Science Forums 2

[Turtle]

You all look like a good group, so off we go. In deference to Tormod, we shall hasten slowly. I thought initially to take you into the cave by the main entrance, but Maddog mentioned fractals & I happen to know a discrete side entrance that he may like. This is a recreational expedition afterall. So, there it is, that small square passage; we have to crawl a ways so follow me. ... You wanted fractals & here we are inside a Sierpinski Sponge. Interesting texture in here don't you think? We just have to climb down a few iterations here... and here we are in the Base Ten Chamber of Integers.


___Now to the Katabatak function, K(n). Two principles, addition & repetition, make up the function. It is that operation of repeatedly adding an integer's digits until arriving at a single digit. As in K(1,908) = 1+9+0+8=18, but 18 is two digits so 1+8=9. Another example: K(3,454,671,304)= 3+4+5+4+6+7+1+3+0+4=37, but then 3+7=10, but then 1+0=1. In a bit more rigorous terms, the Katabatak Function is a conditionally recursive algorthm. Steady now; I know the function is the prime operater for that red-headed step-child of math, numerology. I know too that here in the Base Ten Chamber, the K function is congruent modulo 9.
Enough for now; I'm tired. Sleep on it & tomorrow we'll start fresh on a fractal path.