- 3 hours ago
- 129337

Mind-Boggling Food Realizations[distractify]

Previously: Genious Shower Thoughts, Dog Shower Thoughts

(via raphisachocolatecookie)

Source: tastefullyoffensive- 8 hours ago
- 77321

is it your own skin though? As in you grew it, on your own body, from birth?

This skin was grown yes. On a human body. That is mine. I’m not a robot

Ok ok I’ll believe you… If you first tell me what this says:

I don’t need to prove myself to you how dare you, I love breathing oxygen

(via awkwardvagina)

Source: punlich- 8 hours ago
- 63

- 22 hours ago
- 4304

Whites riot over pumpkins in NH and Twitter turns it into epic lesson about Ferguson, aka Black Twitter Wins Again (with some nice Ally Assists), aka

The Best of #PumpkinFest, PT 2. #staywoke

Beyond ridiculous the difference in response , they show up with paintball guns for this but nope Fergus on gets armoured personel carriers

(via foxaveclocs)

Source: socialjusticekoolaid- 1 day ago
- 6511

- 1 day ago
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- 1 day ago
- 406

(click through the images to view in high-res)

Penrose tilings are an example of the non-periodic tilings discussed in the last post. Recall that these are tilings that cover the entire infinite plane leaving neither gaps nor overlaps. Whats nice about these tilings is that the set of tiles used to construct the Penrose tilings only consists of two different basic shapes consisting of quadrilaterals.

Whats even more remarkable about Penrose tilings is that using just these two shapes it is possible to construct infinitely many different tilings that cover the infinite plane. This infinity is infinitely bigger in size than the countable infinity of the whole numbers ( 1, 2, 3, 4, and so on), but rather equivalent to the uncountable infinity associated to the real numbers (which includes all whole numbers, fractions, and decimals with infinitely many digits).

Despite the existence of these infinitely many different Penrose tilings, there is one peculiar property they all exhibit. Consider any finite region, or patch, of one particular Penrose tiling. Then it is possible to find an exact copy of this patch in

any otherdifferent Penrose tiling! Moreover, this patch occurs infinitely often in different spots in any given tiling! Note that this is true of any patch of any size no matter how big as long as its finite. This implies that if you were only able to examine a finite part of any Penrose tiling, you could never really distinguish that entire tiling from any other tiling. Thus, different Penrose tilings are only perfectly distinguishable in the infinite limit of the entire plane.The images shown above display finite regions of Penrose tilings. They are constructed using an elegant "cut-and-project" method (also used here), which involves projecting the points of the integer lattice in 5-dimensional Euclidean space, onto a certain 2-dimensional plane. Connecting adjacent projected points in this plane by lines then yields a Penrose tiling.

Further reading:

- Penrose Tiles to Trapdoor Ciphers by Martin Gardner
- Algebraic Theory of Penrose’s Non-periodic Tiligns of the Plane by N.G. de Bruijn
- The Empire Problem in Penrose Tilings by Laura Effinger-Dean
Image Source: Wikipedia

(via spring-of-mathematics)

Source: intothecontinuum