• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
Specialist
• Course subject Mathematics
• Areas of interest Digital Arts, Computer Science, Mathematics, Physics, Algorithms and Data
• Academic career PGRD
• Course convener
• Jacob Shapiro
• Mode of delivery In Person
• Co-taught Course
• Offered in First Semester 2025
Fractal Geometry and Chaotic Dynamics (MATH6116)

This course might not be offered in 2024. Please contact admin.teaching.msi@anu.edu.au for advice if you need this course to graduate.

This course introduces basic mathematical techniques of fractal geometry and dynamical systems, aimed towards understanding and modeling natural shapes and forms from leaves to coastlines. Basic topological and geometrical language to describe and model rough, ("fractal") objects is developed. Relationships between fractal geometry and discrete dynamical systems and chaotic dynamics are emphasized, including symbolic dynamics, stability of attractors, bifurcations and routes to chaos.

The key ideas are introduced in an intuitive way. The key definitions and theorems are stated but few proofs of theorems are given. However, graduate students will have to attend additional lectures which will provide rigorous mathematical foundations and will be assessed separately from undergraduate students.

In computer laboratory sessions students learn how the mathematical results can be applied in practice by running and modifying simple Python programs.

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

Upon successful completion of this course, students will have the knowledge and skills to:

1. Be able to construct and analyse a wide range of fractals.

2. Be able to analyse 1-D dynamical systems in terms of attractors, basins and cascades of bifurcations.

3. Understand how to use fractal geometry to model rough data and natural shapes.

4. Be familiar with Hutchinson theory of deterministic fractal sets and measures, and be able to prove basic theorems and solve problems in the area.

5. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from fractal geometry.

6. Ability to use their deep knowledge and understanding of fractal geometry to formulate responses to complex concrete and abstract problems.

7. Ability to communicate their understanding and skills in fractal geometry with colleagues and non-experts and apply their knowledge in an occupational situation.

## Indicative Assessment

• Projects 10% (LO 1-4)
• Assignments 30% (LO 1-4)
• In-class Quizzes 20% (LO 1-4)
• Final exam - 40% of total mark (LO 1-4)

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

Three lectures per week and regular workshops

## Requisite and Incompatibility

Incompatible with MATH3062

You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.

## Prescribed Texts

Fractals Everywhere, by Michael F. Barnsley, Third Edition (2012,  Dover).

Fractal Geometry - Mathematical Foundations and Applications, Kenneth Falconer (Wiley,2000)

## Fees

Tuition fees are for the academic year indicated at the top of the page.

Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees

Student Contribution Band:
1
Unit value:
6 units

If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Where there is a unit range displayed for this course, not all unit options below may be available.

Units EFTSL
6.00 0.12500
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.

The list of offerings for future years is indicative only.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.

### First Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
2549 17 Feb 2025 24 Feb 2025 31 Mar 2025 23 May 2025 In Person N/A

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