In this introductory unit I'll say what fractals are
and give a number of different ways to think about fractals and self similarity.
The main technical content of this unit is the idea of the self similarity dimension.
You'll learn what this is
and how to calculate this for simple mathematical fractals.
To get started in this video,
what are fractals?
Well, the first way I think about a fractal
is that it's an object that's self similar
That means that is made of of copies of itself;
smaller copies of itself.
A classic example is this fern, it is a fern, a fern shape.
I picked it outside my office.
And a fern is made of smaller shapes that look like a fern.
So, these two things look, not identical, but they're very similar shapes.
So, to see that, maybe this will work.
So, it's a shape that is made out of a shapes that are similar to it.
And it continues this self similarity over several scales.
Let's see if I can do this.
So here is...
part of a fern,
and this part of a fern came from this, this look like a little bit similar.
And then, this looks like this.
So, fractals are objects that are self similar.
They're made of smaller copies of themselves,
and this self similarity extends over several scales or several size generations
In contrast, a person, the outside of a person,
is not self similar.
Here it's a person, or, Ok, not a person a doll.
And the arm of a person does not look like a small copy of a person.
That would be really creepy, if it did.
We would say that this shape, a person shape, is not a fractal.
Is not self similar, because it's not made of smaller copies of itself.
Whereas the fern is a fractal, because it's self similar.
Now, there are lots of examples of fractals in nature,
that you've seen all around you.
One example is a mountain range,
so a mountain range is made of, if you think about it, is a big bump.
It is a mountain, and on that big bump,
there are smaller bumps that, look like a mountain.
So, there are little mountains on top of the big mountain,
and then smaller mountains on top of the smaller mountains, and so on and so on.
And these little bumps on top of bumps,
they don't look identical, but they look similar.
So, mountains are fractals.
Another example of a fractal is a tree.
This picture is of a sycamore tree, and you can see this branching structure;
kind of like a fern, it is repeated in several scales.
That branches have smaller branches off of them
that are similar to the main branch.
Then, those small branches have smaller branches too off of them and so on.
So the same shape, or a similar shape repeats over many different scales.
Another example is this Romanesco broccoli.
That has a spiral, green spiral shapes.
And you can see that the broccoli is made of a green spiral,
and those green spirals are made of of green spirals,
and those green spirals are made of a smaller green spiral, and so on.
So, I would say that this Romanesco broccoli is a fractal as well.
And just to give one more example, a vascular system.
Here, there is the vascular system for this leaf.
You can see that it has a nice fractal structure.
The shape branched,
and then, branched again, and branched again.
And the veins and arteries inside of us, and inside of all mammals and creatures,
also have this fractal structure.
We'll talk about the implications of that when we talk about metabolic scaling.
That's the short introduction to fractals.
Fractals are self similar objects.
In the next several videos I'll introduce some mathematical fractals
and you'll learn how to calculate their dimension.