MUNCHING SQUARES

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# MUNCHING SQUARES - PowerPoint PPT Presentation

MUNCHING SQUARES. A plot of the cells on a grid satisfying bitwise XOR (x, y) &lt; 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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### 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

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)

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 = 1

000 XOR

000

000

Is 0 < 1?

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 = 1

000 XOR

001

001

Is 1 < 1?

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 = 1

000 XOR

010

010

Is 2 < 1?

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 = 1

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 = 1

001 XOR

000

001

Is 1 < 1?

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 = 1

001 XOR

001

000

Is 0 < 1?

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 = 1

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

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) == i

t&i^j < t|i

i^j^t < i|j|t

t div ~i == t div ~j

i^j|t < j&t

i^t^j mod 5

j ^ i < i & t

j & 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) == i

i^t+2&j

but

computational

thought

not just coding