The theory of fractal geometry provides a general framework for studying sets that had been thought to be exceptional oddities. This is an active area of research, and 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 various 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 examines applications, including data compression, examples from number theory, dynamical systems, and Julia sets.
Successful study of this module should enhance your skills in understanding complex mathematical texts, constructing solutions to problems logically and communicating mathematical ideas clearly.
You’ll get help and support from an assigned tutor throughout your module.
They’ll help by:
Online tutorials run throughout the module. While they’re not compulsory, we strongly encourage you to participate. Where possible, we’ll make recordings available.
Course work includes:
You’ll have access to a module website, which includes:
You’ll also receive course notes covering the module's content, including explanations, exercises, and solutions to aid your understanding of the concepts and associated skills and techniques contained in the set book.
Set books:
You can study this module on its own or use the credits you gain towards an Open University qualification.
M835 is an option module in our:
Fractal geometry (M835) starts every other year – in October.
It will next start in October 2027.
We expect it to start for the last time in October 2029.
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.
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There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.
If your income is not more than £25,000 or you receive a qualifying benefit, you might be eligible for help with some of these costs after your module has started.
There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.
This module may have an optional study weekend. There will be a charge to attend in person or online. If attending in person, you’ll also need to pay for your travel, and accommodation if you need it. More details will be available after the module has started.
If you study this module as part of an eligible qualification, you can apply for a postgraduate loan to support your study costs. To find out more, see Postgraduate loans in England.
If you study this module as part of an eligible qualification, you can apply for a postgraduate loan to help with your tuition fees. To find out more, see Postgraduate tuition fee loans in Northern Ireland.
If you study this module as part of an eligible qualification, you can apply for a postgraduate loan to help with your tuition fees. To find out more, see Postgraduate loans in Scotland.
If you study this module as part of an eligible qualification, you can apply for a postgraduate loan to support your study costs. To find out more, see Postgraduate loans in Wales.
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Read more about Open University Student Budget Accounts (OUSBA).
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Over 30,000 employers have used the OU to develop staff so far. If the module you’ve chosen is geared towards your job or developing your career, you could approach your employer to see if they will sponsor you by paying some or all of the fees.
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We know that sometimes you may want to combine payment options. For example, you may wish to pay part of your tuition fee with a debit card and pay the remainder in instalments through an Open University Student Budget Account (OUSBA).
We know that sometimes you may want to combine payment options. For example, you may get support from your employer to pay part of your tuition fee and pay the remainder by credit or debit card.
For more information about combining payment options, contact an adviser.
Please note: your permanent address/domicile will affect your fee status and, therefore, the fees you are charged and any financial support available to you. The fee information provided here is valid for modules starting before 31 July 2026. Fees typically increase annually. For further information about the University's fee policy, visit our Fee Rules.
