CSCI 4446/5446 Course materials:

General information and administrivia
 A version of CSCI 4446 is available through
the Complexity Explorer
MOOC platform housed by the
Santa Fe Institute. We'll be supplementing the course
with some of these materials during CSCI 4446/5446 this spring. These
MOOC materials may be useful to you in other ways as well, especially
if you have to miss a lecture. Please go to that website, register
for the course, and look around a bit (including through the
``supplementary materials'' page).
 Problem Set 1: logistic map. You
can
use
the logistic map app on the Complexity Explorer MOOC to check that
your solutions are correct (look in the "supplementary materials"
tab). Also, you may wish to take some time this week to review
section 1 of the ODE notes listed below if your knowledge of
differential equations is at all rusty.
 Problem Set 2: bifurcation diagrams
and Feigenbaum's constant. Again, you can use the Complexity Explorer
logistic map app mentioned above to check your solutions.
 Problem Set 3: fractals. For some
examples of fractals in the wild,
click
here or
here. If you missed the classes in which I talked about fractals,
this video
is a good makeup.

Problem Set 4: RungeKutta and the driven pendulum equations.

Final
Project Guidelines: you can find tech reports that compile
projects from some previous semesters (2010, 2011, 2012, and
2015) here.
Search for the title "Projects in Chaotic Dynamics..."

Problem Set
5: adaptive RungeKutta and the Lorenz and Rossler systems. The
following materials may be useful to you as you do this problem set:

Problem Set 6: Poincare sections. The netnews posts about
numerical dynamics that are listed above (PS5) may be useful here as
well.
 Final Project Details

Problem Set 7: variational equation. See the notes listed below.

Problem Set
8: embedding.
The following materials may be useful to you as you do this problem
set:

Problem Set 9: Lyapunov exponents.
The following materials may be useful to you as you do this problem
set:

Problem Set 10: fractal dimension.
Click
here for a detailed list of the assigned reading for this topic
and
here for a scan of some of that reading (pp166191 of Parker
& Chua).

Problem Set 11: playing with bike wheels, writing Lagrangians, and
starting to explore the twobody problem for a binary star. This
material is covered in the first few sections of the classical
mechanics notes listed below.
Click
here for a picture defining true
anomaly,
here for an interactive simulator that you can use to explore
orbits, and
here for a wonderful lecture on dynamical toys like tops and
rattlebacks.

Some hints
about presentations.

Problem Set 12: integrating the twobody equations. See section 4
of the classical mechanics notes listed below. Here's
an interesting
link that Kristine Washburn found about a variant of this problem.
You may also wish to check out the nbody section of Colonna's webpage
(listed below). Here is
the "Chaos
Hits Wall Street" article that's on the reading assignment.

Problem Set 13: integrating the threebody equations for a
binaryfield star collision. See section 4.2 of the classical
mechanics notes listed below. The "visualization of dynamical
systems" page in the "interesting links" list below has source code
for a lovely visualization of this problem.
Liz's videos and written materials:
Some useful and/or interesting links: (caveat emptor!)
 A great article from Quanta magazine entitled
"The
Hidden Heroines of Chaos" about the people who carried out
Lorenz's computer simulations.
 xkcd's takes on chaos (and
curvefitting)
 A nice
youtube lecture
about fractals (21 min)
 An amazing
animated bifurcation diagram

Riding around on the Lorenz
attractor
 A
transcript of Lorenz's 1972 speech to
the AAAS entitled "Predictability: Does the flap of a butterfly's
wings in Brazil set off a tornado in Texas?"
 Pendulum stuff:
 Henri Poincare didn't only play a formative role in the
foundation of the field of nonlinear dynamics. Among other things, he
came up with the theory of relativity and wrote down e=mc^2 before
Einstein did. Read a bit about
him here.
 The Fyre tool for producing
artwork based on histograms of iterated chaotic functions ,
written by an alumnus of this course.
 Michael Skirpan's
fractal tree generator (= the mother of all solutions to PS3).

CU's
site license for Matlab now covers student computers!

The
visualization of dynamical systems page from the Nonlinear
Dynamics and Time Series Analysis Group at the Max Planck Institute
for the Physics of Complex Systems.
 Video recordings of the lectures from Steve
Strogatz's introductory course on nonlinear dynamics and chaos
 Complexity, the flip side of
chaos: complex
dynamics of a flock of starlings. Here's
the Vimeo version of that
video if you prefer that channel.
 Movies of metronomes synchronizing (modernday equivalent of
Huyghens' pendulum clocks): an array of five
and an
array of 32 (!)
 The
PhET project, an interactive simulator that you can use to explore
all sorts of interesting systems. Click on "Play with sims" and go to
"Physics" for the nbody simulator (called "My Solar System").
 Analog computers for nonlinear dynamical systems: the
Antikythera
mechanism and the
digital
orrery (built by Liz's advisor)
 "Guide to
Takens' Theorem" paper (heavy going, mathematically, but very
comprehensive).
 Rigid body
dynamics in zero gravity on the international space station.
 Jim Roberge's fabulous
lectures about control theory (RIP, wonderful mentor).
 An applet that
simulates the Lorenz equations, allowing you to enter initial
conditions with a mouse click.
 A gorgeous youtube video that zooms in on the
Mandelbrot set.
 Another gorgeous video of an
evolving 3D fractal surface.
 A 'chalkmation' youtube video  complete with music  about the
Mandelbrot
set (warning: a bit of foul language at the end).
 The
TISEAN timeseries analysis toolkit. The TISEAN site has binaries
for UNIX & windows. 'brew install tisean' works on Macs if you're a
brew user. Here are some examples of
how to run all of this from MATLAB.
 Chaos in the path of a Roomba
 Chaotic music & dance stuff:
 NASA's movie of
Hyperion tumbling
 Remember that wonderful
"powers of ten" video from highschool physics?
 SIAM's dynamics
tutorials, many of which were contributed by grad students in courses
like this one.
 Wolfram's Mathworld site.
 The
FAQ for sci.nonlinear. A fabulous resource.
 The Santa Fe Institute,
which has a couple of
great educational programs for graduate students (the Complex
Systems Summer School) and undergraduates (called "Research
Experiences for Undergraduates").
 Some Java
demos developed by Michael Cross, who teaches the CSCI4446equivalent
course at Caltech.
 The Chaos
Hypertextbook
 Helwig Hauser's visualization
of dynamical systems page. The pages above that are interesting,
too.
 JeanFrancois Colonna's
"virtual spacetime travel" page, which includes lots of stuff
about the Lorenz system, pendula, the nbody problem, etc. Very nice
graphics.
 Some sources of economic and other time series data:
 Would you like your own double pendulum?