. From my understanding the more surface area you have the more charge you can get. The problem is the anode swells during charging and then can break or get coated during charge and discharge, reducing the lifetime of the battery. What if you had a fractal space filling curve for the anode that was intertwined by a second space filling curve that remained stationary or receive a small percentage of the total charge so it expanded slightly at the same time as the first curve. The second curve would keep the first curve from expanding too much and breaking and also provide support as it discharged. If you grew the structures as fractals they could possibly self assemble in the battery or grow to fill the battery without swelling too much. 

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