Translation between fractal images and music - Using Grammatical Framework to translate between self-similar fractals, and how the fractals can be interpreted as music
Examensarbete på kandidatnivå
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.
fractals , music , Grammatical Framework , L-systems , formal grammar