Cobweb Applet Exploration Worksheet
Name:
Learning Objectives: Explore cobweb plots for a variety of simple functions and orbits for a number of seeds,
identify fixed points, observe attracting and re
The Mandelbrot Set and Iterating a Complex Function Worksheet
Complex Function: Just as we have real-valued functions where a real input x produces a real output f(x) we
can have complex-valued functi
Complex Numbers Worksheet
Complex Numbers: a + bi where a and b are real numbers and i 2 = 1 .
Complex Plane: Complex numbers can be visualized with the horizontal axis representing the real component
Block Fractals Worksheet
The following pictures show the first couple of iterations of a fractal made from cubes. By examining the
changes between Stage 1 and Stage 2 you should be able to identify ho
The Quadratic Family Cobweb Exploration Worksheet
Objectives: In this activity you will explore iteration and orbits with quadratic functions, fixed and periodic
points, attracting and repelling fixed
Sierpinski Triangle Area Worksheet
Directions: Complete the table and answer the following questions. Assume the area of the original triangle is 1
square unit.
Iteration n
0
1
2
3
4
5
Number of trian
Koch Curve Length Worksheet
Directions: Complete the table and answer the following questions. Assume the length of the original segment
is 1 unit.
Iteration n
Number of segments added at stage n
Leng
Iterating Functions Worksheet: When a butterfly flaps its wings
Consider the function f ( x ) = x 2 + 0.1875 . Using Excel or your calculator (especially the ANS button), find the first
few iterates o
Iterating Functions Worksheet: Exploring Orbits
Objectives: In this worksheet we explore several functions, look at orbits using Excel, and describe the
behavior we observe. In this activity we become
Iterating Functions Handout
Function: A machine for doing things
with numbers. Given a function f and an
input x the output is call f(x).
Iterating a Function: Evaluating a function over and over usin
Fractal Workshop
Dimension Worksheet
Name_
Recall that the an object scaled by by a factor of S generates N copies of the
original object then the dimension D satisfies the relationship N = S D . Find
Dimension and Fractals
We say a line is a one-dimensional object, a plane is a two-dimensional object, and a
cube is a three-dimensional object. Consider these modes of transportation:
A train moves i
Definition of a Fractal
Sources:
Hans Lauwerier. Fractals: Endlessly Repeated Geometrical Figures. Princeton, NJ: Princeton
University Press. 1991.
Robert L. Devaney. A First Course in Chaotic Dynamic
Block Fractals Worksheet
The following pictures show the first couple of iterations of a fractal made from cubes. By examining the
changes between Stage 1 and Stage 2 you should be able to identify ho