Mathematical Art Research Papers - Academia.edu (original) (raw)
The role of geometry in human movement is not as evident as the presence of geometric configurations in art, architecture and design. In this paper, I summarize how my research on geometric configurations transitioned, from theoretical... more
The role of geometry in human movement is not as evident as the presence of geometric configurations in art, architecture and design. In this paper, I summarize how my research on geometric configurations transitioned, from theoretical explorations and computational design, to built objects and movement practices. The geometric properties of the icosahedron, one of the five regular polyhedra, are applied to interpret the proportions of the human body, guiding and inspiring movements leading to mindfulness. Introduction: The Geometry of Movement Galileo Galilei poetically defined the universe as “written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures” [1]. Mathematics and geometry are essential in the understanding of the physical world, not only as foundation of science, but also as components in the human-made world and the built environment. Geometry is not only a means in physical sciences but also guides and inspires arti...
Resumen: En este artículo se menciona cómo el resurgimiento del estudio de los Conjuntos de Julia se dio gracias a la difusión de las computadoras personales y luego se propone la vía artística para aumentar y enriquecer la imagen mental... more
Resumen: En este artículo se menciona cómo el resurgimiento del estudio de los Conjuntos de Julia se dio gracias a la difusión de las computadoras personales y luego se propone la vía artística para aumentar y enriquecer la imagen mental sobre los Conjuntos de Julia. Esta vía incluye lo matemático, lo lúdico, lo artístico y lo computacional; y se argumenta que no son disjuntos ni disociados a pesar del rechazo general por parte de las comunidades académicas tradicionales y de las comunidades de críticos de arte. Después se mencionan algunas colecciones significativas de Arte Computacional o Arte Matemático Generado por Computadora, y finalmente se presentan cuatro creaciones artísticas basadas en Conjuntos de Julia a manera de ejemplo utilizando el lenguaje CFDG. Palabras clave: Graficación por Computadora, Fractales, Conjuntos de Julia, CFDG, contextfree, Arte Matemático, Arte Computarizado, Arte Matemático Generado por Computadora. Abstract: This article mentions how the resurgence of the study of Julia Sets was due to the diffusion of personal computers and then the artistic way is proposed to increase and enrich the mental image on Julia Sets. This way includes the mathematical, the playful, the artistic and the computational approach; and it is argued that they are not disjointed or dissociated approaches despite the general rejection by traditional academic communities and art critics communities. Some significant collections of Computational Art or Computer-Generated Mathematical Art are mentioned, and finally four artistic creations based on Julia Sets are presented as an example using the CFDG language.
Descripción Este es un jardín de plantas fractales rodeando un gran árbol cuadrado representando una Ceiba. He usado cuatro algoritmos recursivos determinísticos que dibujan «ramas que tienen ramas». Uno de los algoritmos divide sus ramas... more
Descripción Este es un jardín de plantas fractales rodeando un gran árbol cuadrado representando una Ceiba. He usado cuatro algoritmos recursivos determinísticos que dibujan «ramas que tienen ramas». Uno de los algoritmos divide sus ramas en dos ramas, otro divide sus ramas en tres ramas, otro en cuatro y el último en cinco ramas. Cada árbol también depende de una posición, ángulos de las ramas, tamaño, proporciones entre las ramas y sus ramas hijas, el número de subdivisiones (niveles), posición relativa de brote de las ramas hijas, y de un color. Description This is a garden of fractal plants surrounding a large square tree representing a Ceiba. I have used four deterministic recursive algorithms that draw "branches that have branches". One of the algorithms divides its branches into two branches, another divides its branches into three branches, another into four and the last into five branches. Each tree also depends on a position, divided branch angles, size, proportions between the branches and their daughter branches, the number of subdivisions (levels), relative positions of sprout of the daughter branches and color.
The role of geometry in human movement is not as evident as the presence of geometric configurations in art, architecture and design. In this paper, I summarize how my research on geometric configurations transitioned, from theoretical... more
The role of geometry in human movement is not as evident as the presence of geometric configurations in art, architecture and design. In this paper, I summarize how my research on geometric configurations transitioned, from theoretical explorations and computational design, to built objects and movement practices. The geometric properties of the icosahedron, one of the five regular polyhedra, are applied to interpret the proportions of the human body, guiding and inspiring movements leading to mindfulness.