A Visual-Based Duplication of Self-similarity

Abstract

A visual-based duplication methodology for self-similarity, together with some interesting results, is presented in this paper based on its recursive nature. Initiator, Base-line and Pattern are the three key components of this methodology. Initiator is simply a set of line segments, while base-lines are used to present the coordinate system for patterns. Patterns are composed of line segments and some objects. The relationship between line-segments and base-line are transformations for the purposes of shifting, scaling and rotation. The combination of pattern and base-line is called a Generator. The use of line segments to describe the basic patterns and the recursion positioning systems are the characteristic of the methodology. Unlike L-systems, it is unnecessary to specific syntax for a pattern, and no input of data either for transformation as iterated function system. Among many others, some applications of the method include recursion, fractal, chaos and visual design as well. This methodology has been successively implemented on a PowerPoint version of Mathematical Presentation System (MathPS). Indeed, it can be embedded in any drawing software in the hope of further popularization.