Name: Freaky Dot Patterns - Numberphile
Uploaded: 2020-03-30T05:22:39.000Z
Duration: 7 min 22 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Adverbs of degree

they'll say this is not random because it's far too uniform, you know.

Really, Poisson... That kind of thing would have more gaps and so forth.

But it's random enough and what I'm about to show you

works with any sufficiently random dots. OK.

Now, I photocopied this on a transparency.

The exact copy, I put one on top of the other.

Interestingly boring, shall I say, really amazingly boring.

But now, let's shift the transparency against the bottom sheet a little bit

and the reason, actually in retrospect, is not too surprising because

whatever I'm doing to the transparency is a Euclidean motion

and we know that a Euclidean motion in 2D is always a rotation.

Actually it could be a translation, but a translation is a rotation with a center at  infinity.

those traces of rotation, so to speak, under your eyes.

What's happening is that the original random dots

and images are close enough to the original dots.

And when you have a situation like that, human eyes cannot help connecting the dots.

The dots are connected and you see those small segments in your eyes

and then you see those trajectories of the rotation

and they lose all correlation and you don't see anything.

Now, let's suppose that for example this common center of all the concentric circle is too high

So when I first tried this I naturally shifted the transparency

in the direction that I want to move the center,

I'm going to move it up and down in this direction.

And when I move the transparency sideways, it goes up and down.

So the motion of the center is always perpendicular

to the direction in which I'm moving the transparency, that's really strange.

Now, once you notice this you can actually figure out what's happening by calculation.

So let's say this is a line and that's another line,

and one has been rotated into another, so that's the center of rotation.

That's where they intersect, so to speak.

Now, let's say that I move the image sideways

and you can see that the point of intersection actually goes up and down

So, although I'm moving the knife horizontally,

the intersection point is going up and down vertically.

So that's more or less why if you move the transparency horizontally the center goes vertically

and if you move it vertically it goes horizontally.

Next, I'm going to show you another example.

This is the same picture as the previous one, but only shrunk a little bit.

I went to the photocopier and hit the shrink button.

It shouldn't be shrunk too much, maybe this is 96% of the original

because if you shrink it too much, again, you lose the correlation and you don't see anything.

And of course you see those spirals, because in addition to the rotation that's present from the previous one,

and if I now adjust the rotation so it gets rid of the rotational component

and make it pure translation then you get this radial pattern.

OK, so that was the random end of the experiment.

Let's try the other end, which is the regular end of the spectrum.

And we'll begin by seeing something that is very classical.

Square lattice, and I took an exact photocopy of this on the transparency,

Now, nothing interesting is happening. Let's start rotating this.

And, as I keep rotating, it resolves into a smaller and smaller pattern

and at 45 degrees it becomes the smallest,

and around that point you see there's some kind of wave that comes in and out, that's quite curious.

eventually, this pattern becomes larger and larger,

and it becomes a blur and keeps going and so on,

and I have rotated by 90 degrees, because that's the period, if you like.

This is called a moiré pattern, which is quite well known.

You can do the same thing with another kind of lattice;

this is lots and lots of equilateral triangles that have been put together

and colored in an automated fashion black and white.

And if I put the photocopy of this on top, again you see nothing.

a ghost comes in and then resolves into this kind of thing.

I think at this stage, most people see black walls

partitioning the plane into white triangles.

These triangles become smaller and smaller,

and they kind of go away and resolve into the smallest scale,

and then, if I keep rotating, these come back.

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Freaky Dot Patterns - Numberphile

eventually

present

slightly

pattern