Friday, January 18, 2013

Do you play with Fibonacci?

Leonardo Pisano Bigollo died in 1250 so I doubt you'll be playing D&D or any other RPG with him anytime soon. Maybe later though. Leonardo, know to many as Fibonacci, made a certain number sequence very popular when he published Liber Abaci in 1202. Fibonacci made a great contribution to math in the west and as role players we should be thankful to him.  He introduced the Hinud-Arabic numeral system.  You know those numbers : 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 we use every day.  Without him 3d6 would look like IIIxVI and WotC would have registered DXX instead of D20.

Before I go into talking about the use I've given to the this number sequence in my game let me talk about it first.  The sequence I'm refereeing to is known as the Fibonacci numbers.

Fibonacci numbers looks like the following:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169... etc. etc. etc.

As you can see the numbers grow and grow, but they're neither linear nor exponential. If we were to draw it out the image created would look like this.  Creating the very familiar image of a shell.

The Fibonacci numbers are also closely related to phi the golden ratio (1.6180339887498948482...).
The Fibonacci numbers are found all over the place in nature.  For starters in a sea shell as shown below.

Notice how each square is exactly the same size as every number on the series?
1, 1, 2, 3, 5, 8, 13

But they're present in plants too.  You can find more examples here

And bees! Did you know that the number of grandparents a bee has is a Fibonacci sequence? Read here for more detail.

As it so happens I've come to use the Fibonacci series as well when doing game design. In developing the combat and fatigue mechanism I included the Fibonacci series as the growth rate for fatigue points. When looking at the activity table you can see the row labeled Fatigue Rate. As the character takes more actions per round more points are needed and we move from left to right. This represents the rise in the character's heart rate and it's an indicator of fatigue.

(Fibonacci numbers in green for clarity)

When developing this I tried all types of numbers. Linear growth, exponential, logarithmic, you name it. Only when I put the Fibonacci numbers into the table did things begin to work as I wanted them to.

This gets me thinking. Shouldn't we as game designers look deeper into this and include such a number series in our games a bit more often? It is after all present all over nature, shouldn't it be present in our games when we creating a make believe reality.

Know any games that have numbers like these in them? Let us know!

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