MT4513 Fractal Geometry

2025 to 2026 Semester 2

Curricular information may be subject to change

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 10

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

Not automatically available to General Degree students

Planned timetable

12.00 noon Mon (weeks 2, 4, 6, 8, 11), Tue and Thu

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof K J Falconer

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Prof Kenneth Falconer

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

The aim of this module is to introduce the mathematics used to describe and analyse fractals and to show how the theory may be applied to examples drawn from across mathematics and science. The module discusses the philosophy and scope of fractal geometry; and may include topics such as dimension, representation of fractals by iterated function systems, fractals in other areas of mathematics such as dynamical systems and number theory, Julia sets and the Mandelbrot set.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2503 AND ( PASS MT3501 OR PASS MT3502 OR PASS MT3503 OR PASS MT3504 )

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (weeks 1 - 10) and 1 tutorial (weeks 2 - 11).

Scheduled learning hours

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

Be able to calculate the box-counting and Hausdorff dimensions of many fractals
Be able to represent self-similar and other fractals in terms of iterated function systems and thus deduce their dimensions
Appreciate how fractals arise across mathematics and the sciences
Understand the definitions and basic properties of Julia sets and the Mandelbrot set and their relationship