Un enfoque computacional para el análisis de composiciones artísticas

Los nuevos enfoques que surgen del análisis de obras de arte con herramientas computacionales tienen el potencial de ofrecer diferentes perspectivas a las obras de arte recreadas en medios digitales. Este artículo pretende revelar las relaciones implícitas entre las composiciones de Mondrian con diferentes representaciones visuales. En el ámbito del estudio, las composiciones completadas entre 1938 y 1943, que tienen una fuerte relación geometría-color, se investigaron primero a través de un enfoque basado en píxeles. En el método de fragmentación empleado a seguir, las similitudes y diferencias se expresan con datos transferidos de píxeles a matrices numéricas en dos pasos diferentes: 1) Entre los artefactos en pares, y 2) Entre un artefacto y todos los demás artefactos seleccionados. La visualización de las matrices estuvo representada por mapas de color 2D y mapas de textura 3D. Estos estilos de interpretación permiten que las composiciones se expresen de lo general a lo específico y nuevamente de lo específico a lo general, adquiriendo un nuevo significado.Novas abordagens emergem da análise de obras com ferramentas computacionais e têm potencial para oferecer diferentes perspectivas para obras recriadas em ambientes digitais. Este estudo visa revelar as relações implícitas entre as composições de Mondrian com diferentes representações visuais. No âmbito do estudo, as composições concluídas entre 1938 e 1943, que possuem uma forte relação geometria-cor, foram discutidas pela primeira vez com uma abordagem baseada em pixels. No método de fragmentação seguido, as semelhanças e diferenças são expressas com dados transferidos de pixels para matrizes numéricas em duas etapas distintas: 1. Entre os artefatos em pares, 2. Entre um artefato e todos os outros artefatos selecionados. A visualização das matrizes foi representada por mapas de cores 2D e mapas de texturas 3D. Esses estilos de interpretação permitem que as composições sejam expressas do geral para o específico e novamente do específico para o geral, ganhando um novo significado.New approaches emerging from the analysis of artworks with computational tools have the potential to offer different perspectives to artworks recreated in digital environments. This study aims to reveal the implicit relationships between Mondrian compositions with different visual representations. In the scope of the study, compositions completed between 1938 and 1943, which have a strong geometry-color relationship, were first investigated through a pixel-based approach. In the fragmentation method followed, the similarities and differences are expressed with data transferred from pixels to numerical matrices in two different steps: 1. Between the artifacts in pairs, 2. Between an artifact and all the other selected artifacts. The visualization of the matrices was represented by 2D color maps and 3D texture maps. These interpretation styles allow the compositions to be expressed from general to specific and again, from specific to general, by gaining a new meaning

Diffusion on middle-ξ Cantor sets

In this paper, we study C^ζ -calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in terms of standard calculus, so we must involve local fractional derivatives. We have generalized the C^ζ -calculus on the generalized Cantor sets known as middle-ξ Cantor sets. We have suggested a calculus on the middle-ξ Cantor sets for different values of ξ with 0 < ξ < 1. Differential equations on the middle-ξ Cantor sets have been solved, and we have presented the results using illustrative examples. The conditions for super-, normal, and sub-diffusion on fractal sets are given

Kolmogorov compression complexity may differentiate different schools of Orthodox iconography

The complexity in the styles of 1200 Byzantine icons painted between 13th and 16th from Greece, Russia and Romania was investigated through the Kolmogorov algorithmic information theory. The aim was to identify specific quantitative patterns which define the key characteristics of the three different painting schools. Our novel approach using the artificial surface images generated with Inverse FFT and the Midpoint Displacement (MD) algorithms, was validated by comparison of results with eight fractal and non-fractal indices. From the analyzes performed, normalized Kolmogorov compression complexity (KC) proved to be the best solution because it had the best complexity pattern differentiations, is not sensitive to the image size and the least affected by noise. We conclude that normalized KC methodology does offer capability to differentiate the icons within a School and amongst the three Schools

Fluid Dynamics of Watercolor Painting : Experiments and Modelling

In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington\u27s experiments has now been clarified. One specific set of such recent studies, which motivates this thesis, concerns the fluid dynamics behind Jackson Pollock\u27s drip paintings. The physical processes and the mathematical structures hidden in his works have received serious attention and have made the scientific pursuit of art a compelling area of exploration. Our current work explores the interaction of watercolors with watercolor paper. Specifically, we conduct experiments to analyze the settling patterns of droplets of watercolor paint on wet and frozen paper. Variations in paint viscosity, paper roughness, paper temperature, and the height of a released droplet are examined from time of impact, through its transient stages, until its final, dry state. Observable phenomena such as paint splashing, spreading, fingering, branching, rheological deposition, and fractal patterns are studied in detail and classified in terms of the control parameters. Using the one-dimensional (1-D) Saint-Venant differential equations, which are a simplification of the three-dimensional (3-D) Navier-Stokes equations from fluid dynamics, we created a computer-simulated, mathematical model of a droplet splash of watercolor paint onto a flat surface. The mathematical model is analyzed using a MATLAB code which considered changes in droplet height, radius, and velocity of dispersal over time. We also implemented a stochastic version of the Saint-Venant equations which captured the random fingering patterns of a droplet splash. Initial conditions for height, radius, and velocity of a radially spreading droplet were given at the onset of the simulation. Dynamic viscosity and fluid density were parameters incorporated into this system of differential equations, which could be easily adjusted in the MATLAB code for the paint type to be simulated. The stochastic nature of our model was designed to recreate the complex behavior of water splashes, the non-homogeneity of the watercolor paper, and the resulting patterns. We then computed the fractal dimension of each computer-generated droplet image to compare theoretical and experimental values. Analysis of the set of data consisting of over 10,000 trials was conducted to determine any significant statistical correlations among the spreading pattern, the number of fingers, viscosity, density and fractal dimension. Finally, we extended the system of differential equations based on the Saint-Venant equations to include the effects of temperature upon the paint-spreading pattern. In a similar manner, we compared the theoretical values of fractal dimensions generated by our MATLAB model to the experimental results for paint droplets on a frozen substrate

