playing with the exponential curve

Feb 1, 2014  

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).

{% img center http://britton.disted.camosun.bc.ca/firdau1.jpg %}

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}]

{% img center http://farm3.staticflickr.com/2853/12244178256_251f9fcfae_d.jpg %} {% img center http://farm6.staticflickr.com/5496/12243600435_e6faac3bbb_d.jpg %} {% img center http://farm6.staticflickr.com/5547/12244178226_2258c2c2ce_d.jpg %} {% img center http://farm3.staticflickr.com/2882/12243785163_3822d7299b_d.jpg %} {% img center http://farm8.staticflickr.com/7332/12243785183_6243378edf_d.jpg %}

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!