munching squares
Post on 14-Jan-2016
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MUNCHING SQUARES
A plot of the cells on a grid satisfying bitwise XOR (x, y) < n for consecutive values of n. n = 1, 2, .... grid size
It is thought that it was discovered by Jackson Wright on the RLE PDP-1 around 1962
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The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
000 XOR000000Is 0 < 1?
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
000 XOR001001Is 1 < 1?
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
000 XOR010010Is 2 < 1?
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
001 XOR000001Is 1 < 1?
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
001 XOR001000Is 0 < 1?
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binarySet n = 1
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binary
Set n = 2
111
110
101
100
011
010
001
000
000 001 010 011 100 101 110 111
The colour of each pixel is determined by comparing the bit XOR (exclusive or) of its row and column indices with the selected threshold (n)
Convert cell indices to binary
Set n = 3
Good expressions:j ^ i < t (original munch squares)i == j^t((i | t) mod (j | t))j mod (t+1) == it&i^j < t|ii^j^t < i|j|tt div ~i == t div ~ji^j|t < j&ti^t^j mod 5j ^ i < i & tj & i < t ^ (t mod 3)(t div ~i^j) < (t div ~j^i)(i&t) mod ((j&t)+1)(i&t) mod ((j&t)+1) == ii^t+2&j
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