# Several species of small furry animals

In connection with John Baez' recent mention of hamsters in mathematical physics, I started wondering what other small furry animals have found their way into pure mathematics papers. Some searching found the following:

"Hubbard's rabbit" (aka "Douady's rabbit" or "the rabbit") refers to this fractal Julia set: Fractal rabbit (Notice that this web page's comment, "Note that the image looks like a 'fractal rabbit,'" is not all that helpful. Douady and Hubbard thought this image had a resemblance to the Playboy bunny logo back when they were doing research on this in the 1980s. (They were the ones who first proved that the Mandelbrot set is connected.)) The black region in this picture is the "rabbit." It is the set of all points in the complex plane that do not go off to infinity under iteration of the map f(z) = z^2 + c where c = -0.12 + 0.75i. The quadratic map z^2+c has critical point z=0, and in the rabbit's case the iteration of z=0 leads to an attractive period three cycle. I'm not sure what a Dehn twist is, but this is what they're talking about.

Thanks, that makes more sense. It looks at least as much like a rabbit as some constellations look like their namesakes.

RT Curtis invented the miracle octal generator, or MOG, which is a slang term for a cat. I think that's where the kitten comes from, the cat. http://web.usna.navy.mil/~wdj/m_12.htm Thane http://www.plambeck.org

Thanks. I didn't try searching for "cat" as it seemed likely to have far too many false positives, but that makes a lot of sense as an explanation for the terminology.

One day, when browsing the stacks, I came across a section of the Robertson-Seymour opus, and while I was idly flipping pages, I saw a few lemmas and theorems devoted to the properties of "hairy animals", and yes, this was formally defined. I wish I remember which section it is. I guess the hairy ball theorem doesn't count since it was never formally referred to that way. -- Suresh

Unable to ferret out any more examples, I was once again left wondering what exactly is a "pict" and what was it doing in that cave.

Ancient inhabitant of Britain before the Celts took over, I think, named "pict" because they had painted themselves psychadelically with wode. But the WP article about them says nothing about caves, so...

Who can read about gerbes without thinking of small, hamster-like animals? Cheap, but I felt it was worth contributing. Thane plambeck.org

I don't think I even know what the differences between hamsters and gerbils are, and Wikipedia didn't help much. In the first version of this post, I wrote "gerbil" even though Baez' post was about hamsters... But apparently a gerb is a short cylindrical pyrotechnic device.

Search the web for "Mickey Mouse Decomposition."

Three unrelated Mickeys!

- Feng, Q.; Jensen, R. Supercomplete extenders and type 1 mice. I. Ann. Pure Appl. Logic 128 (2004), no. 1-3, 1–73. MR2060548. I'm not sure what a mouse is but it has something to do with models of set theory involving extremely large cardinals.
- Curtis, R. T. The Steiner system S(5,6,12), the Mathieu group M
_{12}and the "kitten". Computational group theory (Durham, 1982), 353–358, Academic Press, London, 1984. MR0760669. The kitten (it says in MR) is "a device that allows the hexad in the Steiner system S(5,6,12) containing a given 5 points to be computed with ease." - Pilgrim, Kevin M. An algebraic formulation of Thurston's combinatorial equivalence. Proc. Amer. Math. Soc. 131 (2003), no. 11, 3527–3534. MR1991765. Includes a discussion of "Hubbard's rabbit problem", which involves determining the combinatorial class of a Dehn twist of a quadratic function for which the critical point has period three. Whatever that all means.

### Comments:

**tomster0**:

**2006-12-26T16:16:51Z**

"Hubbard's rabbit" (aka "Douady's rabbit" or "the rabbit") refers to this fractal Julia set: Fractal rabbit (Notice that this web page's comment, "Note that the image looks like a 'fractal rabbit,'" is not all that helpful. Douady and Hubbard thought this image had a resemblance to the Playboy bunny logo back when they were doing research on this in the 1980s. (They were the ones who first proved that the Mandelbrot set is connected.)) The black region in this picture is the "rabbit." It is the set of all points in the complex plane that do not go off to infinity under iteration of the map f(z) = z^2 + c where c = -0.12 + 0.75i. The quadratic map z^2+c has critical point z=0, and in the rabbit's case the iteration of z=0 leads to an attractive period three cycle. I'm not sure what a Dehn twist is, but this is what they're talking about.

**11011110**:

**2006-12-26T16:29:44Z**

Thanks, that makes more sense. It looks at least as much like a rabbit as some constellations look like their namesakes.

**None**: MOGs and kittens

**2006-12-26T17:19:03Z**

RT Curtis invented the miracle octal generator, or MOG, which is a slang term for a cat. I think that's where the kitten comes from, the cat. http://web.usna.navy.mil/~wdj/m_12.htm Thane http://www.plambeck.org

**11011110**: Re: MOGs and kittens

**2006-12-26T18:02:42Z**

Thanks. I didn't try searching for "cat" as it seemed likely to have far too many false positives, but that makes a lot of sense as an explanation for the terminology.

**None**:

**2006-12-26T19:16:22Z**

One day, when browsing the stacks, I came across a section of the Robertson-Seymour opus, and while I was idly flipping pages, I saw a few lemmas and theorems devoted to the properties of "hairy animals", and yes, this was formally defined. I wish I remember which section it is. I guess the hairy ball theorem doesn't count since it was never formally referred to that way. -- Suresh

**isosc**:

**2006-12-29T14:54:11Z**

Unable to ferret out any more examples, I was once again left wondering what exactly is a "pict" and what was it doing in that cave.

**11011110**:

**2006-12-29T16:53:55Z**

Ancient inhabitant of Britain before the Celts took over, I think, named "pict" because they had painted themselves psychadelically with wode. But the WP article about them says nothing about caves, so...

**None**: Gerbes

**2007-01-03T17:26:39Z**

Who can read about gerbes without thinking of small, hamster-like animals? Cheap, but I felt it was worth contributing. Thane plambeck.org

**11011110**: Re: Gerbes

**2007-01-03T18:38:03Z**

I don't think I even know what the differences between hamsters and gerbils are, and Wikipedia didn't help much. In the first version of this post, I wrote "gerbil" even though Baez' post was about hamsters... But apparently a gerb is a short cylindrical pyrotechnic device.

**None**: Mickey Mouse

**2007-01-05T19:59:27Z**

Search the web for "Mickey Mouse Decomposition."

**11011110**:

**11011110**: Re: Mickey Mouse

**2007-01-05T21:41:43Z**

Three unrelated Mickeys!

- Jaglom, I. M.; A\v skinuze, V. G. Idei i metody affinnoi i proektivnoi geometrii. Chast'c I: Affinnaya geometriya. Gosudarstv. Ucebno-Ped. Izdat. Ministerstva Prosvesc. RSFSR, Moscow 1962. MR0170246. Affinely transformed Mickeys as an example of geometric transformation.
- Conforti, Michele; Cornuéjols, Gérard; Kapoor, Ajai; Vuskovi'c, Kristina. A mickey-mouse decomposition theorem. Integer programming and combinatorial optimization (Copenhagen, 1995), 321--328, Lecture Notes in Comput. Sci., 920, Springer, Berlin, 1995. MR1367991. A Mickey mouse is a subgraph of an undirected graph forming a cycle with two chords that together with some cycle edge form a triangle.
- Lewis, John L.; Vogel, Andrew. On pseudospheres that are quasispheres. Rev. Mat. Iberoamericana 17 (2001), no. 2, 221--255. MR1891198 A "Mickey mouse construction" is used to smooth out bumps on topological spheres.