To simplify this we can write it as a basic formula, where x is the length of the first line and y is the length of the second line:

x, y, x+2, y+2, x+4, y+4, x+6, y+6, and so on, until the 'backbone', which is (x+a)+(y+b)+2 i.e. two units longer than the two previous lengths added together.

And it gets simpler. The second line must always be 2 units long in order to separate it from the last line of the interlocking key.

So in the above equation y = 2, so it can be rewritten x, 2, x+2, 4, x+4, 6, x+6, 8 and so on.

The first 7 key patterns that this gives for x = 1 and x = 2 are

From this you should be able to see the pattern and create your own absurdly convoluted key patterns, if you so wish.

There is now just a single piece of information stopping you from using these keys. Remember that key patterns are repeat patterns; in other words, the same pattern is repeated to fill a larger area. What we need to know is how many units high and wide the pattern is. Of course the key itself is the repeating pattern, but for our purposes (actually fitting the keys into an area), it will be far simpler to find a square or rectangular section that will repeat itself horizontally and vertically.

The number of units needed for the pattern to repeat itself horizontally and vertically for each of the above patterns are as follows:

key horizontal vertical

key horizontal vertical

So now that we have understood the basic geometry of key patterns, it is time to find out about drawing them.

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