Katabatak Math-An Exploration In Pure Number Theory

[Racoon]

wow ive seen a hole in the cave light is shining down i can see whats happening ive stopped tripping over rocks and can now identify them

:cup:

 

Illuminating :)

 

Turtle gifted me 2 high quality Katabatak graph prints.

They are hanging on a wall

 

Katabatak is the straw that stirs the drink! :rolleyes: :D

[TheBigDog]

Welcome to the expedition anglepose!

Welcome to the expedition anglepose!

Welcome to the expedition anglepose!

 

Bill

Bill

Bill

 

I love the sound in this cave.

I love the sound in this cave.

[Queso]

Yeah the echo in this cave reminds me of a place I used to end up when I would dream on full moons,

 

There is a 20ms slapback coming from that rock over there, you hear it?

And if you listen closely you can actually see your voice with your ears Disperse down the main shaft, and flood into those Huge chambers down there that lead to the surface.

The decay here lasts for 11 seconds!

Not to mention how much reverb just occurs in damp reflective rock surfaced tunnel-like Caves.

 

Your walls are colorful, guys. ;)

[anglepose]

I have stumbled apon a new corridor, at least i think its new excuse me if im repeating.

If you take a katabatak addition tabl but instead of adding like usal between the x and y axis you add from the top axis to the bottom axis and from the left to the right axis then you get "double katabatak" very boring when in addition but wait till i get to "double katabatak multiplication" then you find intresting results.

This might need some more explaining

[ATTACH]491[/ATTACH]

[anglepose]

Heres a big boulder now double katabatak multiplication. it generates intresting patterns for art and math maybe music.

It is done by *** i said in my last post multiplying the left and right axis togethr then the top and bottom.

take your answer from each and add them together then using k plus the two numbers until you get a single digit.

I admit i dont explain things very well so you might not get

[ATTACH]492[/ATTACH]

[anglepose]

i have created a larger neater peice of art

[ATTACH]493[/ATTACH]

[Queso]

Music....

 

Yes, that makes perfect sense.

 

Time to experiment.

[TheBigDog]

Here is a music experiment in Katabataks. Fill into the key your own 9 music symbols so they match with the colors(maybe 8 notes and a rest or such a matter).

Now play the 'score' either along a row or column, either forward or reverse, or possibly as chords & in accord with your color key.

Listening forward to hearing it,

Turtle

Hmmmm.... I wonder if I can program that....

 

Bill

[TheBigDog]

Here is some analysis from the Numberator on Katabatak of the Anomalies...

 

k(n) base 10:

Strange - 7(3)

Bizarre - 1(1), 2(3), 4(1), 5(2), 8(3)

Peculiar - 1(1), 2(2), 3(1), 4(1), 5(6), 7(1), 8(16)

Curious - 1(1), 2(1), 3(1), 4(2), 5(3), 8(4)

 

This is the collection of the first 53 anomalous strange numbers. The totals are: 1(3), 2(6), 3(2), 4(4), 5(11), 7(4), 8(23). Notably 6 and 9 are absent from this set. :rose: And 8 is the k(n) for 43.4% of the numbers!

 

Bill

[TheBigDog]

Push me pull you!

:hihi:

:hihi:

I redded the K3's as something to look into further, because as we all recall (:lol:) any number with a Base Ten Katabatak transform of 3 divides by 3 & if even by 6 as well. Aha!:hihi:

:cup:

They are the first Curious (48684) and First Peculiar (2892) anomalies.

 

Bill

[Chacmool]

Your Turtle Highness, you make mathematics such an exciting exploration! :)

 

PS I love your new avatar! :confused:

[TheBigDog]

My print is here! My print is here! Right here in my hand I hold an image from within the Katabatak cave rendered by Turtle himself! I am going to run out and get a frame for it and get it up on the wall.

 

Whoo Hoo!!! :wink:

 

Bill

[Chacmool]

O happy day! My Turtle print has arrived! It's BEAUTIFUL! :) All who gaze upon this masterpiece are in awe and rendered speechless, before turning green with envy. :doh: Thank you, Turtle! Thank you, thank you, thank you!

 

And thanks also to those who got it to me safely here at the tip of Africa. Isn't it great Turtle - your Katabatak genius is now being admired on the other side of the world. :)

[Chacmool]

It is beyond my fondest dreams Chacmool.:) I am particularly interested to hear what people say about it (after regaining their speech of course:hihi: ). What words do they use? How does their mood change? How long do they look before looking away? What questions do they ask? Does it remind them of anything, or not?

Oooopss...running on again.:lol: Anyway Chacmool, thank you from this side of our world.

:hyper:

:shade:

:cup:

People's reaction usually goes something like: "WOW! :eek2: What's that? It's beautiful/awesome/amazing/interesting/fascinating!" People are absolutely intrigued by it, and they usually don't stop staring until I put it away. Like moths to a flame... My sister is a maths teacher, and I can't wait to show it to her students (it's school holiday at the moment).

[TheBigDog]

Proof positive that the picture has arrived. And sitting in it's honored place on the mantle. We havn't hung any pictures yet. Hell, we only moved in two years ago!

 

Thanks again Turtle!

[Chacmool]

Reviewing some of the other Katabatak Figurate patterns we find another that is square:

base six katabatak figurate number pattern on square matrix

With the wave of my magic wand & several hours with paper & pigment I have constructed the base six katabatak figurate number pattern on triangular matrix. Leftmost, the generator; rightmost, tiling the plane.

 

PS If you plan to go in, you'll need your Key

Ooh Turtle, this is just to gorgeous! Most exciting and interesting :hyper: Onward, explorers!

[TheBigDog]

Turtle, remember thou art mortal! Man nor reptile nor any combination thereof can live on beautifully graphed katabatak transformations alone. :hyper:

 

But if you are going to keep this up, you need to fill me in on how you do them. I am puzzled by what you are producing, and really want to understand it. I really like the triangular ones. But I want to understand all of them! :)

 

Can I bribe you out for a primer (although I know you have done this before) :beer: :beer: :beer: :beer: :beer: :beer: A sixpack of the finest microbrew.... for you.

 

Bill