# Fibonacci sequence goes technoir, gets lagged

From the MAKE Flickr pool

Industrious experimentalist Eric Archer shares more of his synth dreams made real with this sequencer based on the Lagged Fibonacci number generator –

Fans of the Golden Ratio know that it is built-in to the Fibonacci Sequence, being the ratio of S(n)/S(n-1) when n is very large.

But lets make it more complicated.

The Lagged Fibonacci Generator is a generalized version that looks at a wider “history window”; instead of the two previous numbers, it lets you go back farther in the list with parameters j and k.

S(n) = S(n-j) + S(n-k)

These numbers are limited to whatever bit depth you choose to represent them. Whenever the addition generates a “carry”, it rolls over at zero again and outputs a carry flag. For example, if you’re using 8 bits, the m value is 2^8, or 256. What happens then is magic because instead of an ever-increasing string of numbers, you get a set of numbers that hop around back and forth between zero and m. The complexity of the sequence grows rapidly with larger j and k values, but its never random or chaotic.

You might remember Lagged Fibonacci from it’s day job as an encryption algorithm. Enjoy the relevant handdrawn circuit diagram and further explanatory text here.

And if you haven’t yet had your daily dose of hypnotic oscillography, take a moment to stare into the violent beauty that is the LFG algorithm –

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### Collin Cunningham

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