# Previous Blue Wash Discussion

### From Math Images

Back to Blue Wash page and current Blue Wash Discussion page

## Contents |

## Checklist

1. Are the words that you define bold? YES 2. Do you have references and other interesting links? YES 3. Did you cite your pictures, or say if you created them? YES 4. Have you considered all of the comments on the discussion page? YES 5. Have you looked over everyone else’s pages, and linked to the relevant ones? YES

## Drexel

There are at least two possible applets/animations for this page:

- An animation showing the gradually creation of a fractal using the
**Basic Recursive Method**(the image at the top of the page). This method does not involve*k*, and is completely random. This new animation could be based on the existing (very basic) animation, but would include more iterations and have multiple initial rectangles. - An applet letting users change the
*k*value using the**Inclined Recursive Method**(the two images under the corresponding section). The variable whose value is affected by*k*is random, but also is governed by rules of probability. See Probability Distributions for more information about the statistics behind this.

- An animation showing the gradually creation of a fractal using the

You may have the contact the artist to ask for more information about these images because the website is not very detailed.

Another piece of information that I just read about here [1] is that after about 8 iterations, the image barely changes. It will be interesting to observe this in the animation. I also suggest looking at the links under the *Teaching stuff* section on this page [2].

Click here to view the applets that Mike created, and let us know which applet of the two applets for each method should be used for the page.

Basic Method:

**Blue Wash Applet (updates 1 at a time)**

**Blue Wash Recursive Applet (updates all at once)**

Inclined Method:

**Blue Wash with gradiant Applet (updates 1 at a time)**

**Blue Wash Recursive with gradiant Applet (updates all at once)**

Other comments:

#### Abram 7/9

Sorry I wasn't clear in my comments before. I meant method 1 (basic method) vs. method 2 (inclined recursive method), not basic description vs. more mathematical section.

Anyway, this page looks great, and there are just two very small changes I would like to see.

Anna, I'm not seeing the "if's" hanging out all alone. I believe you that they're there -- I'm just unclear what you are talking about, so I will let you and Rebekah work out that one.

*I believe I just fixed this, so we'll see what Anna says about my revision.*

As for the changes that I would like to recommend, first, can you actually describe the artist and what he was trying to achieve with these fractals in the basic description, not at the end. It could add a lot to the reader's satisfaction to know, for instance, that this guy is a computer scientist who has a long-standing interest in art, and found this way to design a simple computer program that could create a nice image (or whatever happens to be true).

*Unfortunately, the artist was a bit vague about his description of the motivation between this fractal. I spent of bit of time scrounging about his site and I couldn't find any more information about this project except what was on the fractal page...which I don't really understand. I tried to look up what Gaussian speckle patterns are, but I couldn't find any more information.*

"The first set of images are coloured random fractal patterns. They were generated with a scientific intent, we needed to project fractal patterns onto smooth surfaces in order to get better triangulation off them when using stereo range finding. We had previously used Gaussian noise patterns, but I thought that coloured fractals should be better suited to our range mapping process which worked by pyramid decomposition of left and right stereo images. The coloured patterns that I generated turned out to be much more attractive to look at than Gaussian speckle patterns".

Second, the text in the basic description of method 2 is still a bit ambiguous on one point:

The second method involves adjusting the brightness of the sections gradually to make an inclined plane in brightness. The brightness of the line where the rectangle is split is determined randomly, and the sub-rectangles then form an increasing or decreasing plane in brightness to meet the brightness of the dividing line.

It's still hard to tell whether you mean each rectangle has a brightness gradient or collections of rectangles have a brightness gradient. You could fix this by simply adding "within each subrectangle" to the first sentence above and replacing "the sub-rectangles then form..." with "the two resulting subrectangles then each form..." in the second sentences.

