Fractals -- repeating patterns found in the natural world, in art and in science -- play an important role in describing a wealth of intricate, complex systems, from clouds and lightening to the distribution of links on webpages. Using only very basic mathematical notions, this course offers an introduction to fractals and chaotic phenomena and examines their role in science and the natural world. A hands-on session provides the opportunity to create fractal structures similar to those associated with turbulence.
Fractals: Repeating Patterns in Nature and Science
This is an In-person course which requires your attendance to the weekly meetings which take place in Oxford.
Overview
Programme details
Course starts: 25 Jan 2024
Week 1: Introduction: Why fractals?
Week 2: Real and mathematical fractals
Week 3: Dimensions and the box-counting method
Week 4: Some famous fractals
Week 5: Fractals in the natural world
Week 6: Practical session: Make and analyse a fractal structure
Week 7: Applications: Fractal antennas
Week 8: Determinism and predictability: a short history
Week 9: Chaotic behaviour
Week 10: Randomness and nonlinearity
Recommended reading
All weekly class students may become borrowing members of the Rewley House Continuing Education Library for the duration of their course. Prospective students whose courses have not yet started are welcome to use the Library for reference. More information can be found on the Library website.
There is a Guide for Weekly Class students which will give you further information.
Availability of titles on the reading list (below) can be checked on SOLO, the library catalogue.
Preparatory reading
- Chaos and Fractals: An Elementary Introduction / Feldman, David P
- Chaos: Making a New Science / Gleick, J
- The Fractal Geometry of Nature / Mandelbrot, B
- Chaos under Control: The Art and Science of Complexity / Peak, D. and Frame, M
Certification
Students who register for CATS points will receive a Record of CATS points on successful completion of their course assessment.
To earn credit (CATS points) you will need to register and pay an additional £10 fee per course. You can do this by ticking the relevant box at the bottom of the enrolment form or when enrolling online.
Coursework is an integral part of all weekly classes and everyone enrolled will be expected to do coursework in order to benefit fully from the course. Only those who have registered for credit will be awarded CATS points for completing work at the required standard.
Students who do not register for CATS points during the enrolment process can either register for CATS points prior to the start of their course or retrospectively from between January 1st and July 31st after the current academic year has been completed. If you are enrolled on the Certificate of Higher Education you need to indicate this on the enrolment form but there is no additional registration fee.
Fees
| Description | Costs |
|---|---|
| Course fee | £257.00 |
| Take this course for CATS points | £10.00 |
Funding
If you are in receipt of a UK state benefit, you are a full-time student in the UK or a student on a low income, you may be eligible for a reduction of 50% of tuition fees. Please see the below link for full details:
Tutor
Dr Marina Debattista
Marina Debattista has a PhD in Physics specialising in quantum field theory and is currently interested in the popularisation of science.
Course aims
To provide an introduction to the concepts of fractals and chaotic behaviour in natural phenomena, and to the basic mathematical ideas behind them. Students are expected to gain an understanding of basic principles of physical theories, and to be able to communicate their understanding using the appropriate scientific terminology. The course materials are designed to encourage analytical thinking and to illustrate the uniftying power of fractals as tools of describing a wealth of natural phenomena and artifacts.
Course Objectives:
- The main objective of the course is to offer the basis of understanding of the notions of fractals and chaotic behaviour in natural phenomena.
- To develop an understanding of fractals as tools of analysing complex phenomena.
- To gain an overwiew of the role and applications of fractals.
Teaching methods
- Power point presentations
- Classwork/discussions/debates
- Reading scientific papers
- Video presentations/computer simulations
- Practical demonstration of how to create fractal structures
Learning outcomes
By the end of this course students will be expected to:
- understand the basic principles of fractals and chaos;
- communicate their understanding using the appropriate scientific terminology;
- assess the validity and reliability of scientific information.
Assessment methods
Students can opt to submit either
Option A) A portfolio of exercises and questions
or
Option B) An essay of 1,500 words. In this case student are encouraged to submit a formative plan of the assignment to be submitted and receive feedback on, before the end of the course.
Students must submit a completed Declaration of Authorship form at the end of term when submitting your final piece of work. CATS points cannot be awarded without the aforementioned form - Declaration of Authorship form
Application
To earn credit (CATS points) for your course you will need to register and pay an additional £10 fee per course. You can do this by ticking the relevant box at the bottom of the enrolment form or when enrolling online.
Please use the 'Book' or 'Apply' button on this page. Alternatively, please complete an enrolment form (Word) or enrolment form (Pdf).
Level and demands
Most of the Department's weekly classes have 10 or 20 CATS points assigned to them. 10 CATS points at FHEQ Level 4 usually consist of ten 2-hour sessions. 20 CATS points at FHEQ Level 4 usually consist of twenty 2-hour sessions. It is expected that, for every 2 hours of tuition you are given, you will engage in eight hours of private study.