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Title

The Effect Of R-Factor On The Summation Of Cantor'S Dust In The Cantor Fractal

School Name

Heathwood Hall Episcopal School

Presentation Topic

Math and Computer Science

Non-Mentored

1st Place

Abstract

The purpose of this research is to determine the relationship between the r-factor of a Cantor Fractal C and the approached value of the summated lengths of removed line segments from each iteration of C. This was performed on a Python 2.5.1 program, where a recursive function returned the number of lines segments removed at the iteration and the total lengths of these removed line segments, starting at the first iteration. This is done by indirectly using an L-system. The mean, median, and mode were found to have values of approximately 1. With a range of 0.135297701585457, the minimum of the dependent variable was found to be 0.864702298414543 and the maximum 1. The standard deviation was 0.02609877259. After performing the ANOVA test, it was found that the data was not statistically significant, as the F-value was less than the F-critical value, rejecting the hypothesis. Thus, there was no correlation between the r-factor and the approached lengths of the summated removed line segments for any Cantor Fractal C, and the null hypothesis was accepted.

Owens 204

Start Date

4-16-2016 9:45 AM

COinS

Apr 16th, 9:45 AM

The Effect Of R-Factor On The Summation Of Cantor'S Dust In The Cantor Fractal

Owens 204

The purpose of this research is to determine the relationship between the r-factor of a Cantor Fractal C and the approached value of the summated lengths of removed line segments from each iteration of C. This was performed on a Python 2.5.1 program, where a recursive function returned the number of lines segments removed at the iteration and the total lengths of these removed line segments, starting at the first iteration. This is done by indirectly using an L-system. The mean, median, and mode were found to have values of approximately 1. With a range of 0.135297701585457, the minimum of the dependent variable was found to be 0.864702298414543 and the maximum 1. The standard deviation was 0.02609877259. After performing the ANOVA test, it was found that the data was not statistically significant, as the F-value was less than the F-critical value, rejecting the hypothesis. Thus, there was no correlation between the r-factor and the approached lengths of the summated removed line segments for any Cantor Fractal C, and the null hypothesis was accepted.