Here is a heavily commented version

of the logistical map code

that I showed you.

Matlab syntax for definition of a function

starts with the word "function"

and then there are square brackets

around the stuff that you want that function to return.

followed by an equal sign.

Then there is the function name

and in parentheses the arguments to this function.

The sqaure brackets in matlab

are how you define a vector.

Down here in the command window

I'm defining the row vector.

It has three elements. 1,2,3

so this line right here

the first line of the program

is setting up a vector that has no elements in it

and I'm setting that up so I can stuff the iterates

of the logistic map into that.

On line 5, I'm setting up an internal variable

to store the current iterate

and I'm setting it's value to the inital condition

that was passed to the function.

Then we go into the loop that produces

the end iterates that were required of this function.

In matlab, you don't specify the beginning

and endpoints of the index of a loop.

Rather, you give the for loop the a vector

containing the values you wanted it to index.

In this particular case I'm making a vector

that starts at zero and goes up to N.

Let me show you how that works.

By default the spacing in the vector is one.

If you want to change that you can.

By doing something like this

So, this for loop is going to get executed

for the index value 0,1,2,3,4,5,6 and on up to N.

And, what the guys of the for loop do

are two things.

First, this line right here. It takes all the iterates

you have computed so far,

sticks the current iterate onto the tail end of it

makes a new vector out of that

and replaces the old value

in the list of iterates you produced so far

with that new augmented value

let me show you how that works.

Here, I'm making self a row vector

called foo.

That has four elements

by the way the semi colon in matlab

supresses output.

So if I were to do that same assignment

value to foo and put a semi colon afterword.

It would do it. It just wouldn't tell me

that it did it.

That's why there are all these semi-colons up here.

If I didn't have those matlab would

be telling me everything it did

as it ran that function.

Let's say I want to stick another number onto the tail

end of foo.

I would do it like this

and that returns that vector.

Now, notice that I did not set that

as the new value of foo.

So, if I just look at what's in foo.

I see what was there before.

But I can set that value to the new value

like so.

And now what's in foo.

Is that vector with the new value on the end.

The right hand side of the last line of code

inside the for loop is evaluating the logistic map

for the current value of X.

Then it is replacing the contents of that variable

With that new calculation,

that is the updated calculation and then it loops.