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A finite field is also known as a Galois field. It is part of an area of mathematics known as group theory which is itself a part of abstract algebra

These fields are much used by computers for such things as encoding and security. They are constructed using binary numbers.

For this afghan counting numbers have been converted to binary, added together using special rules, and colours have been substituted for the resulting answers.  

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Finite Field



Double Base


The afghan consists of 256 squares which are stitched together.

There are variations using 4 or 8 colours.



Any type of yarn can be used.

The squares can be knit or crochet. The main instructions are for the crochet squares shown as these squares add extra patterns with their diagonal lines.

The pattern includes ideas for other squares, and for knitting in strips.

The ‘counting numbers’ 0 - 7 are shown in red along each axis of the grid. The black numbers are their binary equivalents.

Each square of the grid shows the answer you get when you add the two binary numbers together, using special rules. These answers have then been converted back to counting numbers and then to colours.

The rules dictate that no new columns are created and no numbers are carried into the next column, as they would be in ordinary addition. The numbers are simply ignored.

The criss-crossing rows of holes are much more obvious in some lighting conditions, adding an extra dimension to the design.

A small area of the design could be used to make a cushion.