If one were to bake a Mandelbrot cake, could one eat all of it?

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When computed and graphed on the complex plane, the Mandelbrot Set is seen to have an elaborate boundary, which does not simplify at any given magnification. This qualifies the boundary as a fractal. Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms).

So here’s the question. If one could bake a cake that didn’t just approximate a fractal like the Mandelbrot Set, but was in fact fractal, could one eat it? Would slicing into it have any effect at all, given that the edge would be, well, infinite?

All other things being equal, of course, and assuming the existence of a Hausdorff oven and a non-Euclidian cake slicer.

I ask because a college room mate, some years ago, baked me a birthday cake in the form of the Mandelbrot Set. It was a great cake, and to this day I am disappointed that it didn’t last the week.

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