*Ok, and I got rid of "section" and replaced it with "sub-rectangle" to be less confusing.*Ryang1 (7/9)

#### Abram 7/8

It looks like you've addressed Anna's questions. You also did a nice job incorporating the gist of the more mathematical section into the basic description. I have only a couple of small questions/comments that I think are important.

A couple things in the more basic description:

- In the more advanced section, you write "The brightness of the dividing line itself is increased or decreased according to the random variable, and the sub-rectangles a and b have inclined brightnesses that gradually increase or decrease towards the dividing line to match the brightness of the dividing line." This wording is actually much more clear than your basic description of method 2. Can you use this wording (or a very slightly modified version thereof) in the basic description in place of what is already there, and remove this description from the more mathematical section?
- The description of method 2 should make it clear that here, as in method 1, the brightness offset decreases with smaller rectangles.
- You say that method 2 gives a more painterly effect. It would help to have a picture in that section of a fractal generated using method 1 in addition to the one generated using method 2.

*I hope I addressed all your commments, because for some, I wasn't sure if you were referring to*method*1 and 2 or*basic*vs.*mathematical*explanation.*

I'm also curious, is it random whether the dividing line between rectangles is horizontal or vertical, or is there some algorithm?

*I think it is just random, but the artist wasn't clear about this.*Ryang1 (7/9)

#### Ryang1 (7/7)

I know that I refer to the applets a few times on the page even though they are not yet embedded - they are coming soon!

#### Anna 7/7 (still not addressed by 7/9 am)

I'm not quite sure how to tweak it, but the basic method description is a bit unclear to me. I think my biggest problem, honestly, is the way those "if"s are hanging out there, all alone, and uncapitalized. Could you maybe edit the format of this first to see if it fixes the problem?

*Gotcha.*Ryang1 (7/9)

#### Anna 7/6

I can see that you're going to write a basic description for the two other methods, and I think that that's most of what this page needs.

I also love the little animation!

*Thanks!'*Ryang1 (7/7)

#### Abram 6/25

Rebekah, this page is really interesting and well-presented.

Most of the section that supposedly requires statistics and calculus actually requires neither of them, or can also be stated in ways that require neither. For this reason, and because the page is so interesting, see how much of the content you can move to or summarize in the basic description. For example:

- The entire introduction to the more mathematical section can be part of the basic description.
- The line "the mean of the probability density function of the random offset value is proportional to the square root of the area of the sub-rectangle" can easily be made accessible to non-stats folks as something like: "the brightness offset chosen is random, but the program is designed so that on average, a smaller rectangle will have a smaller brightness offset than a larger rectangle."
- Similar summaries can be made for the constraints on the random variable in the inclined recursive method.

In any case, there are a couple sentences that are just little bit confusing:

- In the opening of the more mathematical section, the sentence that begins "an interesting observation" is generally confusing. The paragraph also made me wonder if somehow the diminishing brightness offset was a consequence of the process used to create the image rather than a constraint put on the program that created the image.
- Don't use the word contractive -- it's unnecessary jargon.
- What you mean by "inclined brightness" is not immediately clear, so don't wait for two lines to explain what you mean by the term. Instead, explain it right away.

Again, this page is for the most part very well-written. These are pretty small details.

*Thanks for your suggestions, especially the one about providing more details of the actual methods in the***Basic Description**section. I wanted to address the method in both a**Basic Description**and**A More Mathematical Explanation**, with the specific math being used in the latter, so I hope I haven't made the explanations too redundant.- Ryang1(7/7)

### Gene, 6/19

More Math exp: "reveals the basic formula"--is it a formula? maybe a construction technique?

Maybe subsection title "Inclined Recursive Method--a more painterly effect" or something. We want folks to check out this fun variation.

k is a constant that the constructor can vary. Boy, would I like to have it set up so folks could play with k!

Do leave titles even when material is hidden.

Nice clean job, Rebekah.

*Thanks, I implemented your suggestions, but I think we'll have to talk about having the titles shown even when the material is hidden in our next meeting.*- Ryang1