L1PMA+L2WPMA / THE PARTHENON ART

NATIONAL TECHNICAL UNIVERSITY OF ATHENS SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING

ReENGINEERING THE ART THROUGH THE LENS OF L1PMA & L2WPMA:

THE ETERNAL YOUTH OF THE PARTHENON ART Architecture, Marble Sculpture, Metallurgy & Pottery

vol. 3

Dr. ATHANASIOS G. LAZAROPOULOS

Dr. Athanasios G. Lazaropoulos email: AGLazaropoulos@gmail.com Dec. 2014 The cover synthesis is based on Caryatids (Korai) of the Acropolis Museum

Introduction Piecewise Monotonic data Approximation (PMA) methods have been introduced by Demetriou and Powell [1]-[3]. Among the various methods proposed to perform PMAs over the years, Demejriot’s L1PMA and L2WPMA have recently made their debut in artistic fields [4], [5].

By applying PMAs across rows and lines of images assuming a predefined number of monotonic sections, digital visual works of the real life reveal a more subversive artistic character.

In this art book, the previous aesthetic experience of applying L1PMA and L2WPMA in photographs and paintings is further elaborated. Actually, the visual result of PMAs in monochrome pictures has recently attracted flattering comments by photograph artists and, here, these two PMA methods are mainly focused on this black-white transformation; the PMA transformation of the sublime ancient Greek art. Pottery, metal vessels, figurines, monumental sculptures, architectural monuments and coins define the protagonists of this art book.

Concluding this Introduction, the knowledge light of the ancient Greek art is combined with the modern pure mathematics of L1PMA and L2WPMA creating a seductive engineering-based artistic view.

Valuable material has been collected by Acropolis Museum and British Museum [6], [7].

The Parthenon The Monument Once the Sacred Rock of Acropolis had been cleared of the ruins left behind from the Greco-Persian Wars, the Athenians created an architectural miracle in order to symbolize and reflect their dominance over the ancient world: The Parthenon.

PMA method: L1PMA Number of monotonic sections: 2, 3 and 4 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Grayscale and Multicolor

The Parthenon The Pediments The pediments are the triangular spaces formed by the horizontal and raking cornices of the roof at each end of the Parthenon. Actually, the pediments were the last parts of the temple that were able to receive sculptural decoration

View of the west pediment of the Parthenon

PMA method: L1PMA Number of monotonic sections: 3 and 5 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Multicolor

Pediments comprised colossal statues in the round and the themes were drawn from Attic mythology PMA method: L1PMA Number of monotonic sections: 5 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 4 pixels Color: Multicolor

The east pediment depicted the birth of the Goddess Athena from the head of her father The west pediment illustrates the dispute between Athena and Poseidon for the claim of the land of Attica PMA method: L2WPMA Number of monotonic sections: 10 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 5 pixels Color: Grayscale

The Parthenon The Metopes There were 92 metopes. Metopes were the first parts of the entablature to receive sculptural decoration. Each one reproduced a self-contained scene that has been taken from legendary battles. In fact, these scenes symbolized significant victories of the Athenians and their Gods.

Scene from the Gigantomachy where Hermes defeats a giant PMA method: L2WPMA Number of monotonic sections: 3, 5 and 7 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Multicolor

The Parthenon The Frieze In contrast to the mythological subjects of the metopes and pediments, on the Parthenon frieze, the sculptor of the Parthenon (Pheidias) chose to depict the greatest festival of the city in honor of the Goddess Athena: the Great Panathenaia

View of the west and south frieze of the Parthenon

PMA method: L2WPMA Number of monotonic sections: 7 and 11 Approximation polarization: Horizontal Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Multicolor

The Propylaia Erechtheion In the Propylaia stood works of art made by great sculptors. The area around the Erechtheion was considered as the most sacred place of the Acropolis. The Erechtheion was a complex marble building in the Ionic order, an exceptional artwork

The Caryatids from the south porch of the Erechtheion

PMA method: L1PMA Number of monotonic sections: 3, 4 and 6 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Multicolor

Rear view of the Caryatids from the south porch of the Erechtheion PMA method: L1PMA Number of monotonic sections: 4 and 6 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Grayscale

The city of Athens, the Erechtheion and Caryatids

PMA method: L2WPMA Number of monotonic sections: 3, 5 and 7 Approximation polarization: Mixed Contrast: Yes Real/Approximation residual: No Cube dimension: 1 pixel Color: Multicolor

