Module Handbook-Mathematics-Universitas Brawijaya
Module Handbook
Module Name: Introduction to Fractal Geometry
Module Level: Bachelor
Abbreviation, if Applicable: MAM61207 Sub-Heading, if Applicable: -
Courses included in the module, if applicable
Introduction to Fractal Geometry Semester/term: 5th/ 3rd year
Module Coordinator(s): Chair of the Lab. Analysis Lectures(s) Corina Karim, S.Si.,M.Si.,Ph.D.
Ratno Bagus E.W., S.Si.,M.Si.,Ph.D.
Language Bahasa Indonesia
Classification within the curriculum
Elective Studies Teaching format / class
hours per week during semester:
150 minutes lectures per week.
Workload: Total workload is 4.5 ECTS, which consists of 2.5 hours lectures, 3 hours structured activities, 3 hours independent learning, 16 week per semester, and a total 136 hours per semester including mid exam and final exam.
Credit Points: 3
Requirements according to the examination
regulations:
Students have attendance at least 80% on Introduction to Fractal Geometry class and registered as examinees in the academic information system.
Recommended prerequisties
Students have taken Introduction to Discrete Dynamic Systems course (MAM61306) and have participated in the final exam of the course.
Module objectives/intended learning outcomes
After completing this course the student should have:
CLO 1 : ability to recognize and exemplify fractal spaces and completeness of fractal spaces.
CLO 2 : Ability to classify and explain transformation on fractal spaces such as affine, Mobius, Analytic transformations, contraction mapping on fractal space and Iteration Function System (IFS).
CLO 3 : Ability to determine the fractal dimension of a set by using Box Counting Dimensions, Theoretical Fractal Dimensions, and Hausdorff - Besicovitch fractal dimension.
CLO 4 : Ability to prove and analyze the fractal interpolation:
Fractal Interpolation functions and dimensions of fractal interpolation functions.
CLO 5 : Ability to create a fractal program with a deterministic algorithm and random iteration algorithm.
Content: Topics :
1. Introduction and Basic Definition: Metric Spaces: review of metric spaces, topology in metric space and properties.
Module Handbook-Mathematics-Universitas Brawijaya 2. Fractal Spaces: definition of Fractal Space, completeness of
fractal space, contraction mapping on fractal space and Iteration Function System (IFS) .
3. Fractal Dimension: Box Counting Dimensions, Theoretical Fractal Dimensions, Hausdorff - Besicovitch Dimensions of the various examples in fractals.
4. Fractal Interpolation: Fractal Interpolation functions and dimensions of fractal interpolation functions.
5. Fractal Programming: fractal program with a deterministic algorithm and random iteration algorithm.
Soft Skill Attribute Discipline, honesty, cooperation and communication Study / exam
achievements:
The final mark will be weighted as follows:
No. Assessment methods (component, activities). Weight
1. Assignment 20 %
2. Quiz 20 %
3. Mid examination 30 %
4. Final examination 30 %
Final grades is defined as follow: A : 80 < Final Mark ≤ 100 B+ : 75 < Final Mark ≤ 80
B : 69 < Final Mark ≤ 75
C+ : 60 < Final Mark ≤ 69
C : 55 < Final Mark ≤ 60
D+ : 50 < Final Mark ≤ 55
D : 44 < Final Mark ≤ 50
E : 0 ≤ Final Mark ≤ 44
Forms of Media Slides and LCD projectors, laptop/ computer, whiteboards.
Learning Methods Lecture
Literature 1. Michael F. Barnsley, 1993, Fractals Everywhere, Academic Press Inc.
2. Kenneth Falconer, 2003, Fractal Geometry: Mathematical Foundation and Applications 2nd Edition, John Wiley &
Sons, England.
3. Heinz-Otto Peitgen, Hartmut Juergens, Ditmar Saupe, 2004, Chaos and Fractals: New Frontiers of Science, 2nd Edition, Springer-Verlag, New York.
Notes:
