It’s not truly a classic “game” by definition – there are rules, but no goal or challenge (unless you define them for yourself).
As example of computer programming, it’s fairly elegant and surprisingly simple, leads to fairly interesting/complex results and writing it is a really good coding practice, because it’s about applying logic to 2D grid / array, which is fairly common thing for beginner programmers to learn. Also, processing a set of rules every tick is what all video games do. So it landed in every programming textbook and classroom.
The “fame” is overrated, but it serves as really good example to bring up when talking about simple rules producing complex things – every area of life has some sort of element that everybody knows and makes it easy to use as an example. Other similar things in life exist – like DNA is a strand of acids, but can generate all the insane diversity of life, or Mandelbrot set is just couple mathematical formulae, but when visualized, will blow your mind. Game of Life is in such class.
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