A caryatid is a sculpted female figure serving as an architectural support On the Parthenon, caryatids take the place of columns supporting the entablature on their heads

PMA method: L1PMA Number of monotonic sections: 5 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Grayscale

The Gallery of the Slopes of the Acropolis Sanctuaries The slopes, caves and plateaus of the Acropolis hill were the settings in which gods, heroes and nymphs were worshipped in their sanctuaries

Clay spindle whorls, dedications of women to the sanctuary of the Nymphe PMA method: L1PMA Number of monotonic sections: 3, 5, 7 and 9 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Grayscale

PMA method: L1PMA Number of monotonic sections: 9, 11 and 13 Approximation polarization: Horizontal Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Multicolor

Clay Nike (Acroterion) PMA method: L1PMA (top) and L2WPMA (down) Number of monotonic sections: 3 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 2 (left) and 5 (right) pixels Color: Grayscale and Multicolor

The Archaic Gallery Hekatompedon Archaic is the period that is characterized by the development of the city-state and the great achievements in the economy, art and intellectual life. At the same time, the transition from aristocracy to democracy started to occur

PMA method: L1PMA (top) and L2WPMA (down) Number of monotonic sections: 2 (top) and 6 (down) Approximation polarization: Vertical (top) and Horizontal (down) Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Grayscale

The Votives Archaic The site of the Acropolis was filled with votive offerings, dedicated to the Goddess PMA method: L1PMA Number of monotonic sections: 2-5 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Grayscale

These votives are considered to be tokens of piety and marks of financial and artistic development PMA method: L2WPMA Number of monotonic sections: 5, 7 and 9 Approximation polarization: Horizontal Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Grayscale

The Persian or Scythian horseman PMA method: L1PMA Number of monotonic sections: 5 and 7 Approximation polarization: Horizontal Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Grayscale

The “Kore vijh jhe exes of a sphinw”

PMA method: L1PMA Number of monotonic sections: 2-6 Approximation polarization: Vertical Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Multicolor

The Votives Classical & Hellenistic These votives are among the most precious offerings of the Acropolis.

PMA method: L1PMA Number of monotonic sections: 4, 6, 8 and 10 Approximation polarization: Horizontal Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Grayscale

The votives of Classical and Hellenistic periods depict gods, heroes and mortals from the legendary and historical past of Athens like the head of youthful statue of Alexander the Great PMA method: L2WPMA Number of monotonic sections: 2 and 4 Approximation polarization: Vertical Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Multicolor

The Parthenon Marbles in British Museum East Pediment PMA method: L2WPMA Number of monotonic sections: 3 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Grayscale

The Parthenon Marbles, also known as the Elgin Marbles, are a collection of Classical Greek marble sculptures that originally were part of the temple of Parthenon and other buildings on the Acropolis of Athens

Parthenon Selene Horse PMA method: L2WPMA Number of monotonic sections: 1-7 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Grayscale

Section of Frieze

PMA method: L1PMA Number of monotonic sections: 5 and 7 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 3 pixels Color: Multicolor

Statuaries from the Pediments

PMA method: L2WPMA Number of monotonic sections: 7 Approximation polarization: Mixed Contrast: No Real/Approximation residual: No Cube dimension: 1 pixel Color: Grayscale

Athens is one of the oldest named cities in the world.

Athens became the leading city of Ancient Greece while its cultural achievements during the 5th century BC laid the foundations of jodax’s western civilization

References [1] I. C. Demejriot and M. J. D. Povell, “Leasj sqtares smoojhing of tniuariaje daja jo achieue piecevise monojonicijx”, IMA J. of Numerical Analysis, vol. 11, pp. 411-432, 1991.

[2] I. C. Demejriot, “L1PMi: i Forjran 77 Package for Besj L1 Piecevise Monojonic Daja Smoojhing”, Computer Physics Communications, vol. 151, no. 1, pp. 315-338, 2003.

[3] I. C. Demejriot, “Algorithm 863: L2WPMA, a Fortran 77 package for weighted least-squares piecewise monotonic data approximation." ACM Transactions on Mathematical Software (TOMS), vol. 33, no. 1, pp 1-19, Mar. 2007.

[4] http://issuu.com/lazaropoulos/docs/l1pma [5] http://issuu.com/lazaropoulos/docs/l2wpma [6] http://www.theacropolismuseum.gr/ [7] http://www.britishmuseum.org/