Translation between fractal images and music - Using Grammatical Framework to translate between self-similar fractals, and how the fractals can be interpreted as music
Typ
Examensarbete på kandidatnivå
Program
Publicerad
2019
Författare
ANDERSSON, Helena
BERGSTEN, Alfred
BRANDSTRÖM, Boel
ENGSMYRE, Gustav
KNOPH, Eli
MEIJER, Edvin
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
This bachelor’s thesis concerns the translation between certain types of self-similar
fractals, and the interpretation of said fractals as music. The fractals used in this
project are the Dragon curve, the Sierpinski triangle, the Hilbert curve, the Gosper
curve, and the Koch square snowflake. All these fractals can be described by Lindenmayer systems, or L-systems, consisting of an alphabet, an axiom and a set of
rules. These systems can be viewed as a type of formal grammar, and thus the
programming language Grammatical Framework, or GF, can be used to generate
strings that represent the fractal images. GF is based on functional programming
and is used for translation between languages – natural as well as formal. With
GF it is possible to translate between the fractal images (e.g. from a Koch square
snowflake to a Sierpinski triangle). The fractals and the translation between them
are visualised in a GUI in the form of a web application. Information about the
fractals (such as phrases, the coordinates for the different line segments that the
fractal images consist of etc.) is temporarily stored in a data structure constructed
for this project. The instructions for graphically rendering the fractal images are
used to create a musical representation of the fractals. A straight line in the graphical representation means ”play note”, and turns mean ”raise/lower the pitch”. The
pitch is changed with respect to the angle of the turn, and the duration of the notes
is decided stochastically. In order to make the music harmonic, all pieces of music
are created from a certain scale, e.g. C-major.
Beskrivning
Ämne/nyckelord
fractals , music , Grammatical Framework , L-systems , formal grammar