I’ve really been enjoying a series of posts by Mark Dominus on his blog, The Universe of Discourse. The Cosmic Call was a series of radio messages sent in 1999 and 2003 aimed at various nearby stars (in case there are any intelligent aliens there to receive the message). It is fascinating to consider the question: how do you communicate with other intelligent beings who may be very different from us? The messages were encoded as simple bitmap images and tried to build up from very simple arithmetic to more complicated things.
Mark has already covered the first five parts of the (23-part) message, with more to come. You should see if you can decipher each part before reading the explanation! The first part is shown below.