Hello and welcome to unit 2 of the course.

In this unit, I’ll talk about a number of different mechanisms

that can be used to generate fractals.

And we’ll see that there are lots of ways of making fractals

and often some surprisingly simple processes can lead to

some really interesting and arguably complex or complicated outcomes.

I had originally planned also covering

the box counting dimension in this unit.

But I have decided that it makes

more sense to do it in a separated unit.

So that will be the next unit after this one.

So this unit again will be about generating fractals.

And it will be a little more qualitative and exploratory.

The number of analysis will come back again in unit 3.

So to get a started a quick story and an example.

This morning I was in my backyard and

in the backyard we have planted an elderberry bush.

And the elderberry bush had lots of berries that were ripe

So I decided to that was time to harvest them

so that’s why I did for a good bit this morning.

Instead of making a test for unite 1 which is

probably what I should have been doing.

Anyway

So I picked a bunch of the elderberries

and I brought them in a big bowl inside

and this is what they look like.

And then you need to pull the berries off

sort of one by one

not gonna but the stems.

And then I put the berries in the freezer.

So here is another view of the elderberries.

This is what a bunch of them looks like

and this was couple maybe 2 months ago.

this was a flower and here was attached to the plant

and then flower turns to the berries

through the magic of botany I guess.

And in order to pick these berries so that you can use them

You need to pick them off one or several of a time like this.

And also I was doing this morning

and after you do that for a while

you are left with just the stem from

the flower of the elderberries are gone.

Let me show you what that looks like.

there

so I wasn’t expecting that other way should have.

But one point as I was doing this

it looks down and suddenly ha ! fractals

so then it has been while admiring this shape

I really like it I like the color purple.

Purple is my favourite color.

In the branching pattern I think it’s really really interesting.

From the main branch there are 4 that branch off

and then there is one to the stem

that continues so 1,2,3,4 and one continues

and then that hard to see

that pattern repeats again.

1,2,3,4 and then the stem in the middle.

So there is the branching is similar.

It’s not exactly the same.

And then I here at the edges

with the berries are those follow

a somewhat different pattern

So in any event my bowl filled up with these sorts of shapes

and I spent a while admiring them this morning.

So I suspect that similar things might happen to you

that you’ll suddenly notice fractals

where you were not expecting to see one

now that you have sort of fractals in your eyes and in your minds.

You’ll probably start to noticing them all over the place.

And some of them are I think really interesting and beautiful shapes.

So what I have done is I have created

a discussion forum devoted to fractal pictures, fractal images.

So I am hoping that you’ll see

some fractals in your everyday life as a travelling around.

May be you’ll take a picture to and post them there.

And we’ll have a big gallery of fractals

from our lives and we can look at.

Also in this unit we’ll be experimenting

with computer programs that generate lots of fractals

And in my experience and I’ll show you this shortly in the unit.

Every now and again you come across

you somehow build a fractal and it just looks really cool.

better know the other ones.

And so may be that’s something also

you could post in the fractal gallery forum.

If you build a nice fractals on a computer

some algorithm turned out really good

or some random set of parameters looked really nice

take a picture of that, take a screenshot and post that as well.

so that’ll be fun

may be in this way get some discussions going

and another way to get to know each other on the forums.

If we all post it some different fractals photos

and don’t worry if they are not great photos,

great quality photos.

I’ll post photos but I am not a good photographer.

The main point is to share ideas

and get some discussion started.

Ok, so, again the main point,

the main goal of this unit is to think about

different ways of building fractals.

There are lots of different processes and

procedures that have fractals as results.

And so we’ll start exploring this

by thinking again about the Koch curve.

And then how we could vary the Koch curve

to make shapes are a little more interesting

and a little more realistic.

So let’s get start it.