# 1997-98NEW MEXICOHIGH SCHOOLSUPERCOMPUTINGCHALLENGE Interim Report

 Team Number: 018 School Name: Bloomfield High School Area of Science: Mathematics Project Title: Fractal Images of Music Project Abstract: http://mode.lanl.k12.nm.us/97.98/abstracts/018.html Interim Report: http://mode.lanl.k12.nm.us/97.98/interims/018.html Final Report: http://mode.lanl.k12.nm.us/97.98/finalreports/018/finalreport.html

The goal of our project is to write a program which would create fractal images with the aid of musical notes. Fractals and music are similar from the perspective that both use set patterns to develop the ultimate outcome. Both fractals and music can be easily manipulated through math and computers. One way to manipulate the music is through a program called MIDI. MIDI is a computer program in which you can, through manipulation techniques, alter existing music, or even create new music.

Fractals are geometric patterns. These patterns are replicated within the original pattern an infinite amount of times. The more times a fractal is repeated within itself, the more complex and beautiful the overall pattern vbecomes. The simplest type of fractal which can be created on a computer is a self-similar fractal. A self-seimilar fractal image is repeated perfectly within itself.

Geometric fractals created on a computer are obviously more predictable than those found in nature. One of the most predictable fractal images is the Stripinski Triangle. The Stripinski Triangle is a perfect equilateral triangle. The three vertices of this triangle, for our experiment, will be called B, A, and D. The letter B will be placed at the top of the triangle, the A in the lower left corner, and the D will be in the lower right corner.

The Stripinski Triangle works like this:

• Randomly pick a point within the triangle's boundaries,
• Determine a way to objectively choose a number between one and six and choose it;
• If the number picked is either one or two, draw a straight line exactly halfway from the randomly chosen point to vertex B:
• If the number is 3 or 4, draw a straight line halfway from the end of the first line to vertex A;
• If the number is 5 or 6, draw a line from the end of the second line halfway to vertex D.
• Continue this process an infinite amount of times (or until satisfied with the data acquired.)

Through musical notes our random number will be chosen. The musical scale consists of seven main pitches plus five irregular pitches. A number or combination of numbers consisting of 1 through 6 will be assigned to each pitch. When that particular note is run through the program, the assigned number will be chosen and the line will be drawn in the triangle. Whatever the music may be, the musical scale will cover all notes played.

To execute this project, we will be using the programming language FORTRAN 77. We chose this language because it was felt that it could best be used to manipulate the numbers with which we were dealing.

This project will be carried out by our supercomputing team which includes Raven Gary, Derek Betsuir, Ian Walker, Nathan Bachert and Eric Seo. Raven is our head researcher (in charge of finding exactly what a fractal is and how to manipulate them). She found most of her information on the Internet. Derek is our leading FORTRAN programmer. It was felt that through his knowledge of BASIC he would be the most qualified to write code at this time. Nathan is our HTML consultant. He is in charge of fine-tuning our web page to its finest quality. As well as having an extensive knowledge of the workings of a computer. Ian edited and helped write our interim report. Eric coordinated the group schematics and worked with everyone on their individual jobs. Although each of us focused on an individual objective, we are all contributing to the final product.

### Team Members:

New Mexico High School Supercomputing Challenge
http://mode.lanl.k12.nm.us