Secret messages hidden inside equations

October 1st, 2007 | Categories: general math, math software, mathematica, matlab | Tags:

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<br /> \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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  1. Amanda
    October 7th, 2007 at 17:57
    Reply | Quote | #1

    Like it! I suppose it’s a new take on “Hello World” for the advanced user!

  2. tdstephens3
    October 10th, 2007 at 03:38
    Reply | Quote | #2

    have you plotted its derivative?

  3. Matt H
    October 16th, 2007 at 11:42
    Reply | Quote | #3

    It’s like a really advanced version of writing “hello” on a digital calculator.

    *goes and dusts off his TI-83*

  4. Amanda
    November 8th, 2007 at 21:48
    Reply | Quote | #4

    Here’s a really weird one – I haven’t tried it myself, but it’s almost unbelievable:
    http://www.kirchersociety.org/blog/2007/02/02/tuppers-self-referential-formula/
    If I’m reading right, the formula actually plots itself. Hope you like.

  5. Andrea
    August 23rd, 2008 at 00:57
    Reply | Quote | #5

    Math is behind everything!
    I love it!

  6. hooman.khosravi.72@gmail.com
    November 29th, 2009 at 17:05
    Reply | Quote | #6

    are you still intrested?? let me khow i have some very very cool stuff

  7. Mike Croucher
    November 30th, 2009 at 18:33
    Reply | Quote | #7

    Yep, I’m still interested :)

  8. Arkapravo
    June 11th, 2010 at 05:42
    Reply | Quote | #8

    EXQUISITE ! …… that f(x,y) looks more like a function straight our of ‘Potential Theory’, then again I guess it is more aesthetic ! :-)

    I guess that it should be possible to do on MATLAB.