Sunday, 13 January 2008


Whilst toasting my crumpets for breakfast, I hit 'random article' on Wikipedia which is an occasional thing I do if I am waiting for something else to download, or indeed if I am simply at a loose end. (Today I was on MSN with my bro' who lives in Shanghai and we were chatting back and forth).

Normally I find I know something about the article and then I am off on some trail or another, however, I haven't got a scooby what 'The valence of the portrait' means which was today's random article, and frankly I reckon I can live reasonably in such ignorance.

Any ideas?

here it is:


Given a quadratic map f_c(z) = z^2+c\, from the complex plane to itself and a repelling or parabolic periodic orbit {\mathcal O} = \{z_1, \lz_n\} of f\,, so that f(z_j) = z_{j+1}\, (where subscripts are taken modulo n), let Aj be the set of angles whose corresponding external rays land at z_j\,. Then the set {\mathcal P} = \{A_1, \ A_n\} is called the orbit portrait of the periodic orbit {\mathcal O}. All of the sets A_j\, must have the same number of elements, which is called the valence of the portrait.

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