RANDOMNESS

[The Kakama]

My first post was dumb.

Same.

[Vortex]

sound illusion

I heard that quite a lot ago. It was creepy D:

[ENIHCAMBUS]

sound illusion

Funny and realistic.

[The Kakama]

sound illusion

I heard this some time ago, it was cool.
But now, I feel vaguely nauseous hearing it again.

[The Abacus]

I heard of it from a friend fairly recently – I listened to it and found it interesting

[Vurn]

http://www.pastelportal.com/forum/viewt ... 170#p21634

http://www.pastelportal.com/forum/viewt ... 210#p22025

Wow.

Having obtained the seperate formulae for the number of Alpha and Beta lines in a g-tree of a given k, we calculate its sum:

a+b.JPG (2.44 KiB) Viewed 1333 times

which works for values greater than 0.
All g-trees treated as graphs with Alpha and Beta lines treated as nodes have an Euler cycle; k=1 has a hamiltionian cycle, k=2 has a hamiltonian path. All graphs of k>2 don't have a hamiltionian path.
The v-name values
As defined before, each member has a distinct v-name. For a given family of n, each v-name of a n+1 family member has 1 more letter, except for n=0. The family of n=1, which consists of m and f, has the v-number of two, henceforth defined as the sum of the numbers of the letters in the v-names of all the members of a given family or g-tree. Hence, for n=2 v=8, and for n=3 v=24. With this we obtain the formula for the v-number for specific families: it is n*2^n, for n>0.
For whole g-trees of a given k, the formula for the v-number is, as follows:

v(k).JPG (1.66 KiB) Viewed 1333 times

Palindromic v-names
V-names of certain members are palindromes, i.e. they are the same when read from both the right and normally, from the left. All previously defined border members exhibit this property, but they aren't the only palindromic members. For example, all palindromic members of the family n=3 are 3m, 3m, mfm and fmf, while its non-palindromic ones are 2m-f, 2f-m, m-2f and f-2m. The formula for the number of palindromic members in a family of n is 2^((n+1)/2) for odd n's and 2^(n/2) for n that is even.
The formula for the number of palindromic members of whole g-trees of a given k is given by

p(k).JPG (6.62 KiB) Viewed 1333 times

[Cone]

Smutek, zimno, halucynacje z niedożywienia i śmierć. Takie jest życie.

[Boingo]

No trees were harmed in the posting of this message, however several electrons were inconvenienced.

[zombieshooter]

Well, the electrons kinda were trying to go through your computer back to the positive pole, so you are just allowing them to do that and using it in your advantage. A win-win scenario.

[Boingo]

*groan*
Fine. You win
Joke my cousin made:
"What happened after the electron spent a minute in the asylum computer?
He was discharged."
I found it vaguely funny.
The parents did not.