Fractal+Equasions

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Title
The music of Math

Problem Scenario
 I am trying to see if I can generate sound using fractal equations.

Broad Question
What are the effects of fractal generated sound will have on humans?

Specific Question
Does fractal sound improve concentration as binaural sounds is claimed to?

Hypothesis
When using a Julia set of equations the sound will effect the results of the test negatively vs. using Mandelbrot set equation generated sound.

Independent Variable:
Two types of fractal generated audio.

Dependent Variable:
Amount of puzzle complete.

Variables That Need To Be Controlled:
Ambient noise in room No practice time

<span style="color: #500050; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Vocabulary List That Needs Explanation
<span style="background-color: #ffffff; color: #500050; display: block; font-family: arial,sans-serif; font-size: 13px;"><span style="background-color: #ffffff; color: #500050; display: block; font-family: arial,helvetica,sans-serif; font-size: 9pt;">Audio: Sound

<span style="background-color: #ffffff; color: #222222; font-family: arial,helvetica,sans-serif; font-size: 9pt;">Fractal Design: A self similar graphical pattern plotted by a self similar equation <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 13px;"><span style="font-family: arial,helvetica,sans-serif; font-size: 9pt;">Self similar: <span style="color: #222222; font-family: arial,sans-serif; font-size: 9pt;">In mathematics, a //<span style="font-family: arial,sans-serif; font-size: 9pt;">self //<span style="color: #222222; font-family: arial,sans-serif; font-size: 9pt;">- //<span style="font-family: arial,sans-serif; font-size: 9pt;">similar //<span style="color: #222222; font-family: arial,sans-serif; font-size: 9pt;">object is exactly or approximately similar to a part of itself. <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 9pt;">Complex Number: Is a number that can be put in the form a + bi, where a and b are real numbers and i is the imaginary unit

<span style="color: #500050; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">General Plan
<span style="background-color: #ffffff; color: #222222; display: block; font-family: arial,helvetica,sans-serif; font-size: 9pt;"> Have test subjects (students) in a room, one at a time, for ten minutes, to solve a 1000 piece puzzle while they're exposed to the extremely annoying noise generated by the fractal equations, then determine their performance by the number of properly placed pieces.

<span style="background-color: #ffffff; color: #222222; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Potential Problems And Solutions
<span style="background-color: #ffffff; color: #222222; display: block; font-family: arial,helvetica,sans-serif; font-size: 9pt;">Person(s) must not have prior experience with this puzzle

<span style="background-color: #ffffff; color: #222222; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Safety Or Environmental Concerns
<span style="background-color: #ffffff; color: #222222; display: block; font-family: arial,sans-serif; font-size: 13px;">Audio level too damaging

<span style="color: #500050; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Resources and Budget Table

 * Item || Number needed || Where I will get this || Cost ||
 * Chaos Pro Free fractal generator || 1 || Google.com || FREE ||
 * Audio Paint || 1 || Google.com || FREE ||
 * Gold Wave v5 || 1 || Google.com || FREE ||

<span style="color: #500050; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Detailed Procedure
<span style="background-color: #ffffff; color: #500050; display: block; font-family: arial,sans-serif; font-size: 13px;"><span style="background-color: #ffffff; color: #500050; display: block; font-family: arial,helvetica,sans-serif; font-size: 9pt;">1. Obtain Chaos Pro 2. Obtain Audio Paint

3. Generate A Fractal photo using Chaos Pro

4. Render the Fractal Image

5. Export The Fractal image to any given location

6. Open audio Paint 7. Import the fractal photo

<span style="background-color: #ffffff; color: #222222; font-family: arial,helvetica,sans-serif; font-size: 9pt;">8. Make length of the audio file TEN minutes.

<span style="background-color: #ffffff; color: #500050; display: block; font-family: arial,helvetica,sans-serif; font-size: 9pt;"> 9. Convert the Fractal Picture to Audio 10. Export sound

10. Obtain a puzzle 11. Obtain a person 12. Play music while person solves Puzzle 13. Record data

<span style="color: #500050; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Time Line
<span style="background-color: #ffffff; color: #500050; display: block; font-family: arial,sans-serif; font-size: 13px;"><span style="background-color: #ffffff; color: #500050; display: block; font-family: arial,helvetica,sans-serif; font-size: 9pt;">2/26/13 Testing initiates in block 10 2/27/13 Testing concludes in block 10 <span style="background-color: #ffffff; color: #500050; display: block; font-family: arial,sans-serif; font-size: 13px;"> **<span style="font-family: Georgia,'Times New Roman',Times,serif; font-size: 9pt;">Data Table **


