Jatsko's YouTube and other media ventures

[towerofnix]

Vsauce-Michael's T-shirt looks kind of like those diagrams you were making..



edit: Oh cool, he discusses it at the end of his latest video!

[Jatsko]

As soon as I saw that VSauce released the new video, I had to see it. And I saw the shirt design right away.

There's a fun little program I downloaded that allows you to make this design and a bunch of others with different mod input values and scalar values:

http://demonstrations.wolfram.com/Modul ... OnACircle/

It requires CDFplayer to run (free download)

http://demonstrations.wolfram.com/downl ... layer.html

[Vortex]

cool, it works in Mathematica too

EDIT: I noticed I can export my programs to CDF too. There I have the solution to share the programs for your next maths videos

[Jatsko]

Great

I have ideas

[Jatsko]

I've been playing around with more Pisano circle stuff, and I've realized that there's much more to be done with this stuff.

The entire time we've been looking at writing the remainders along the outside of the circle and making a bunch of connections from remainder to remainder in the period.

But what about writing the entire period around the edge of the circle? Then what you can do is connect every single point with the same remainder value.

I tried this out with Fib (mod 10), which has a period length of 60. So that means all the 1s were connected to each other, all the 2s, all the 3s, etc.

The result was a pattern that was not vertically symmetrical like before, but instead it has rotational symmetry.

f60.jpg (752.08 KiB) Viewed 4513 times

Moreover I noticed that the amount of remainders in the period repeats:

# of 0s = 4
# os 1s = 8
# of 2s = 4
# of 3s = 8
4=4
5=8
6=4
7=8
8=4
9=8.

I also drew out the new period circles for mods 1 through 6. Below is the original circles from the last video and underneath is the new set of circles (with Roman numerals to differentiate) and listed under those is how many times each number appears on the circle.

pis compa.png (978.89 KiB) Viewed 4513 times

So there's an expansion to this exploration

[Vortex]

That's very cool

Since you're joining every point to every other point with the same label, the resulting graph is a superposition of complete graphs. I can turn it into a program, though if the sizes of the period are too big it might not look good since the points would be too close together.
I don't know why the amount of numbers in each period is also periodic, but it doesn't seem to hold up in all cases not?

[towerofnix]

What was that livestream a couple of hours ago? It looks like I missed something interesting D:

[Vortex]

It was a music track Jatsko made, if I understood well.

[Jatsko]

Not quite. I use a snippet of a track from the album Language of Red Goats by Halo Manash as the audio for my YT intro. Thought I would play the whole album.

[Vortex]

Oh, I see. I was confused by the "feat. Halo Manash" thing, I thought he was your collaborator XD