Talk:Anne Burns' Mathscapes

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Response to Checklist

Original response to checklist, in black, completed by Kate 17:29, 19 July 2011 (UTC)

References and footnotes

  • Images cited on click through
  • Link to Anne Burns' paper given in references section
  • Waiting to hear back from Anne Burns regarding permission to use images!
This is kind of a big deal. I started this page based on pages that other people had made years ago, and I'm not sure they asked her permission. I sent her an email but haven't heard back yet.

Good writing


  • The images are interesting in and of themselves
  • Basic Description and Why It's Interesting explain that the point is mostly just that these pictures are cool

Quality of prose and page structuring

  • Subject headings and first paragraphs explain the purpose of each section
  • Relevance of each section to topic is obvious
  • Simpler explanations are at the top of each section

Integration of Images and Text

  • Images are referred to explicitly
  • Captions and text explain the purpose of each image

Connections to other mathematical topics

  • Links to Blue Fern, which is related in being a fractal image that looks like a plant

Examples, Calculations, Applications, Proofs

  • Numerical examples and proofs aren't really applicable or would be complicated beyond the scope of the page
  • Visual examples are given at every stage however

Mathematical Accuracy and precision of language

  • All statements are accurate to the best of my knowledge
  • Unfamiliar terms are explained


  • Paragraphs are short, relevant images are used throughout
  • Page has been viewed at a variety of widths, nothing really weird happens

Pre-final review comments:

General Comments

  • Rebecca 01:42, 12 July 2011 (UTC) I don't have any big suggestions for this page. I think it's great the way it is... there are just a few small things I would change.
  • Chris 7/13/11 I'm so glad you made this page. I love her work and it's amazing to think that she created something so natural looking and beautiful simply using mathematical rules. It got me to read her article that you referenced and I'll be looking for ways to introduce her work to my students.

Old comments:

xd 20:46, 14 June 2011 (UTC) If you want to expand on this page, I feel maybe you can do a few specific and yet simple example of how to recursively create plant or generate 3D mountain.

Kate 16:55, 15 June 2011 (UTC): That's a good idea, but I'm not sure my own computer skills are up to it. I think I'll ask the CS people if they can make an applet for it.

Section-specific comments

Basic Description

Old comments:

  • Htasoff 15:35, 20 June 2011 (UTC)Make this section start after the main image. Use: <br style="clear: both" /> before the section title to do this.
Kate 16:59, 20 June 2011 (UTC): good tip, thanks!
  • Htasoff 15:35, 20 June 2011 (UTC)I hate to be nit-picky, but reconsider your the sentence.
  • Htasoff 15:35, 20 June 2011 (UTC)What is "fractal methods"? If it is a specific process, then define it. If not, then perhaps say something like: "... using fractal geometry."
Kate 17:00, 20 June 2011 (UTC): This paragraph was taken from one of the pre-existing pages that I got these pictures from. I agree that there's a lot of problems with it, I think I'll just scrap it and write my own.

A More Mathematical Explanation


  • "Notice that the second image didn't change, because it's string didn't contain an L."
  • Rebecca 01:49, 12 July 2011 (UTC) I would say "Notice that the second flower didn't change from Image 5 to Image 6 because the string didn't contain an L." It's just a little confusing because it could be read to mean that the second image is image 6.
Kate 14:44, 14 July 2011 (UTC): Good point, changed.
  • Chris 7/13/11 The Plants section is terrific. The text and images work so well together to give the reader a clear understanding of how she created the plant forms.

I couldn't initially find Image 4 because my screen was only open to about 2/3 the size of my monitor screen. I was able to find it when I opened it larger. I don't know enough about the technical aspects of this to make suggestions, but thought you should know.

Kate 14:44, 14 July 2011 (UTC): Fixed.

Old comments:

  • Htasoff 15:35, 20 June 2011 (UTC)Explain "recursive replacement" because I didn't find it when I did a quick search on the Blue Fern page.

