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Microsoft Word - IJART0702-0307 JENSEN_no downsample.doc Int. J. Arts and Technology, Vol. 7, Nos. 2/3, 2014 247 Copyright © 2014 Inderscience Enterprises Ltd. Aesthetics and quality of numbers using the primety measure Kristoffer Jensen AD:MT, Aalborg University Esbjerg, Niels Bohrsvej 8, 6700 Esbjerg, Denmark E-mail: [email protected] Abstract: The Farey sequences can be used to create the Euler totient function, by identifying the fractions for number n that did not occur in all Farey sequences up to n – 1. This function creates, when divided by n – 1, what is here called the primety measure, which is a measure of how close to being a prime number n is. The quality of a number sequence can be determined using the primety, which is further generalised to real numbers through the use of real numbered Farey sequences. Ambiguous and interesting results are obtained in this process; for instance it seems that all integers approach full primety when investigated in the real domain. The corresponding numerical sequences are furthermore shown to have interesting artistic properties. In particular the fractal behaviour is interesting. To further investigate fractal ambiguity, common fractals are extended with random elements, which render softer or more varied shapes. Keywords: Farey sequences; totient function; primety; self-similarity; fractals. Reference to this paper should be made as follows: Jensen, K. (2014) ‘Aesthetics and quality of numbers using the primety measure’, Int. J. Arts and Technology, Vol. 7, Nos. 2/3, pp.247–260. Biographical notes: Kristoffer Jensen obtained his Masters in Computer Science in 1988 at the Technical University of Lund, Sweden, and his DEA in Signal Processing in 1989 at the ENSEEIHT, Toulouse, France. His PhD was delivered and defended in 1999 at the Department of Computer Science, University of Copenhage

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