Controlling & Comparing The Blue Wash Fractal
Controlled Blue Wash Fractal |
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Controlled Blue Wash Fractal
- Different steps taken to control the Blue Wash Fractal on GSP. My goal was to iterate the rectangle so that it divides in half horizontally the first time and in half vertically the second time and so on. GSP was used to rotate the direction in which the rectangle is cut vertically and horizontally.
Contents
Basic Description
The Blue Wash Fractal is a random fractal composed of one large rectangle randomly broken down into sub-rectangles and shaded or colored in using either variations of the Basic Method or Inclined Method (as shown on Blue Wash Fractal Page.However, this variation of the Blue Wash Fractal is controlled using GSP. Basically, the rectangle is sub divided in half, or sub-rectangles,vertically and horizontally.The sub divisions alternate from dividing vertically in half to dividing horizontally in half. The resulting image creates a fractal of similar rectangles.
A More Mathematical Explanation
In order to construct the controlled Blue Wash Fractal I first constructed rectangle ABCD and the mid [...]
In order to construct the controlled Blue Wash Fractal I first constructed rectangle ABCD and the midpoints of sides AD and BC. After, you select points A,B,C, and D. Here's how the iteration box should look: A-B B-F (MidPoint of line BC) C-E (Midpoint of line AD) D-A
After, to iterate the whole half of the rectangle add a new map and use the reciprocal of the previous map A-B-A B-F-E C-E-F D-A-B
Why It's Interesting
The Blue Wash Fractal is a very eye catching and colorful fractal to begin with. Another element that adds to its interest is the randomness of the fractal. However, how similar the blue wash fractal is to the golden rectangle physically is another factor that adds to its uniqueness.
How the Main Image Relates
The Main Image of the controlled Blue Wash Fractal is similar in appearance to the Golden Rectangle. However there are a few key differences between the two Rectangles. For example the Golden Rectangle is based off of the Fibonacci numbers: 1, 1, 2, 3, 5, 8. The foundation of the Golden Rectangle is also the two squares in the center with a perimeter of 1 which provide a basis for the fibonacci numbers when creating the Golden Rectangle(Explained thoroughly in link below). However, the Controlled Blue Wash Fractal is composed of rectangles that iterate forever into smaller rectangles within the original perimeter of the square.
Teaching Materials
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Related Links
Additional Resources
http://mathforum.org/mathimages/index.php/Fibonacci_Numbers http://mathforum.org/mathimages/index.php/Blue_Wash
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