In 1974, the astro­nomer Frank Drake sent a math­em­at­ic­ally-based bin­ary mes­sage to the stars (spe­cific­ally the M13 glob­u­lar cluster), using a radio tele­scope. What was the mes­sage, and how was it constructed?

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(L) The Arecibo Mes­sage string, arranged in 73 rows and 23 columns. Even in text, your eye can see pat­terns emer­ging. © The same mes­sage shown as a shaded grid, mak­ing the pat­terns more clear. ® The same image col­or­ized for dis­cus­sion. [Images by S. Lar­son; R image from Wiki­me­dia Commons]