- Code MATH3062
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Digital Arts, Computer Science, Mathematics, Physics, Algorithms and Data
This course has been adjusted for remote participation in Sem 1 2021 due to COVID-19 restrictions. On-campus activities will also be available.
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, all students are invited to sit in on the HPO special lectures which provide the rigorous mathematical foundations.
In computer laboratory sessions students learn how the mathematical results can be applied in practice by running and modifying simple Python programs.
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. (HPO only) Be familiar with and able to prove basic theorems and solve problems in the area of Iterated Function Systems and fractal (Hausdorff, Minkowski) dimensions.
- 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)
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WorkloadThree lectures per week and regular workshops.
Requisite and Incompatibility
Fractals Everywhere, by Michael F. Barnsley, Third Edition (2012, Dover).
HPO only: Fractal Geometry - Mathematical Foundations and Applications, Kenneth Falconer (Wiley,2000)
Tuition fees are for the academic year indicated at the top of the page.
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- 6 units
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