Integrating holism and reductionism in the science of art perception

The contextualist claim that universalism is irrelevant to the proper study of art can be evaluated by examining an analogous question in neuroscience. Taking the reductionist-holist debate in visual neuroscience as a model, we see that the analog of orthodox contextualism is untenable, whereas integrated approaches have proven highly effective. Given the connection between art and vision, unified approaches are likewise more germane to the scientific study of ar

Music and time: tempomorphism: nested temporalities in perceived experience of music.

This thesis represents the results of a theoretical and practical investigation of acoustic and electro-acoustic elements of Western music at the start of the twentyfirst century, with specific attention to soundscapes. A commentary on the development of soundscapes is drawn from a multidisciplinary overview of concepts of time, followed by an examination of concepts of time in music. As a response to Jonathan Kramer's concept of `vertical' music (a characteristic aesthetic of which is an absence of conventional harmonic teleology), particular attention is paid to those theories of multiple nested temporalities which have been referred to by Kramer in support of non-teleological musical structures. The survey suggests that new musical concepts, such as vertical music, have emerged from sensibilities resulting from the musical and associated styles of minimalism, and represent an ontological development of aesthetics characteristic of the twentieth century. An original contention of the debate is that innovations in the practice of music as the result of technological developments have led to the possibility of defining a methodology of process in addition to auditive strategies, resulting in a duality defined as 'tempomorphic'. Further observations are supplied, using findings derived from original creative practical research, to define tempomorphic performance, which complete the contribution to knowledge offered by the investigation. Tempomorphism, therefore, is defined as a duality of process and audition: as auditive tool, tempomorphic analysis provides a listening strategy suited to harmonically static music; as a procedural tool, it affords a methodology based primarily on duration

Music and time : tempomorphism : nested temporalities in perceived experience of music

This thesis represents the results of a theoretical and practical investigation of acoustic and electro-acoustic elements of Western music at the start of the twentyfirst century, with specific attention to soundscapes. A commentary on the development of soundscapes is drawn from a multidisciplinary overview of concepts of time, followed by an examination of concepts of time in music. As a response to Jonathan Kramer's concept of 'vertical' music (a characteristic aesthetic of which is an absence of conventional harmonic teleology), particular attention is paid to those theories of multiple nested temporalities which have been referred to by Kramer in support of non-teleological musical structures. The survey suggests that new musical concepts, such as vertical music, have emerged from sensibilities resulting from the musical and associated styles of minimalism, and represent an ontological development of aesthetics characteristic of the twentieth century. An original contention of the debate is that innovations in the practice of music as the result of technological developments have led to the possibility of defining a methodology of process in addition to auditive strategies, resulting in a duality defined as 'tempomorphic'. Further observations are supplied, using findings derived from original creative practical research, to define tempomorphic performance, which complete the contribution to knowledge offered by the investigation. Tempomorphism, therefore, is defined as a duality of process and audition: as auditive tool, tempomorphic analysis provides a listening strategy suited to harmonically static music; as a procedural tool, it affords a methodology based primarily on duration.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Mathematical surfaces models between art and reality

In this paper, I want to document the history of the mathematical surfaces models used for the didactics of pure and applied “High Mathematics” and as art pieces. These models were built between the second half of nineteenth century and the 1930s. I want here also to underline several important links that put in correspondence conception and construction of models with scholars, cultural institutes, specific views of research and didactical studies in mathematical sciences and with the world of the figurative arts furthermore. At the same time the singular beauty of form and colour which the models possessed, aroused the admiration of those entirely ignorant of their mathematical attraction

Aesthetic complexity: practice and perception in art & design

My research investigates the aesthetics of visual complexity in the practice and perception of visual art and design. The aim is to understand visual complexity in terms of the relationship between the objective properties of images and subjective properties of perception. I take a computational and empirical approach to this subject, incorporating methods from information theory, computer graphics, complexity theory and experimental psychology. For testing, I create cellular automata programs to generate stimulus images, and borrow other types of visual material from students and professional artists, designers and craftspeople. Visual complexity is measured in two ways: Firstly, an objective measure of complexity is based on the compression of digital image files, which provides an information-based scale of order to randomness. Secondly, psychophysical techniques are employed to measure the subjective complexity of the images and other aesthetic judgements. Research in complex systems theory and experimental aesthetics suggests that we can expect an inverted ‘U’ correlation between the two measures of complexity

