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About algorithmic worldsIntroduction
The piling operator
This pattern was inspired by a work at complexification.net.
"Invaders" refers to Space Invaders, one of the first informatic games, released in 1978. This game consisted in shooting from a spacecraft on extraterrestrial "invaders". Because of the poor resolution of the computer screens at this time, the latter were coarsely represented by two-color 10x10 pixel matrices.
The "Invaders" pattern divides the plane into squares, and further
divides these squares into pixels. It attributes randomly to each of these pixel an index value
among two possible ones. Interestingly, if one forces a vertical mirror
symmetry on each of these pixel matrices, and provided the number of
pixels is not too big, patterns reminiscent of Space Invaders appear. For instance, the image below depicts 5x5 pixel invaders.
Here are 7x7 pixel invaders (note the three-eyed octopus in the third row, second column).
Of course, it is not necessary to impose a vertical symmetry. The following invaders have an order four rotational symmetry.
Finally here are 20x20 pixel
invaders with an order four dihedral symmetry (the symmetry group of
the square, with vertical, horizontal and diagonal mirrors).