*Here’s a guest post full of awesome from The Man (illustrated by ME!):*

Today I will share with you a discovery I have made in the field of Cat Mathematics which I have entitled the **Fibonacci Cat Sequence**. I will also describe the risks of the **Fibonacci Cat-scade Scenario** and attempt to determine the **COCL Limit**.

Just as a brush-up, the Fibonacci Sequence is that neat little pattern of numbers where you add the last two elements to get the next one. If (1,1,2,3,5,8,13,21,34,55,…) rings a bell, good for you. If not, don’t worry– the maths will make sense soon.

First we must seed the sequence with the values F(0) = 0 and F(1) = 1. Imagine as follows:

I start out with no cats. [F(0) = 0]

But someone gives me a cat. [F(1) = 1]

For a while, I am happy with one cat. [0 + 1 = 1, so F(2) = 1]

**REAL WORLD EXAMPLE #1
**

**The Wife and I had no cat. Then we adopted Mehitabel, and we are happy with her. So far, so good.**

After a while of having one cat, many people decide to get a second kitty as a playmate. [1 + 1 = 2, so F(3) = 2] And after getting a second cat, a third little kitty would be so cute in the mix, no? [1 + 2 = 3, so F(4) = 3]

**REAL WORLD EXAMPLE #2:**

**My Honored Grandmother had two cats, meek little Tabby and a big black Maine coon cat named Pharaoh. When my father moved up there to Massachusetts with her, he brought along our old cat Tom. (The fifteen-hour car ride from Indiana to Massachusetts with an ill-tempered, half-drugged part-Siamese is a tale better left for another time.) So by adding a third cat to the mix, we were a stable position. And when poor Tabby passed away, Honored Grandmother adopted spritely Henry.
**

So far the Fibonacci Cat Sequence is fairly linear, except for a little dawdling there at the beginning. But here’s where things start to take off. Once a person has three cats, they may not simply get a fourth cat. They will immediately get a fifth cat. [2 + 3 = 5, so F(5) = 5]

**REAL WORLD EXAMPLE #3:**

**My aunt passed away a bit ago, and she had two cats, Sassy and Ginger. So those two cats came to live with my father and Honored Grandmother. And then they had five cats. Not too long ago, Pharaoh fell ill and passed away as well, and then there were four.**

**BUT FOUR IS AN UNSTABLE POSITION IN THE FIBONACCI CAT SEQUENCE. NATURE WILL NOT ABIDE IT.**

**Just recently, one of Stockbridge’s most celebrated residents, Mary Flynn, passed away, leaving behind her cat Andy. Andy has come into Honored Grandmother’s care, and now they once again have five cats**.

From here, the sequence really starts to take off. [3 + 5 = 8, so F(6) is 8; 5 + 8 = 13, so F(7) is 13; 8 + 13 = 21, so F(8) is 21, etc.]

And this is where the danger really begins, in a phenomenon I would like to tentatively call the **Fibonacci Cat-scade Scenario**. The further you go past three cats, or F(4), the more out of control your cat-hoarding tendencies get, until you suddenly are up to your eyeballs in fur-buckets. Once you have five cats, you cannot simply get a sixth or seventh– you must get an eighth. Once you have eight cats, you cannot simply get a ninth, tenth, eleventh, or twelfth– you must get a thirteenth.

We must now examine the risks of becoming a Crazy Old Cat Lady (COCL). [I use the term COCL in a gender-neutral sense: both men and women can become Crazy Old Cat Ladies, and the term is simply being used out of respect for tradition.] Estimates vary as to when precisely a person becomes a COCL, and future research will need to investigate how age, gender, and actual insanity modify this number. My work here is primarily to create a mathematical backbone of sorts for those future investigations.

For now, I will postulate that the divergence point between a strict linear model and the Fibonacci model at F(4) is the **COCL Limit**. Once you have more than three cats, you are in danger of being a Crazy Old Cat Lady.

In the case of Honored Grandmother, I’ll give her a pass, partially because my father lives there in the house with her (so two of the cats could be his, and three of the cats could be hers), and partially because she’s the most awesome, tough-as-nails octogenarian I know. But for others tempted to expand their cat-families to F(5) and beyond… *beware*.