1. Introduction

The purpose of this study is to explore new methods of creating forms. Relative motions seem to be a promising mechanism in this regard. Findings from earlier studies suggest that the trajectories of multiple-level relative motions can result in highly unpredictable complex shapes. Furthermore, these shapes may turn out to be visually appealing with proper colorization according to their frequencies of visits. Different kinds of motions, as well as various combinations of those motions, have been experimented in this study. The expectation, although unrealistic, is to come up with something as unique and overwhelming as the fractal images created by Mandelbrot (Mandelbrot, 1978).

There are many interesting forms in nature, among them nautilus and snow flakes might be the most well-known. Astonishing harmony of mathematics and aesthetics can be found in these forms that they seem to be created by certain mystical and formidable power. Although we do not know what that power is, form creation in itself can be highly fascinating.

A geometric form can be regarded as the trajectory of a point moving in space. A horizontal line is regarded as the trajectory of a point moving from left to right or from right to left, or a circle if the point orbits another point with equal distance on a plane.

It would be easier to predict the geometric form if object's movement is based on static coordinate system. However, if the coordinate system itself is also moving, the trajectory could become complicated and unpredictable. For instance, the trajectory of a basketball's motion is vertical if the player stands still. The trajectory of the ball becomes a unique curve (in this case a parabola) when the player runs. The velocity of the player also influences the trajectory.

Mathematics and physics might be useful tools for creating complex geometric forms. The fractal images of Mandelbrot Set is an example. The pictures are extremely complex, but the underlying rules are relatively simple. The possibilities are practically endless, and they call for further and deeper exploration.

Pencil drawing, oil painting, sculpture, and architecture etc. are all different methods to create forms. It is relatively easy to create new forms with one of these existing methods. It is, however, highly difficult to create a new method in itself. For that we should pay homage to Mandelbrot and Asakura for their pioneer researches on fractals and light constitution. The images they showed to the world are so overwhelming that they encourage us to set sail for different possibilities.It appeared to us that chaotic relative motions might turn out to be another new method to create forms. This new method may benefit the fields of arts and design in the future. When that becomes the case, the significance of this study will be self-evident.

Since the images are trajectories of relative motions, they vary in time. It has always been very difficult to determine the most appropriate time to obtain the best image. Furthermore, the trajectories were recorded in pixels on computer screen. The images obtained are all bit-mapped with the resolution of 72 dpi. As a result, the size of the images is strictly limited.

Different combinations of relative motions lead to different images. Even different parameters of the same motions result in tremendous differences. There are simply too many variables to manipulate that the possibilities are endless. This fact can be sometimes quite bewildering, because there seemed no way to tell where or when to stop a journey.

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