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Fractal geometry

In recent years there has been an explosion of interest in the mathematics of fractals – sets whose geometry we cannot easily describe 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 an outstanding representation of shapes of natural phenomena such as clouds, mountains and ferns. This module examines the theory of fractals and their geometry and examples of its application.

Qualifications

M835 is an option module in our:

Module

Module code
M835
Credits

Credits

  • Credits measure the student workload required for the successful completion of a module or qualification.
  • One credit represents about 10 hours of study over the duration of the course.
  • You are awarded credits after you have successfully completed a module.
  • For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.
30
Study level
Across the UK, there are two parallel frameworks for higher education qualifications, the Framework for Higher Education Qualifications in England, Northern Ireland and Wales (FHEQ) and the Scottish Credit and Qualifications Framework (SCQF). These define a hierarchy of levels and describe the achievement expected at each level. The information provided shows how OU postgraduate modules correspond to these frameworks.
OU Postgraduate
SCQF 11
FHEQ 7
Study method
Distance learning
Module cost
See Module registration
Entry requirements

Find out more about entry requirements.

Module details Entry requirements Module registration Study materials

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.

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.

Course work includes

4 Tutor-marked assignments (TMAs)
Examination

Future availability

Fractal geometry (M835) starts every other year – in October.

This page describes the module that will start in October 2025.

We expect it to start for the last time in October 2029.

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.

Entry requirements

You must have passed one of the following modules:

Or one of the discontinued modules M826, M828 and M832.

We recommend 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.

Register

Start End Fee Register
04 Oct 2025 Jun 2026 Not yet available

Registration closes 11/09/25 (places subject to availability)

Register
This module is expected to start for the last time in October 2029.

Future availability

Fractal geometry (M835) starts every other year – in October.

This page describes the module that will start in October 2025.

We expect it to start for the last time in October 2029.

Additional costs

Study costs

There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.

Study events

This module may have an optional in-person study event. We’ll let you know if this event will take place and any associated costs as soon as we can.

Ways to pay for this module

We know there’s a lot to think about when choosing to study, not least how much it’s going to cost and how you can pay.

That’s why we keep our fees as low as possible and offer a range of flexible payment and funding options, including a postgraduate loan, if you study this module as part of an eligible qualification. To find out more, see Fees and funding.

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 Ventura 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

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 pages.

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