In recent years there has been an explosion of interest in the mathematics of fractals – sets whose geometry cannot easily be described in classical terms. There’s no simple definition but all fractals have a highly intricate structure. Many fractals contain copies of themselves at many different scales, and computer pictures have shown that such sets (which are often very beautiful) are a very good representation of shapes of natural phenomena such as clouds, mountains and ferns. This module deals with the theory of fractals and their geometry, and looks at examples to which the theory can be applied.
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No current presentation
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This module is expected to start for the last time in October 2025. |
What you will study
The theory of fractal geometry provides a general framework for the study of sets that had been thought to be exceptional oddities. This is an active area of research and both the theory and applications of fractal geometry are still being developed.
The module is based on the set book Fractal Geometry: Mathematical Foundations and Applications (Third edition) by K. J. Falconer (Wiley), which is in two parts.
Part I has eight chapters dealing with the general theory of fractals and their geometry.
Part II looks at examples of fractals to which the theory of Part I can be applied. These examples are drawn from a wide variety of areas of mathematics and physics.
The module begins with an introductory chapter covering the necessary background material. Next we study the material in chapters two to four of the book, which introduce appropriate definitions of dimension and methods for calculating such dimensions.
The second half of the module looks at applications including data compression, examples from number theory, dynamical systems and Julia sets.
You will learn
Successful study of this module should enhance your skills in understanding complex mathematical texts, constructing solutions to problems logically and communicating mathematical ideas clearly.
Entry
To study this module you must declare the MSc in Mathematics (or another qualification towards which the module can count) as your qualification intention.
Normally, you should have also completed at least one of the entry modules of the MSc in Mathematics (F04), Calculus of variations and advanced calculus (M820) or Analytic number theory I (M823).
All teaching is in English and your proficiency in the English language should be adequate for the level of study you wish to take. We strongly recommend that students have achieved an IELTS (International English Language Testing System) score of at least 7. To assess your English language skills in relation to your proposed studies you can visit the IELTS website.
If you have any doubt about the suitability of the module, please speak to an adviser.
Qualifications
M835 is an optional module in our:
This module can also count towards M03, which is no longer available to new students.
If you have a disability
The material contains small print and diagrams, which may cause problems if you find reading text difficult.
To find out more about what kind of support and adjustments might be available, contact us or visit our Disability support website.
Study materials
What's included
You’ll have access to a module website, which includes:
- a week-by-week study planner
- course-specific module materials
- audio and video content
- relevant computer software and associated guidance
- assessment details and submission section
- online tutorial access
- access to student and tutor group forums.
You’ll also be provided with course notes covering the content of the module, including explanations, exercises and solutions to aid your understanding of the concepts and associated skills and techniques that are contained in the set book. You will need to obtain your own copy of the set book, and only the set book as printed by the publisher will be permitted in the examination, and not a version you have printed yourself.
Computing requirements
You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11), or macOS (10.15 or higher).
Any additional software will be provided or is generally freely available.
To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).
Our module websites comply with web standards, and any modern browser is suitable for most activities.
Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.
It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop as described above.
Materials to buy
Set books
- Falconer, K.J. Fractal Geometry: Mathematical Foundations and Applications (3rd edn) Wiley £40.50 - ISBN 9781119942399
Teaching and assessment
Support from your tutor
Throughout your module studies, you’ll get help and support from your assigned module tutor. They’ll help you by:
- Marking your assignments (TMAs) and providing detailed feedback for you to improve.
- Guiding you to additional learning resources.
- Providing individual guidance, whether that’s for general study skills or specific module content.
The module has a dedicated and moderated forum where you can join in online discussions with your fellow students. There are also online module-wide tutorials. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part. If you want to participate, you’ll likely need a headset with a microphone.
Assessment
The assessment details can be found in the facts box.
Students also studied
Students who studied this module also studied at some time:
Future availability
Fractal geometry (M835) starts every other year – in October.
This page describes the module that will start in October 2023.
We expect it to start for the last time in October 2025.
How to register
We regret that we are currently unable to accept registrations for this module. Where the module is to be presented again in the future, relevant registration information will be displayed on this page as soon as it becomes available.
Regulations
As a student of The Open University, you should be aware of the content of the academic regulations which are available on our
Student Policies and Regulations website.