Okay I would like to show you a really
cool procedural drawing that you could
do yourself straight away, right now. It's
called a Hitomezashi stitch pattern. It's
a way of visibly mending clothes;
and usually they are very rigid in their
pattern, but since we're mathematicians
we can play around with some
probabilities and see what we can do. Do
you want to give me some 1s and 0s?
(Brady: What do you want me to do, just say some numbers?)
So I'm- I actually love this,
different ways of finding 1s and 0s;
so why don't you give me a phrase and
we'll do the vowels 1s and the
consonants 0s? - (May the force be with you.)
Okay
'May
the
force be
with you'.
Okay so as long as you've got- - (Where's the U?)
I didn't come here to spell.
So as long as you've got two different
states you can do this, so it can be 1s
and 0s, vowels and consonants, odds and
evens; like play around with it, find a
good way that you want to decide if you
are starting on or off. So we're doing
vowels, we're going to start off,
consonants we're going to start on. And
what I mean by that is this, it's stitching. So
M - consonant please. So we're going to
start on which means right from the
get-go I'm going to put a stitch there,
this one put one here, miss one, put one
here, this one, put one here. Okay and just
as if you were stitching clothes we're
gonna stitch
along the way.
Okay.
Next one,
a, is a vowel so we're starting off. Ao
I'm gonna miss one to start with - it's
just one phase over - so miss one, and then
we can put my stitch here,
here, and here, okay. And I'm going to
continue on. Y, vowel or consonant? - (It's a consonant)
One that likes to pretend it's a vowel.
Now we have a nice little wave going
across the way, and we need our stitches
going vertical; will we just use pi for
that? We'll just use the digits of pi,
odds and evens?
I like finding fun ways of deciding what
you're gonna do. Okay so go 3,
1,
4, 1, 5, 9,
2,
6,
3,
5,
8,
9- - (Now you're just showing off.)
3.141592
65358979
3233238
4626
4
3383
2795. - (Well done!)
028841971
(You could be making it up and I wouldn't know.)
So same thing again, but we're gonna
do odds will start off, evens will start
on and we'll go down the way.
Yeah it's a nice picture.
It's fun to procedurally generate things,
so this came from 'may the force be with
you' and pi. It's a cool way to add
randomness into your drawing. The cool
thing you can do with this is you can
then go and colour it in. As far as I've
found they're always too colorable, which
makes sense to me but I don't know if
there's a proof out there, but you can
always colour it in with just two colours.
But I think we can do a little bit
better, I think we can investigate this
further.
So one thing to think about in maths
when you learn something new, this is now
some knowledge that you have, is think
how could I change this? What are the
limits? What could I do with this?
Immediately I thought that's really nice,
like I like how it looks on the square
grid, but I wonder what it would look
like on an Isogrid, so where you've got
your 30 or 60 degrees. So I put it onto
an Isogrid and then I wondered
what would the differences be if
you changed how random it was? So pi,
probably normal, probably got an even
distribution of odds and even numbers.
'May the force be with you' that's a bit
random but what if we did something like-
saw maybe a 10% chance of putting down
a 1 and then a 20% chance of putting
down a 1; and so on. What do you think
you would see happening in the pattern?
Would there be anything to see, is it
totally random? If it was completely zero
percent chance of getting a 1, so it's
just all 0s, you're all starting in
the off state, what do you think's gonna
happen?
(Well you'll just get like)
(big straight lines and shoots that you)
(could fall down and things like that.)
Yeah it looks a lot more rigid. So I mean
I've switched it up onto the Iso paper
just so that we can play around with it,
always always have fun with your maths,
play around with it, enjoy it. Let's
see what this looks like. Okay, so if you
were always starting in your off state...
And then we'd have to do it in this
direction here,
and one more direction to go this way.
(Oh three now?) - Yeah, uh-huh.
You know, always you can just add another
dimension to things.
Okay, totally rigid, you can see a pattern
going on there, and that is the
probability of starting in the on
position is 0 and the probability of
starting in the off position is 1. And
then you just introduce more and more
randomness to it. So my question is, once
we get to the probability of the on
position being 0.9, do you think that's
going to be incredibly random, less
random - what do you think is going to
happen there? - (Intuitively you'd think it)
(just becomes a little bit less random,)
(but I've also made enough of these)
(videos to know that introducing just a)
(little bit of change can make things go)
(chaotic on me so-) - Yeh, it's not chaotic, I
do love when chaotic things happen, but
this is not chaotic. Probability of
starting on
we're going to go with 0.1, probability of
starting off is 0.9.
Now I need to randomly generate these.
Okay cool, and now
I'll make this into a picture.
Okay
so this is what it looks like now that
we've got the probability of starting in
the on position at
0.1. So there's a 1 in 10 chance of
starting in the on position. It came up a
little bit more than one one in ten, but
that happens, it's still a 1 in 10
chance that it would have happened. - (What)
(do I interpret from that? It kind of-)
It looks- well what do you think? Do you
think it looks wildly different? Same?
(A couple of times- you know, obviously it)
(looks the same down that part and then)
(it looks like it's gone a bit skew whiff there.)
Yeah, uh-huh, so you can think of this as
like the baseline pattern, this is it
with no randomness and then we've
introduced a little bit of randomness. So
you can see there are some similarities,
there are some differences. I got this
wrong when I made my first prediction
about what was going to happen when I
started playing around with the
randomness of this pattern. I thought, you
know, it starts rigid, that makes sense,
and then as I get more and more random
it's going to get progressively more
weird looking and chaotic perhaps. I was
wrong. So,
I think that you can get it from what's
going on here, but actually the the point
where it becomes most random and least
looking like this is at the 50:50 mark.
And then it starts becoming rigid again
but one phase out. And that's because if
you are starting in the on position, you
know with a 0.1 percentage or 0.1
probability,
then your off position is 0.9. When you
get to 0.9 they've just flipped over, so
you're in essence doing the same thing,
you've got the same probability going on
again at 0.9. So
do you want to see what 0.5 would look
like, the most random one, and then we'll
have a look at the probability switched
over.
And this is where the most hectic
pattern happens.
Yep it's pretty pretty hectic looking.
It's
pretty unrecognisable from the first one,
nice pattern,
a little bit more random, and then you
can see it's kind of losing losing the
plot a bit.
It's a nice way to say that. It is
getting hectic in here. And then it gets
progressively more rigid again and goes
back into another pattern. Okay, so now
the probability of starting on
is gonna be 0, we're not going to
start on at all. And the probability of
starting off is
certainty, that is happening. - (So it's)
(the mirror of that one?) - Yeah.
It kind of looks like it just moves over
a wee bit.
Starting on each time
and
ready for the massive anti-climactic
surprise that it did not in fact become
more and more random, it got more random
up to 0.5 and then it became less random
again and it looks exactly the same, it's
just moved over a wee bit. You should
always just think what can you change,
what can you play around with? Make a
prediction, see if you want- like you know
if you want to guess what's happening or
you could just see what happens, just play
around with things and see what happens.
(So this is used by people who are like)
(sewing and stitching things?) - Yeah, uh-huh.
So if you like if you get a hole in your
pocket or your sock or whatever, you
can stitch it on the front and it looks
really cool, who wouldn't want that
stitched on the front of their shirt you know?