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.