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Leeds Thesis Template 1 The classification and analysis of spirals in decorative designs Alice Edith Humphrey Submitted in accordance with the requirements for the degree of Doctor of Philosophy The University of Leeds School of Design August 2013 2 The candidate confirms that the work submitted is her own, except where work which has formed part of jointly-authored publications has been included. The contribution of the candidate and the other authors to this work has been explicitly indicated below. The candidate confirms that appropriate credit has been given within the thesis where reference has been made to the work of others. Chapter 3 – Analysis and Classification Method includes material published in: Humphrey, A. and Hann M.A. (2012) Steps Towards the Analysis of Geometric Decorative Motifs Using Shape-matching Techniques. in R.Bosch, D.McKenna and R.Sarhangi (eds) Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture. Phoenix, Arizona: Tessellations Publishing. pp.495-498. The method proposed and examples presented in this paper were the candidate's work. Prof. M.A.Hann presented the paper at the conference and provided comments and advice as to the phrasing of the published paper. This copy has been supplied on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement. The right of Alice Humphrey to be identified as Author of this work has been asserted by her in accordance with the Copyright, Designs and Patents Act 1988. © 2013 The University of Leeds and Alice Humphrey 3 Acknowledgements I am grateful for the help and advice of my supervisor Prof. Michael Hann throughout the course of the research and to Dr. Briony Thomas for her help during the early stages of the work. Antonia Lovelace at Leeds City Museum; Dr. Ashley Cooke and Lynne Heidi Stumpe at Liverpool World Museum; Rachel Grocke at the Oriental Museum, University of Durham and Andrew Parkin at the Great North Museum provided generous access to their collections which was much appreciated. I am grateful to the survey participants for their time and effort. I would also like to thank Tom Humphrey for his help with writing the analysis applet and Prof. Charles Taylor for advice on statistical analysis. This research was funded by a School of Design scholarship from the University of Leeds which was much appreciated. I am very grateful for the support and patience shown by my family throughout the writing of this thesis. 4 Abstract Structure in decorative patterning has been used to identify perceptual preferences and broader social and cultural patterning of a society. This thesis proposes a new method of analysis and classification of decorative spirals as a test of whether the analysis of an individual type of geometric decorative motif in isolation can reflect social and cultural trends in a similar manner. The proposed analysis method, which takes a quantitative, bottom-up approach to classification, was compared with a top- down classification method used in previous studies based on mathematical spiral forms. Similarities were found across the two classification methods, both are clearly strongly influenced by the expansion rate of the spiral but the newly proposed method is felt to offer a more flexible approach to the classification of motifs which accommodates gradual variation and the decorative properties of the motifs beyond a simple mathematical curve. The proposed method was tested on four archaeological case studies: Egyptian scarabs of the Middle Kingdom and First and Second Intermediate Periods, Cypriot Bronze Age painted pottery and gold-work, Shang and Western Zhou Dynasty bronze vessels, and Japanese Jōmon Period pottery. Quantification and cluster analysis of spirals in these studies identified variation in motif shape that could be attributed to the production method but the chief finding was one of homogeneity across the four cultures and a limited range of forms of decorative expression which suggests an influence of natural spiral forms on decorative examples across the cultures sampled. An analysis of the possible influence of spiral optical effects arising from disturbances in the functioning of the visual cortex on decorative spirals did not yield significant results. 5 Table of contents Acknowledgements ...................................................................................................... 3 Abstract ........................................................................................................................ 4 List of tables ................................................................................................................. 7 List of figures ................................................................................................................ 8 Chapter 1 Introduction ............................................................................................... 13 1.1 The analysis of design ................................................................................... 14 1.2 Spirals in nature ............................................................................................ 17 1.3 Symbolic meanings of spirals in decorative arts ........................................... 24 1.4 The choice of spiral motifs as a research focus ............................................ 25 1.5 Overview of the thesis .................................................................................. 28 1.5.1 Research questions ............................................................................. 30 1.5.2 Thesis structure ................................................................................... 34 Chapter 2 Definition of terminology and variables and discussion of spirals as subjective visual phenomena ..................................................................................... 36 2.1 The definition of a spiral ............................................................................... 37 2.1.1 Mathematical spiral forms .................................................................. 41 2.2 Decorative spiral classification ...................................................................... 42 2.2.1 Form .................................................................................................... 45 2.2.2 Stylistic variations in decorative spirals .............................................. 46 2.3 Perception of spiral forms ............................................................................. 56 2.4 Endogenous visual phenomena and their occurrence in decoration ........... 62 2.5 Construction techniques ............................................................................... 67 2.6 Summary ....................................................................................................... 70 Chapter 3 Development of the classification and analysis method .......................... 71 3.1 Data collection and processing ..................................................................... 71 3.1.1 Sources of data ................................................................................... 71 3.1.2 Data collection .................................................................................... 73 3.1.3 Data processing ................................................................................... 75 3.1.4 Identification of the centre ................................................................. 92 3.1.5 Precision .............................................................................................. 93 3.2 Identification of form .................................................................................... 94 3.2.1 Creation of the primary path .............................................................. 94 6 3.2.2 Normalisation...................................................................................... 96 3.2.3 Quantification of form ........................................................................ 96 3.3 Quantification of style ................................................................................... 97 3.3.1 Orientation .......................................................................................... 97 3.3.2 Rotational length ................................................................................ 97 3.3.3 Curvilinearity ....................................................................................... 98 3.3.4 Irregularity .......................................................................................... 98 3.3.5 Width of paths and spacing .............................................................. 100 3.4 Methods of comparison .............................................................................. 101 3.4.1 Summarisation of spiral form data ................................................... 101 3.4.2 Variable weighting ............................................................................ 104 3.4.3 Clustering .......................................................................................... 105 3.5 Summary ..................................................................................................... 106 Chapter 4 Background to the case studies .............................................................. 107 4.1 Choice of case studies ................................................................................. 107 4.2 Culturally dependent interpretation of decorative spirals ......................... 108 4.3 Background
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