遞迴性多層次相對運動之幾何圖樣研究

A Study on Geometric Patterns of Recursive Multiple-level Relative Motions

遞迴性多層次相對運動（Recursive Multiple-lever Relative Motion）之軌跡是結合物理運動、數學與視覺藝術三者特性的幾何形態，有別於眾所週知的Fractals Art與LOGO。本研究是在相對運動的基本型態下，建立具有遞迴特性的相對運動，以產生有趣、高度變化與兼具視覺美感的幾何圖樣。操控運動系統間的角度變量直接改變圖樣的形態，本研究先操控一般的角度變量以觀察圖樣的變化，再深入整理角度變量總合的關係性，並分成「調變各角度變量之比率變化」與「順時／逆時角度變量總和平衡」兩種模式，所獲得的幾何圖樣兼具複雜與秩序的形式。以藝術設計的觀點來看，運用遞迴性多層次相對運動所產生的軌跡造形，可以看到無窮盡的圖樣變化。另外探討其它運動型式之幾何軌跡，皆是未來持續研究的課題。

The purpose of this study is to develop methods to control geometric patterns created from trajectories of recursive multiple-level relative motions （R-MRM）. Earlier studies indicated that trajectories of R-MRM can be highly visually appealing, but to certain extend unpredictable. We started from systematically manipulating angular variance and observing according geometric patterns, followed by analyzing the mathematical relationship among individual angles. Research findings suggest that 'ratios of angular variances' and 'balance of total clockwise and counter-clockwise angular amounts'. From aesthetic point of view, recursive multiple-level relative motion can be a promising way of generating interesting patterns, and the possibilities are endless. There exist treasures that call for further exploration.