From Math Images
Jump to: navigation, search

Blue Wash Fractal

The original Blue Wash Fractal is sub divided and colored by a random interval. However, i would like to control the variables that work to make the Blue Wash Fractal, which are the coloring and sub division of the rectangles. I would also like to use different variables to control the sub division to compare and contrast what happens when you use different variables. For example dividing the sub rectangles in one rectangle in half each time and then relating the result the Golden Rectangle and Fibonacci Numbers.

  • Comments and suggestions are appreciated

Update 2-22-12 I worked on typing a Rectangle Construction directions with visuals using both GSP or manually. I did this because inorder to put the Blue Wash Fractal to use you need to first know how to construct a rectangle. Update 2-27-12 Today i worked on figuring out a way to use the Iterate tool on GSP to create my Blue Wash Fractal. I used creating a sierpinski triangle on GSP using the Iterate tool for the basis of Iterating my Blue Wash Fractal.

Hi Jazzlyn,

I used iterations in GSP to create this:

GSP Rectangle Iterate.GIF

Am I right in thinking this is roughly what you were going for? I made it by combining those ideas of rotation and halving that we were talking about on Wednesday. Recall that the problem with just cutting each rectangle in half was that we got this:

GSP Linear.GIF

(The arrows are mine, just showing how the iteration I made translated the points to midpoints.) We can see that this doesn't work because GSP always cuts the rectangles in half in the same direction.

So what we need is for GSP to rotate the direction in which it cuts the rectangle, so that it cuts off the right, then the top, then the left, then the bottom, etc. That means we need to add a translation that rotates the rectangle before it halves it again. When I say "rotate," I don't mean it the way we usually do; I'm not talking about turning the rectangle on its side. Instead, I mean we take every point around the rectangle and translate it to its neighboring point. The resulting rectangle actually looks exactly the same as the original, but GSP has moved each of the points counterclockwise:

GSP Rotation.GIF

Now if we cut the rectangle in half as we did above, it would cut from the top rather than the right, because everything has been rotated to the left by 90 degrees. So my question to you is, how can you combine these two ideas of halving and rotation to put together an iteration rule in GSP that generates the image you want?

-Diana (19:43 3/4/12) [[Controlling & Comparing The Blue Wash Fractal]]