Art and the unconscious : a semiotic case study of the painting process

This dissertation is an attempt to design an interpretation model for the comprehension of unconscious content in artworks, as well as to find painting techniques to free the unconscious mind, allowing it to be expressed through artwork. The interpretation model, still in its infancy, is ripe for further development. The unconscious mind is a fascinating subject—in art production as well as in many scientific fields. This hidden part of the mind, being the source of creativity, constitutes an important foundation for many possible and valuable inquiries in multiple areas of knowledge. In the present study, the unconscious is approached from an art-educational perspective. The nature of the unconscious is addressed through the theories of Carl Gustav Jung and Charles Sanders Peirce, as well as through the information gained from data the author produced herself during the experimental painting process she devised for this study. For psychological distinctions not addressed by Jung, the theories of Sigmund Freud are used to forward this inquiry into the unconscious mind. A research method was created to bring Peirce’s theories into consonance with Jung’s amplification method. Since Peirce’s theories are challenging to read, to avoid misinterpretation, the author used Phyllis Chiasson’s 2001 book Peirce’s Pragmatism: The Design for Thinking as a secondary source. Peirce’s three modes of reality—firstness, secondness, and thirdness—were utilized to interpret artworks. This three-mode reality allows interpreters to reflect on their subjective feelings and then to compare them to collected data. The interpreters’ intuitive self-interpretations often correlate well with the more objective data. In this approach to interpretation, the work of art is seen as a sign, in the Jungian as well as in the Peircean sense, and interpretation seeks to discover a sign’s objects—icon, index, and symbol. Additionally, the objects are studied in combination with Peirce’s designation of the sign’s character elements—sinsign, qualisign, and legisign. Peirce’s theory offers a logical and productive structure for approaching a variety of signs and reaching a multiplicity of interpretations. Jungian theories inculcated a combined psychological and artistic perspective for the interpretation of artworks. Jung’s method of amplification is an effort to bring a symbol to life, and it is used as a technique to discover—through the seeking of parallels—a possible context for any unconscious content that an image might have. In amplification, a word or element—from a fantasy, dream, or, in this study, artwork—is associated, through use of what Jung called the active imagination, with another context where it also occurs. It must be remembered that unconscious images in artworks do not easily open themselves up for interpretation. One way to interpret possibly unconscious images is for the interpreter to become vulnerable by employing his or her own unconscious mind to interpret an artwork; such use of the active imagination can enable a subjective experience of the artwork on the part of the interpreter, who might thereby uncover unconscious content. Moreover, in this study, Jung’s theory of archetypes is employed, in parallel with Peirce’s and Jung’s theories of the sign, to illuminate an artwork’s images by connecting them with collective unconscious archetypes. The author relied upon The Book of Symbols: Reflections on Archetypal Images (Ronnberg and Martin 2010) as the main source for interpreting possibly unconscious elements in the artworks. This approach is especially powerful when artists interpret their own artwork—possibly leading to a galvanizing self-discovery as they revisit past encounters, personal highlights, and other pieces of unconscious content that might reveal previously unknown meaning important to their life. By comparing archetypes to the unconscious content in their own lives, people can discover themselves. Unconscious phenomena were approached on both the theoretical and empirical levels. Different methods and ideas were used to stimulate the author’s unconscious thinking while performing artwork analyses of three paintings: surrealist Salvador Dalí’s (1904–1989) Assumpta Corpuscularia Lapislazulina; abstract expressionist Jackson Pollock’s (1912-1956) The Deep; and one painting by the author herself, and for which the process of painting is videorecorded (www.astagallery.com/academic.html). With regard to the third painting interpreted, the author is the study subject, and her artistic production is used as an opportunity to explore the unconscious mind. During the act of painting, an attempt is made to free unconscious thinking by fusing Dalí’s and Pollock’s methods as well as by testing multiple other methods. The author’s artistic production was conjoined with use of a technique that is called the verbal protocol method, which generates additional data not necessarily visible in the final artwork. This method unseals the artist’s tacit knowledge, which in normal circumstances remains silent. In the verbal protocol method, the author, while engaged in the act of painting, speaks aloud the stream of consciousness that accompanies and guides the art-making activity; the recorded and transcribed monologue from the artistic production is supplied, in both Finnish and English, in appendices. This thinking-aloud technique allows a person to become more self-aware and to create more solutions while struggling with emergent artistic problems. Such narratives can reveal more about the painting than the completed artwork alone can convey. Along with the artist’s finished painting and the videorecorded material, narratives produced during the painting activity were interpreted. Moreover, the discoveries arising from the author’s interpretation of her own artwork are correlated with some of the latest research on the unconscious. This study allows the reader-viewer an intimate glimpse into the author’s subjective painting experience and demonstrates the participation of the unconscious in an artwork’s creation. The interpretations methodology constitutes an interpretation model suitable for other artists and art educators to follow. Keywords: unconscious, art, archetype, mandal