A Configuration-Generating Method Based on A Lattice System

• Main Authors: Chen Hou I, 陳厚逸
• Other Authors: Liu Shun-Jen
• Format: Others
• Language: zh-TW
• Published: 1995
• Online Access: http://ndltd.ncl.edu.tw/handle/17944191923585420813

碩士 === 東海大學 === 建築(工程)學系 === 83 === Opposite to the shape grammars as a phrase structure grammar, I suggest a configuration-generating method as a finite state grammar. This configuration-generating method, as a bottom-up approach, which generates configurations by the relationship among units. This method is based on a lattice system which is named 〝L grammars〞. The methodology of L grammars is founded at the development of formal theory of mathematical logic and linguistic since the end of 19th century, especially focused at the field of computer science such as Turing machine, cellular automata, tiling problem and Wang tile theory. I define L grammars as an infinite lattice space（usually a chess-board- like lattice plane）with a set of rules which de- termine each cell occupied by which symbol. Each symbol cor- respond to a bounded configuration unit. Thus, a lattice plane correspond to a configuration union. The set of rules determine the structure of configuration union. The power of L grammars demonstrated in two ways. First, it''s possible to translate among varied lattice system. Second, it also generates varied configurations such as fractal images two dimensional examples） and crystal models（three dimen- sional examples）. There are some interesting issues about L grammars: the trans- lation from a configuration to symbols, the disjointment of a configuration, and problems occurred at the boundary of con- figuration units. The most important limitation of L grammars is that It''s almost impossible to generate varied scales of a configuration such as circle, arc and curve. Due to these limitations of L grammars, I suggest some other configuration-generating way. Finally, I indicate few direc- tions of the application of L grammars and the continuous studies.