 * Student 1 || Control || 40/1000 ||
 * Student 2 || Mandabrolt || 31/1000 ||
 * Student 3 || Julia || 13/1000 ||
 * Student 4 || Julia || 14/1000 ||
 * Student 5 || Julia || 8/1000 ||
 * Student 6 || Mandabrolt || 67/1000 ||
 * Student 7 || Julia || 8/1000 ||
 * Student 8 || Mandabrolt || 60/1000 ||
 * Student 9 || Mandabrolt || 80/1000 ||

<span style="color: #500050; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">All Raw Data
<span style="background-color: #ffffff; color: #500050; display: block; font-family: arial,sans-serif; font-size: 13px;"> <span style="background-color: #ffffff; color: #222222; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Linked pieces/Total Pieces

<span style="background-color: #ffffff; color: #500050; display: block; font-family: arial,helvetica,sans-serif; font-size: 9pt;"> 40/1000 31/1000 13/1000 14/1000 8/1000 8/1000 67/1000 67/1000 8/1000 60/1000 80/1000

<span style="background-color: #ffffff; color: #222222; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">What I could of done to improve this project
<span style="background-color: #ffffff; color: #500050; display: block; font-family: arial,sans-serif; font-size: 13px;"><span style="background-color: #ffffff; color: #222222; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Larger test groups <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: 13px;">Smaller puzzle w/ starting piece position consistent. Smaller test window

<span style="background-color: #ffffff; color: #222222; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Results
<span style="background-color: #ffffff; color: #222222; display: block; font-family: arial,helvetica,sans-serif; font-size: 9pt;">Students exposed to the Mandelbrot Set sound during the experiment performed better than those exposed to the Julia Set sound.

<span style="background-color: #ffffff; color: #222222; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Conclusion
<span style="background-color: #ffffff; color: #222222; display: block; font-family: arial,helvetica,sans-serif; font-size: 9pt;">The Julia set showed a higher degree of distraction to the subjects as indicated by both their performance and their comprehension to verbal cues during the experiment.

<span style="color: #500050; font-family: arial,sans-serif; font-size: 13px;">** Discussion **
My results supported the project's initial hypothesis, which predicted that the Julia set of fractal sound/equations would affect the test results negatively vs. the Mandelbrot set which enhanced concentration. Though the data seems promising I do not believe results will be persistent since my test group was minuscule

<span style="color: #500050; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Benefit to Community and/or Science
<span style="background-color: #ffffff; color: #222222; display: block; font-family: arial,helvetica,sans-serif; font-size: 9pt;"> It was my hope that given the growing evidence that there is a fractal relationship in all things, that maybe fractals might have a practical application to improve people's concentration.

<span style="color: #500050; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Background Research
<span style="background-color: #ffffff; color: #500050; display: block; font-family: arial,helvetica,sans-serif; font-size: 9pt;">My background research took me many days, I had to learn what fractal equations were. I also had to get a grasp on what Complex numbers were. Inserting the SqRT of -1 into the fractal "Field" was difficult at first to understand but easier as time went on. A complex number is a way of putting (x,y) coordinates into one number with two parts. Usually consisting of a real number and an "Imaginary number" like SqRt of -1 = i. Once you understand why i = i Or why E=M(cc) fractal equations will make more sense. Conventional letters are key in mathematics due to limited space on most anything you would not want to write something that's large lengths unless needed. Abbreviations are awesome.

<span style="color: #500050; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">References
<span style="background-color: #ffffff; color: #1155cc; display: block; font-family: arial,sans-serif; font-size: 13px;">@http://www.angelfire.com/art2/fractals/lesson2.htm

<span style="color: #500050; font-family: Georgia,'Times New Roman',Times,serif; font-size: 13px;">Abstract
<span style="background-color: #ffffff; color: #222222; display: block; font-family: arial,helvetica,sans-serif; font-size: 9pt;"> My project first started with a crazy idea. That was to use fractals to predict future outcome with a finite set of variables, like picking the winning lottery ticket number. There has been extensive research in fractal mathematics where fractal patterns emerge in seemingly random (chaos) data. The more I researched this, the more evident it was that doing so was beyond the abilities of an 8th grader with limited time. As I continued my research into fractals, I uncovered even more research that others had done revealing fractal patterns in problem solving binary trees. Viewing these patterns on the computer, I wondered what they would sound like if the pixels were changed to audio notes. Then, after listening to the various patterns, I was reminded of the binaurial sounds that are claimed to improve concentration or focus. So I wondered if I could do a performance-based experiment comparing two of these sounds and if either would have a positive or negative influence on the test subjects.