The Geometric Forms: orbital and wheelbase-based motion with chaotic terms

The advance of modern technology and computing instruments has made the plastic art of materials and tools in various dimensions possible. In activities of plastic art, the graphic design is called the two-dimensional art, suggesting the artistic activities happen in a 2D space, while the stereoscopic design implies that the artistic form exists in a 3D space. In this case, if the timeline is added to keep records of the graphic motion, this may be also considered a 4D graphic design. Such an artistic genre is regarded as Kinetic Art/Sculpture as well (Lin, 1999). For example, the prominent Russian sculptor of Constructivism, Gabo (1920), has made use of thin long wires to create his famous kinetic sculpture, Standing Wave. This sculpture was vibrating motor-driven by generating a significant oscillation on the strings so that the long still wires can be in the form of curves because of the physical energy seen as Figure 1(a). In the history of Western arts, futurism is seen as people’s rebellion against the artistic phenomenon at that time as well as an inspiration of new ideology. It rises from literary movement in 1909 when Marinetti advocated the termination of all traditional arts and the establishment of a novel genre integrating arts with the living pace of machine era. As soon as the futurism came into being, it soon spread to influence the creation of all fields, such as arts, music, drama, movie, and photography. Futurists are obsessed with the aesthetics of motion and speed, preferring machines and technology to traditional arts. Therefore, they devote themselves in presenting the motion, speed, and the transformation process of objects. In a futurist painting, spatial concept exists no more and the object is never still. Moreover, the objects are moving and intersecting without a stop. Futurism is deeply affected by post-impressionism and cubism. Though it has borrowed numerous features of cubism, futurism still preserves its own uniqueness. For instance, cubism is composed of geometric pictures in a still manner. By decomposing and reconstructing, cubism presents the static aesthetics of machinery. However, futurism focuses on motion and change. It decomposes the movement into fragments, blending them with the development of time to demonstrate the beauty of speed (Shlain, 1993) seen as Figure 1(b). This is a creation of Balla in 1912, named Dynamism of a Dog on a Leash. The walking of dog and the swinging of leash tied on the dog’s neck overlap each other in one single space so that the dog appears to have more than four legs and the leash presents to be more than a curve. Seen as Figure 1(c) is a work created by Duchamp in 1912 and the work is called Nude Descending a Staircase. This creation successfully reproduces the posture of a nude lady walking downstairs in superimposition. Similarly, in Figure 1(d) shows another work of Duchamp in 1923. This time, the artist creates Revolving Glass out of bicycle wheels to demonstrate how the objects are superimposed and integrated as the time evolves. Both these two works present similar expression and concept of the physical features in space. Figure 1: Kinetic Sculpture and Futurism: the aesthetics of motion and change and the beauty of speed To sustain the concept of futurism, any straight lines in a 2D space can be regarded as the collection of a certain vertex moving from the beginning to the termination. Its movement seems to take the geometric forms of relative motion. The geometric forms of relative motions are the digital art forms developed by the researcher over the recent years (Anonymous, 2010, 2012; Anonymous, 2005, 2006). Papers have been published on orbital, polygonal wheelbase, pursuit and weight relative motion digital art forms. The study aimed at investigating the combinations of the relative motion: orbital and wheelbase-based motion which were implemented by chaotic terms, developing a systematic model to control its motion parameters, analyzing how the parameters affect its process of motion, and finally discovering the geometric art forms generated by computing the parameters. Wheelbase-based Motion suggests that the trajectory appears in a straight and direct pattern of motion according to the structures of objective coordinate system, moving back and forth in a two-dimensional space from the beginning to the termination. In order to convenience of research, the study had developed the Relative Motion Creator (RMC) as the study tool to investigate the combinations of orbital and wheelbase-based motion so that it may compile the model of wheelbase-based motion with chaotic terms, complete its motion structure, and operate its motion parameters. The RMC provides the functions of editing relative motion type and motion structure, recursive motion, manipulating motion parameters, editing chaotic term structure, investigating form variations, trajectory computation, color setting and visualization, as well as uploading RMD (Relative Motions Data) to server sharing platform, and the data can be downloaded directly. In RMC, the most simplified relative motion system can be regarded as the concept shown in Figure 2; one fundamental coordinate system contains a subjective and an objective system. Moreover, one of five motion types can be defined between two systems. The RMC tool could be downloaded at http://can.elt.nhcue.edu.tw/cgflab/download.html (a) Gabo(1920) (b) (Balla, 1912) (c) (Duchamp, 1912) (d) (Duchamp, 1923)