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Fractal Analysis Applied to Ancient Egyptian Monumental Art

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Fractal Analysis Applied to Ancient Egyptian Monumental Art FRACTAL ANALYSIS APPLIED TO ANCIENT EGYPTIAN MONUMENTAL ART by Jessica Robkin A Thesis Submitted to the Faculty of The Dorothy F. Schmidt College of Arts and Letters in Partial Fulfillment of the Requirements for the Degree of Master of Arts Florida Atlantic University Boca Raton, Florida December 2012 Copyright by Jessica Robkin 2012 ii ACKNOWLEDGEMENTS The following research paper would not be possible without the patience and understanding of my thesis committee. I am thankful for their invaluable insights, education, and support during my studies. I am particularly grateful to Dr. Clifford T. Brown for helping me to find a path of research that allowed me to do credible and important work. Thank you for introducing me to fractals, for showing me a way to bridge the gap between science and subjectivity, and for helping me every step of the way. Lastly, great thanks go out to my loved ones, whose faith has never wavered. iv ABSTRACT Author: Jessica Robkin Title: Fractal Analysis Applied to Ancient Egyptian Monumental Art Institution: Florida Atlantic University Thesis Advisor: Dr. Clifford T. Brown Degree: Master of Arts Year: 2012 The study of ancient Egyptian monumental art is based on subjective and qualitative analyses by art historians and Egyptologists who use the change in stylistic trends as Dynastic chronological markers. The art of the ancient Egyptians is recognized the world over due to its specific and consistent style that lasted the whole of Dynastic Egypt. This artwork exhibits fractal qualities that support the applicability of applying fractal analysis as a quantitative and statistical tool to be used in this field. In this thesis, I show the fractality of ancient Egyptian monumental art by analyzing black and white line drawings of twenty-eight separate bas-reliefs with three separate programs: Benoit 1.3, ImageJ, and Fractal3e. After preparing the images with GIMP2 software – used to remove non-original lines – I analyzed each image using the fractal box-counting analysis function in the above programs and calculated their fractal dimension, D. The resulting fractal dimension supported the consistency visually identified in the artwork from ancient Egypt, both chronologically and geographically. v FRACTAL ANALYSIS APPLIED TO ANCIENT EGYPTIAN MONUMENTAL ART LIST OF TABLES ..................................................................................................... viii LIST OF FIGURES ..................................................................................................... ix CHAPTER 1. INTRODUCTION AND PROBLEM STATEMENT ............................1 CHAPTER 2. ESSENTIAL CHARACTERISTICS OF ANCIENT EGYPTIAN ART4 CHAPTER 3. ARTISTIC CHANGES IN ANCIENT EGYPTIAN ART ...................14 Old Kingdom, First Intermediate Period Artistic Changes ...................14 Middle Kingdom, Second Intermediate Period Artistic Changes ........16 New Kingdom, Amarna Period Artistic Changes .................................20 Third Intermediate Period, Late Period Artistic Changes .....................23 Graeco-Roman Period Artistic Changes ...............................................24 CHAPTER 4. GEOGRAPHY AND GEOGRAPHIC VARIATION ..........................27 CHAPTER 5. QUANTITATIVE APPROACHES TO ART ......................................30 CHAPTER 6. MATERIALS AND METHODS .........................................................37 CHAPTER 7. RESULTS .............................................................................................43 vi CHAPTER 8. DISCUSSION .....................................................................................124 CHAPTER 9. CONCLUSION...................................................................................134 REFERENCES CITED .............................................................................................136 vii LIST OF TABLES 1. Ancient Egyptian Chronology ...............................................................................5 2. Analysis Results Listed Chronologically ...........................................................123 3. Benoit 1.3, ImageJ, Fractal 3e Data Correlation ................................................126 4. Benoit 1.3 ANOVA Single Factor Results ........................................................129 5. ImageJ ANOVA Single Factor Results .............................................................129 6. Fractal3e ANOVA Single Factor Results ..........................................................129 viii LIST OF FIGURES 1. Ramesses III Battle with the Maritime Nations, Medinet Habu ...................3 2. Limestone Relief from the Chapel of Seti I, 19th Dynasty ............................6 3. Ancient Egyptian Artist Gridlines ...............................................................8 4. Mastaba of Ptah-Hotep, 5th Dynasty, Relief Showing Funerary Offerings ...................................................................................10 5. Black Granite Statue of Amenemhat I, 12th Dynasty ..................................13 6. Examples of Theban Art Style ....................................................................18 7. Canonical Line Grid ....................................................................................19 8. Archaeological Map of Ancient Egypt ......................................................29 9. Illustration of the First Six Iterations of the Middle Third Cantor Set .......................................................................................34 10. The Narmer Palette, Predynastic Period, 0/1st Dynasty ...............................44 11. Scatter Plot of Benoit Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Narmer Palette Obverse .........................................................................................45 12. Scatter Plot of ImageJ Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Narmer Palette Obverse ........................................................................................46 13. Scatter Plot of Frac3 Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Narmer Palette Obverse ........................................................................................46 14. Scatter Plot of Benoit Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes - Narmer Palette Reverse.........................................................................................47 ix 15. Scatter Plot of ImageJ Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes - Narmer Palette Reverse.........................................................................................48 16. Scatter Plot of Frac3 Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes - Narmer Palette Reverse.........................................................................................48 17. Menes Tablet, Predynastic Period, 1st Dynasty ..........................................49 18. Scatter Plot of Benoit Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Menes Tablet ...................50 19. Scatter Plot of ImageJ Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Menes Tablet ...................50 20. Scatter Plot of Frac3 Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Menes Tablet ...................51 21. Mastaba of Meresankh III, Old Kingdom, 4th Dynasty - Main Room, East Wall, South of Entrance ..............................................52 22. Scatter Plot of Benoit Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Mastaba of Meresankh III, Main Room East Wall, South of Entrance .......................53 23. Scatter Plot of ImageJ Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Mastaba of Meresankh III, Main Room East Wall, South of Entrance .......................54 24. Scatter Plot of Frac3 Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Mastaba of Meresankh III, Main Room East Wall, South of Entrance .......................54 25. Mastaba of Meresankh III, Old Kingdom, 4th Dynasty - South Door Jamb......................................................................................55 26. Scatter Plot of Benoit Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Mastaba of Meresankh III, South Door Jamb.............................................................56 27. Scatter Plot of ImageJ Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Mastaba of Meresankh III, South Door Jamb.............................................................57 x 28. Scatter Plot of Frac3 Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Mastaba of Meresankh III, South Door Jamb.............................................................57 29. Tomb Chapel of Werirenptah, Old Kingdom, 5th Dynasty .........................58 30. Scatter Plot of Benoit Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Tomb of Werirenptah ......59 31. Scatter Plot of ImageJ Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Tomb of Werirenptah ......59 32. Scatter Plot of Frac3 Data Showing the Logarithms of the Box Sizes and Number of Occupied Boxes – Tomb of Werirenptah ......60 33. Mastaba of Sekhemka, Old Kingdom, 5th Dynasty - East Wall, South Section..........................................................................61 34. Scatter
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