By Su Gao, Steve Jackson, Yi Zhang
The articles during this e-book are in accordance with talks given on the North Texas good judgment convention in October of 2004. the most objective of the editors used to be to assemble articles representing assorted fields inside of common sense that will either comprise major new effects and be available to readers with a normal historical past in good judgment. integrated within the e-book is an issue record, together compiled by way of the audio system, that displays essentially the most vital questions in a variety of parts of good judgment. This booklet may be important to graduate scholars and researchers alike around the spectrum of mathematical good judgment
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Extra resources for Advances in Logic: The North Texas Logic Conference, October 8-10, 2004, University of North Texas, Denton, Texas
37 identica! to either the terminals in the left side of rule 1 or the terminals in the left side of rule 2 (or their mirror images). The effect of applying either rule 1 or rule 2 is to replace the section of a curve that passes through (the center of) a square with a curve that passes through (the centers of) the nine subsquares. That is, each application of rule 1 or rule 2 replaces a section of curve P 1 with the corresponding section of curve Pi+l· The center of the marker in the left sides of rules 1 and 2 shows the exact location of the beginning of the terminals added in the right sides of the rules.
The language generated by PSG9 contains exactly the successive stages of the Snowflake curve. As with SG4, if the shape grammar PSG9 is used in serial, the generation process can proceed to different depths in different paris of the shape. For a (serial) shape grammar to detine a language containing only completed stages of the Snowflake curve, it cannot allow the generation process to proceed independently in different paris of the shape. The generation process must be controlled to generate the shape uniformly.
A variation is shown in Figure Sb. A parallel shape grammar, PSGS, that generates these figures is shown in Figure 6a. A generation using this shape grammar is shown in Figure 6b. Ali three rules are applicable to the initial shape. lf rule 3 is applied to the initial shape, the markers are erased, the generation halts, and a shape in the language has been generated. It rule 1 is applied to the initial shape, six terminals are added, the markers are moved, but from that point on only rule 1 is applicable.
Advances in Logic: The North Texas Logic Conference, October 8-10, 2004, University of North Texas, Denton, Texas by Su Gao, Steve Jackson, Yi Zhang