I remember hearing about the apocryphal story about doubling grains of rice on a chessboard. I even tried writing powers of 2 (which at my age then just meant adding 2+2 then 4+4 etc).
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This is obviously the e^x curve, but when you normally see it drawn its self-similarity is not obvious. Mathematica's Manipulate function can help in this regard ...
Manipulate[ListPlot[Table[Power[2, i], {i, 1, n}]], {n, 1, 64}]
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These are screenshots for increasing values of n: Note how they all look the same (except for the first one, where the curve is just starting out), over several orders of magnitude!