Talk:Pop-Up Fractals

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Chris 12:10, 18 July 2012 (EDT)

This looks very good. I have only a few minor suggestions:

  • Check your font size and typeface for the headings in "A More Mathematical Explanation" Note that you have four subheadings; each should get the same font size and typeface. These should be larger/bolder than the subheadings for 2.3.1 and 2.3.2.
  • Fractal Area and Patterns

Line 2 after chart: Change "quantity with" to "quantity by"

  • Finding Section Area: Method 1

Line 1 after chart: Change "distanced" to "distributed"

Hi guys,

I'll start putting your text and pictures into tables. That way you can see what it looks like, and perhaps peruse the source code if you have time to see how its done. I don't plan to add too much in terms of material to the page, bc you've done a good job of covering the bases.

- Awjin (09:39, 6/29/12)


Hello Awjin! Thank you very much for looking at our page and taking on the project. We are both extremely grateful for the feedback and apologize for not responding sooner; we have been busy arranging things after finals, etc.

But we would love to collaborate! However, we are really not that experienced with the formatting of the site (as you can tell), which is where most of the problems lie. But we would love to see how you can improve the page, and if we can help in anyway, please let us know. Again, we apologize for the late reply.

We look forward to your response! - Alex and Gabrielle


Hey, my name is Awjin and I'm a rising sophomore at Swarthmore College. I'll be working with you guys on your page! If you have any questions, feel free to email me at aahn1@swarthmore.edu. I will be leaving more comments as time goes on, so be sure to check up on any updates.

Here are a few of my preliminary thoughts on your page:
I really like the way you guys wrote this page. I could hear your voice throughout both the basic description and the MME. The content is superb, and I feel like this page is almost complete. However, there are some minor organizational/formatting suggestions that I have that will help enhance the way your page looks and reads.

  • Some images could use reworking.
    • The gif of how to fold the fractal is a little unclear, and could use some editing on Photoshop. I can help you with this.
    • It would be great if you could make the images bigger, so that the labels and visuals are clear, and it is easy for the reader to understand what you are referencing in your pictures.
  • Organizing the visuals and the information could help make your page clearer.
    • For example, you don't have to vertically stack text and pictures. Sometimes it helps to put text and pictures side by side. The best way to do this is to use tables. I can help you with this, because it involves a little bit of wiki syntax you might not be familiar with (if you want, you can read up about it here).
    • Reordering some of your information would be helpful as well. For example, in your MME, it would be less confusing if you grouped the definitions of holes, gaps, and steps in a brief introductory paragraph, instead of interspersing them throughout the section.
    • You can generate the mathematical equations and tables in wiki syntax, instead of uploading pictures of them. This makes the section look more seamless.

You guys are on summer break, so I understand if you don't want to work on this anymore. If you do, great! Shoot me an email and we can collaborate. Otherwise, would you mind if I made some edits to it?

I look forward to your response.

Peace,
Awjin (15:19, 6/11/12)


Hey!

Let me say first off that I love your idea. It's very creative. It's amazing that you guys created this. Math is more than equations; it is a hands-on experience and you guys have shown that! I would suggest in your basic description you actual explain Sierpinski's Triangle and how it is basically a process of subdivision. You can go into details about how to construct a regular Sierpinski's Triangle (inscribing a triangle inside another triangle etc). Then you should branch out and explain your model. Do you know what larger question you want to answer as of now? What do you want your reader to take away mathematical from your page?

-Leah

An addendum to Leah's comment: One good way to go about addressing Sierpinski's triangle on this page would be to talk about how your image both is and isn't an example of it. That is, I think you can give just a quick (1-2 sentence) recap of what Sierpinski's triangle is, with a link to the Sierpinski's Triangle page on this site, then move into the specific relationship of that image with yours. Because while there are many similarities, there are also several key ways in which yours is not exactly the same fractal.

-Diana (17:23, 3/4/12)

On Wednesday, it seemed like you guys were a bit stymied by talking about why your formula for area worked. Maybe you should try going back to finding a formula by logic rather than brute computation. Your earlier idea that area here related to triangular numbers is really key. Take what you know about triangular numbers and see how the side lengths of these "triangles" relate to each other. If you find a formula for these side lengths (it's an exponential relationship that you should recognize), you can multiply it with the formula for the value of triangular numbers to create a formula for area in your fractal.

- Leah & Diana (4/1/12 18:01)

Thank you both so much for your comments! We're sorry that we did not get to them sooner. Thanks Leah for giving us the ideas on using the Sierpinski's Triangle as a launch. It's what we plan to do. And thanks Diana for the comparing/contrasting idea! In the outline that we have, we're going to sort of introduce the image, talk about Sierpinski's triangle and it's similarities. Then we want to talk about it's differences and lead on to our index-card problem that explains the concept of same-area-different-perimeter. After that, we plan to focus on the triangular "holes" that pop-up the entire thing, because this seems like the greatest visual different between the Triangle and ours. On Gabrielle's user page, we posted a little explanation on how we plan to go from there. We were just wondering if you guys can check that out and see if that makes sense. We don't really know much about triangular numbers, so we'll do a good amount of research. But we just want to know if our plan sounds good as of now. Thanks so much! :) - Alex and Gabrielle

Great work on the patterns! You've dug deeply into the mathematics of the fractals and created mathematical writing that is accessible to the reader. I love that you discovered how to get the next section number.

My suggestions are below. Overall, you should always use written rather than mathematical form of all section numbers (except 136's). You might also consider putting the section numbers in italics or a different color to distinguish them further.

    • Specific Edits, by Section**
  • Basic Description*

P1: Change sentence 3 to: (For more information on fractals, click on: Fractals.)

It would be very helpful to have a separate picture for each step in the Stage 1 iteration. It is distracting to have the constantly repeating animation by itself while trying to make sense of the steps. You could put the animation in separately further down, or people could click a button to animate.

"The bases are rigged." Do you mean ridged?

  • A More Mathematical Explanation*

P2: I think you mean "next smallest holes." P3: "The One's have changed to be the smallest holes." The ones are already smallest. The "Gaps" picture has a 1 and 2 next to each other. Is that supposed to make 3? It's not clear why one side is 1 and the other 2.

  • After the Stage 5 fractal table*

1. "in table" should be "in the table." 2. "we would multiply 9 (the number of Three's) with 3, which equals 27. 27 in the area of all the Three sections. 3. One multiplies by a number, not with a number. 4. Do you mean "27 is the area of all the Three sections?"

  • The "But wait!" paragraph*

Change "The first deals strongly with triangular numbers." to "The first involves triangular numbers."

Mr. Taranta