FSEM 100D
Georg Cantor, Infinity, and the Cantor Set
Georg Ferdinand Ludwig Philipp Cantor was born in Saint Petersburg, Russia on March
3, 1845. Georg was the son of George Waldemar Cantor, a Danish merchant, and Maria Anna
Bhm, a Russian musician. Canto

Christie Cons
9/24/10
Writing Assignment #2
In the investigation of the orbit diagrams of the quadratic and logistic functions, it shows
the limiting behavior on the vertical axis and the parameter a, on the horizontal axis with the
sequence of numbers ge

Fractals and Iterated Function Systems
Christie Cons 10/22/10
For this assignment, I observed various fractals as attractors by the Iterated Function
Systems. Then, to determine the number of matrix functions within the fractal, I counted how
many pieces

WRITING ASSIGNMENT #3
Christie Cons
For Lab #6, on the periods of the Mandelbrot Set Bulbs, it helped to determine the orbit
as well as the attracting cycles of some given period. A Mandelbrot Set gives information on
long-term behaviors of orbits for the

Christie Cons
9/10/2010
Writing Assignment #1
In determining the dynamics of orbits and chaos, I examined three functions with
fifty iterations to look at the long term behavior of several sequences of numbers. For the first
function that was iterated, wh

Population Models:
Predator-Prey
By David
Peworchi
Introduction
Myths:
Solar
explain world
Eclipses: dragon trying to swallow
sun
Earthquakes:
Models:
angry gods from underworld
understand world, curiousity
Types of Model Systems
Maximum
maximum
N
=K

David Peworchik
Writing Assignment #4: Fractals and Iterated Function Systems
An Iterated Function System (IFS) is a collection of matrices that contract in a set of twodimensional space. They could include one or more transformations, like a rotation, re

David Peworchik
10/7/10
Writing Assignment #3
The Mandelbrot set shows the long-term behavior of the orbits for f(z) = z + C. The
equation for the Mandelbrot set is M = cfw_C = C1 + C2i, where the orbit of z0 = 0 under our
function f(z) = z + C is bounded

David Peworchik
Writing Assignment #1
FSEM 100D
The behavior of the function f(x) = x + C differs greatly depending on the value of the
parameter C. In equation one, when C = 1, every orbit approaches +. An orbit is the sequence
of values for a function w

David Peworchik
Doctor Sumner
Freshman Seminar 100D
Mathematics of Chaos Research Project
Population Models: Predator-Prey
In ancient times, people used myths to try to explain the world around them. For
example, they thought that solar eclipses were caus

WA #4 October 17, 2010
An Iterated Function System (IFS) is a set of matrices (Ai), that shrink each set while
perhaps also rotating, shearing, and reflecting. Fractals are the diagrams of orbits, Julia Sets, and
strange attractors that show their many ch

100D WA #3
A Mandelbrot Set M is a diagram that illustrates what the long term behavior of a
complex orbit looks like, a complex function contains the imaginary number i. For f (z) = z + C.
Mandelbrot Set M = cfw_C = C + CI where the orbit of z = 0 under

WA #2
An orbit diagram is the graph of the long term behavior of the independent variable,
parameter (a), to the dependent variable, limiting behavior (L). On a given orbit diagram you can
see a functions fixed points, orbits, periods, bifurcations, or it

FSEM: Mathematics of Chaos; WA #1
When investigating dynamics of the quadratic equation f(x) = x^2 with different
parameters labeled C, you would find that the functions fixed values, orbits, periodic cycles,
and patterns are all very different. Fixed poi

FSEM 100D: Speaking Assignment #1
Fractal Design Presentation
Fractals are images of a subset of real numbers which are self-similar and whose fractals
dimension is not a whole number. A self-similar object is one who is similar to a magnified part
of tha

Christie Cons
11/19/10
The Henri Poincar Dynamical Life
Jules Henri Poincar was a French mathematician, who made a series of advancements in
geometry, electromagnetism, topology, the philosophy of mathematics, and the theory of
differential equations. He