Math 320: Chaos and Fractals

Final Exam – Thursday, May 19, 2022 – 5:15PM – LSC 316
  • We will have our final exam starting at 5:15pm in LSC 233. Scratch paper and the approved formula sheet will be provided. Bring writing utensils, a small ruler, and a calculator (no cell phones, laptops, or tablets allowed as a calculator). It will cover everything in the course and maybe a few things that aren’t.
  • The Take Home portion of the Final exam is due in Dropbox before 5:15pm on May 19, 2022.

Course Handouts and References

 Math 320 Online

  • Math 320 Online Classroom
  • If we have to pivot to remote instruction this semester, click here to enter our Zoom classroom.
  • Zoom help – Zoom for Scranton students, how to install, how to use, documentation.

Software and Handouts

  • Guess My IFS! – my web app for guessing the IFS that creates a given attractor.
  • Express My IFS! – my web app for drawing the attractor of some simple IFSs.
  • Guess My Address! – my web app for guessing the address of a point in the attractor of an IFS.
  • – login here with your royalid and password to access our Maple software.
  • Maple Chaos Package – the Maple chaos package I wrote for this course
  • Chaos package documentation – the help file for the Maple chaos package above in pdf format
  • Lecture Examples – a Maple worksheet used in lecture to illustrate the concepts defined in the lecture notes
  • Golly – a free cellular automata program for Windows, Mac, and Linux

Homework Assignments

Graph Paper

For creating your fractal works of art.

Tentative Schedule
1 Tue, Jan 27 Introduction
2 Thu, Feb 1 Logic and Proof
3 Tue, Feb 3 Sets, Functions, Sequences
4 Thu, Feb 8 Number Theory and Induction
5 Tue, Feb 10 Discrete Dynamical Systems
6 Thu, Feb 15 Iteration: $3x+1$, Sumerian method, Euclidean Alg,Tag problem
7 Tue, Feb 17 Iteration: Stick figures, GBs, HeeBGBs
8 Thu, Feb 22 Iteration: Newton’s method, Change of base
9 Tue, Feb 24 Iteration: Fractran, Cellular Automata
10 Tue, Mar 1 Introduction to Maple
11 Thu, Mar 3
12 Tue, Mar 8 Midterm Exam
13 Thu, Mar 10
14 Thu, Mar 22 Metric Spaces I
15 Tue, Mar 24 Metric Spaces II
16 Thu, Mar 29 Hausdorf Metric
17 Tue, Mar 31 Chaos
18 Thu, Apr 5 Contraction Mapping Theorem
19 Tue, Apr 7 Complex Numbers
20 Thu, Apr 12 Affine Maps
21 Tue, Apr 19 Iterated Function Systems
22 Thu, Apr 21 Address My IFS
23 Tue, Apr 26 Fractal Data Analysis
24 Thu, Apr 28 Fractal Curves
25 Tue, May 3 Fractal Interpolation
26 Tue, May 5 Fractal Dimension
27 Thu, May 10 Complex Fractals
28 Tue, May 12