#### Title

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

#### School Name

Heathwood Hall Episcopal School

#### Grade Level

10th Grade

#### Presentation Topic

Math and Computer Science

#### Presentation Type

Non-Mentored

#### Oral Presentation Award

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.

#### Recommended Citation

Murali, Athreya, "The Effect Of R-Factor On The Summation Of Cantor'S Dust In The Cantor Fractal" (2016). *South Carolina Junior Academy of Science*. 218.

https://scholarexchange.furman.edu/scjas/2016/all/218

#### Location

Owens 204

#### Start Date

4-16-2016 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.