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Tuesday, February 16, 2010

M208 - TMA01 / Part 2

Started working on it today. The exercises aren't really difficult, I suppose. Well, everything can be turned into a challenge. I am trying to do as much as I can with Mathematica, that way I learn more about Mathematica. I am trying to find a way to visualize the effect of a linear translation on a certain are of the 2D-plane at the moment. I sort of feel the load of the 90 points at the moment. Have to ship all questions by the end of next week.

A research problem which interests me is the Collatz 3x+1 function, which is defined as follows:

3n+1 & \text{if $n$ odd ,}
\frac{n}{2} &\text{if $n$ even.}
Collatz conjectured that recursively applying this function to a number always ends in the loop {1,4,2,1}.
Take for example 9.
f(9) = 28 , f(28)=14 , f(14)=7,  f(7)=22 , f(22)=11 ,f(11)=34 , f(34)=17 , f(17)=52, f(52)=26, f(13)=40 ,f(40)=20, f(20)=10 , f(10)=5 , f(5)=16, f(16)=8, f(8)=4 , f(4)=2, f(2)=1, f(1)=4
et voila...

Try 27, if you dare.

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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)