In this digital age many listeners of music now purchase albums from online digital music stores instead of buying a physical album from the record store. This has created a concern with many regarding the future of the album as a physical medium. This study investigates the impact of the possible death of the album on certain listening habits, the activity of record collecting, the creation of large-scale musical works, music consumerism, and its implications for the creative process on music as art and sound-recording quality. Three realisations have led to the problem statement. Firstly, the album might not have a future in the digital age. Secondly, downloadable songs might not be able to recreate an album experience. The third realisation is that the possible death of the album could create new, exciting challenges to artists as they strive to create art. This study is exploratory in nature - and no hypothesis was generated. The research necessitates qualitative, exploratory, descriptive and contextual approaches. Furthermore, the investigation has led to the collection of mostly new data, constituting a “primary data design” through the implementation of qualitative listening experiments and a focus group, using full-time NMMU students between 18 and 25 years of age. It is herein argued that digital distribution might possibly have an effect on the perception of the album format and might possibly still be a relevant listening experience, valued by young people. Singles and albums are collectable; and good albums are considered artistic and comparable to the large-scale musical works of the past. If the concept of an album does not die out, then high fidelity formats should be able to re-invent the album experience. Listening experiences other than the album experience do exist, and they could generate new ways for artists to create musical art.

Both complex dynamics and the theory of reproducing kernel Hilbert spaces have found widespread application over the last few decades. Although complex dynamics started over a century ago, the gravity of it's importance was only recently realized due to B.B. Mandelbrot's work in the 1980's. B.B. Mandelbrot demonstrated to the world that fractals, which are chaotic patterns containing a high degree of self-similarity, often times serve as better models to nature than conventional smooth models. The theory of reproducing kernel Hilbert spaces also having started over a century ago, didn't pick up until N. Aronszajn's classic was written in 1950. Since then, the theory has found widespread application to fields including machine learning, quantum mechanics, and harmonic analysis. In the paper, Infinite Product Representations of Kernel Functions and Iterated Function Systems, the authors, D. Alpay, P. Jorgensen, I. Lewkowicz, and I. Martiziano, show how a kernel function can be constructed on an attracting set of an iterated function system. Furthermore, they show that when certain conditions are met, one can construct an orthonormal basis of the associated Hilbert space via certain pull-back and multiplier operators. In this thesis we take for our iterated function system, the family of iterates of a given rational map. Thus we investigate for which rational maps their kernel construction holds as well as their orthornormal basis construction. We are able to show that the kernel construction applies to any rational map conjugate to a polynomial with an attracting fixed point at 0. Within such rational maps, we are able to find a family of polynomials for which the orthonormal basis construction holds. It is then natural to ask how the orthonormal basis changes as the polynomial within a given family varies. We are able to determine for certain families of polynomials, that the dynamics of the corresponding orthonormal basis is well behaved. Finally, we conclude with some possible avenues of future investigation.

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