The “aperiodic” part means it doesn’t repeat at a regular interval. Obviously some combinations have to occur more than once with enough tiles.

It doesn’t repeat. Even the 3 areas you circled don’t. They’re VERY close, but if you look at the “north-east” and “south-west” portions of each piece you circled, you’ll notice the differences:

This made me wonder whether it’s only one type of kite that forms the aperiodic tile in the way you did. So I looked at the preprint, and the authors claim that there’s a continuum of kite dimensions one can use to make the ‘hat’. Some of them lead to periodic tiling, but most lead to aperiodic tiling,

I had to figure it out in AutoCAD.

This is a bit tricky. It’s not that no portion of the pattern will ever repeat; in fact any finite portion of the pattern could repeat an infinite number of times ( much like the initial tile itself). The assertion is that the entire pattern is not comprised of some repeating sequence. Consider the difference between…

One way to think of it: Print out two copies of the pattern on a transparent film, such that you can see one through the other. It would not be possible to shift the top copy to any other position where everything lines up. The pattern as a whole never repeats precisely, no matter how large or small you make it.

Those dont repeat though, just like how pi has some repeated strings of numbers doesn’t mean theres a pattern

I gig for Amazon Flex sometimes, and I drop plenty of packages on multimillion dollar doorsteps. Some real cheap generic shit, too.

Unless he went on an Amazon shopping spree on his 18th birthday, it’s easy enough for an 18 year old to not have bought anything on Amazon.

“When I want something, I tell the Help to get it. Then they bring it to me!”

He meant: I’m fucking rich and I have some peasants buy stuff for me on Amazon.

You need to complete all the Archon Quests up to Chapter 2. You will also need to be adventure rank 30.

all i got from this was Kaplan came onboard, tailored the endgame to the whales and WoW went on to make billions, did I get it all?

Yeah! screw Kaplan for growing as a person and becoming more mature over 19 years! I certainly never said or did anything dumb when I was 29 and behind the shield of internet anonymity.

The only part I’m having the most trouble with is he laid out a good plan, but his bullet points have two A’s, and he skipped B. (AACDE) instead of (ABCDE).

was his rant professional? hell no. but it was it so inappropriate for a guild leader that we should cancel you? also hell no. also capital letters are for…

Damn, that’s hilarious.

Only when it is beneficial to their _very specific_ agenda’s... Any other time, it quickly devolves to one of 3 points:

It's hilarious because he doesn't even know how to use the asterisk properly. He still wrote the whole fucking word.

Dude. An asterisk? Really?