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MUNCHING SQUARES - PowerPoint PPT Presentation


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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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Presentation Transcript
slide2

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

slide3

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)

slide4

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?

slide5

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?

slide6

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?

slide7

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

slide8

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?

slide9

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?

slide10

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

slide11

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

slide12

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

slide17

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

my favourite book

but

computational

thought

My Favourite Book

not just coding