So before we sign off,

a few items of business.

First, course evaluations.

There's a course evaluation form

online, there's a link on the site I think

right below this video,

and we'll also send a link to the forum

out by email.

So, your feedback is very helpful for us,

it will help me improve future versions of

this course, it will help improve other

complexity explorer courses, and the

website in general.

So, thanks in advance for taking the time

to fill that out, and your honest and

constructive feedback. Next, I'd like to

acknowledge the funders for the course,

so the main funding for the Complexity

Explorer project is from a grant

from the John Templeton Foundation

to the Santa Fe Institute,

I'm very grateful to them for their support.

and also, we received funding from

individual donations from Complexity

Explorer users, and so, thank you

to everyone who has made a donation.

Also, thanks to all the students

who participated in this course,

who took the time to watch these videos,

and especially those who contributed

ideas and questions in the forum,

one of the most exciting, interesting

parts for me when I do a course like this,

is the ability to interact from people

from all over the world, and see

not just me interacting with you,

but students interacting among themselves.

So, thank you.

So, this brings us to the end of the course.

Fractals and scaling is a powerful idea,

a powerful set of mathematical tools,

that describe a certain type of regularity,

pattern, maybe even simplicity,

across scales, and across a really diverse

set of phenomena. So, physical fractals,

ferns and mountains and clouds,

and coastlines, statistical distributions,

word frequency, earthquake frequency

and the like, and then most recently

in metabolic scaling and urban scaling.

So there are these certain mathematical

patterns and structures, that to

varying degrees, appear across all of

these interdisciplinary systems.

So, I think these are powerful and useful

ideas for the study of complex systems,

or really, whatever you're interested in,

it's a very useful set of ideas and tools

to have in your toolbox.

I enjoy teaching about these ideas,

and thinking about them, they make me

see phenomena in different ways,

and I hope that's been the case

for you as well.

So, thanks again, take care,

and we'll see you around.