Archive for the ‘matlab’ Category

Secret messages hidden inside equations

October 1st, 2007

At the moment I am writing an introductory Mathematica course and was recently looking for inspiration for potential exercises. One website I came across (I have lost the link unfortunately) suggested that you get something interesting looking if you plot the following equation over the region -3<x<3, -5<y<5. It also suggested that you should only plot the z values in the range 0<z<0.001.

\light f(x,y)=e^{-x^2-\frac{y^2}{2}} \cos (4 x)+e^{-3 \left((x+0.5)^2+\frac{y^2}{2}\right)}

Suitably intrigued, I issued the required Mathematica commands and got the plot below which spoke to me in a way that no equation ever has before.

So now I have a question – What other messages could one find hidden inside equations like this? For example, is it possible to generate a three letter word with a relatively simple equation such as the one above? Of course if you were allowed to use very complex equations (and make use of Fourier transforms maybe) then I guess you could spell out whatever you choose but that’s no fun.

If anyone finds other such messages in simple(ish) equations then please let me know.

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