  • Htasoff 15:35, 20 June 2011 (UTC)define: "trigonometric sums" and "3-D transformation".
  • Htasoff 15:35, 20 June 2011 (UTC)The last sentence is too dense and technical heavy.
  • Htasoff 15:35, 20 June 2011 (UTC)"... Burns' plants aren't straight-forward fractals that are exactly self-similar into infinity"
Awkward, try: "... Burns' plants are not (see below) fractals that are precisely and infinitely self-similar"
"simple", "clear-cut", or "perfect" instead of "straight-forward", I recommend "perfect".
  • Htasoff 15:35, 20 June 2011 (UTC)"...some randomization is built in..."
Would sound more natural if you said "... Burns uses some randomization in her equations ..."
  • Htasoff 15:35, 20 June 2011 (UTC)"... can be replaced by a smaller version of the original image, and so on and so on until the pictures are quite complicated."
Not fond of the double use of "and so on". sounds too lackadaisical. Also, tense mix up with "are". Try rephrasing it like this: "... can be replaced by a smaller version of the original image, Which in turn can be replaced by an even smaller version, and so on until the pictures become quite complicated."

Kate 20:20, 6 July 2011 (UTC): Rewrote a bunch of things, addressed all of these points.
  • Htasoff 15:35, 20 June 2011 (UTC)"The pictures can be made to look more natural by using random numbers to vary the length of the branches or the angle at which they connect."
    • Good, clear explanation.

  • Htasoff 15:35, 20 June 2011 (UTC)"Another way to vary an image is to use the deReffye method. In this method, at each stage a branch can either continue to grow, die, or wait until the next stage. Each option has a certain probability, and all the probabilities add up to one."
    • I recommend changing the first sentence to the active voice. If you choose not to, however, then combine the two into once sentence.
    • Instead of just "vary an image" say what you are varying. Either that, or pick another word. You could try "introduce variation," which, though it may sound the same, is more of a complete proposition than simply "to vary".
    • I'm confused by your explanation of the deReffye method. It took a bit of thought to connect the term "stage" with an iteration of the function. Clarify this. Also, I recognize how branches can continue, or die (stop), put the stopping and starting confused me. I assume you don't mean that the branch will stop, and then smaller branches will be suspended above it in mid air where it starts again, which is the first notion that came to mind. If I am correct, you are referring to a branch not being given intermittent size branches, but, rather, skipping that iteration and continuing straight to twigs. Explain that this is what you mean (If indeed it is).
    • Instead of "option" try "outcome".
    • I believe it is only important to say that the probabilities add to 1 if you then explain that is means that there is a 100% chance that every branch will follow at least one of these options (and here I mean option, not outcome). Nevertheless, it is already implied that every branch does at least one of these, so the remark is unnecessary.
  • Htasoff 15:35, 20 June 2011 (UTC)"You can also make the probabilities change over time, so that at later stages, the branches are more likely to die (and thus the plant eventually stops growing)."
    • Introducing the pronoun "you" does not fit with the trend established so far in this section. Also, ditch the parenthesis.

Kate 20:32, 6 July 2011 (UTC): Section re-written. Some of the questions you asked were things I just don't know, because she wasn't clear about it in my source material, but I addressed all the other points.
  • Htasoff 15:35, 20 June 2011 (UTC)The arrangement of the tree images is awkward. try doing two on a first line and one on a second below that. This would be particularly appropriate given that the first two images serve as examples for a different process than that represented in the third image.
Kate 20:32, 6 July 2011 (UTC): I actually think this is fine, and given that I'm hoping to add an applet later, I'm going to leave things where they are for now.
  • Htasoff 15:35, 20 June 2011 (UTC)I don't understand your explanation of string-rewriting.
Kate 20:32, 6 July 2011 (UTC): Re-written and images added. Hopefully it's clearer now.

Clouds & Mountains

  • Chris 7/13/11 The Clouds and Mountains section involves a much more challenging topic to grasp. In Anne Burns' article, she demonstrates how the midpoint displacement rule can be used to create an image that begins to resemble a mountain. I think this piece is needed to help the reader make more sense of how the grid can translate into an image such as a mountain or cloud.

Kate 15:05, 14 July 2011 (UTC): Added some stuff. Is it better now?

Old comments:

  • Htasoff 15:35, 20 June 2011 (UTC)First paragraph has lots of unexplained terms:
    • "two-dimensional height field"
    • "projected" (in what sense)
Kate 23:12, 6 July 2011 (UTC): I can't answer this question, the source doesn't say.
    • "three-dimensional image into two-dimensional space"
  • Htasoff 15:35, 20 June 2011 (UTC)"Over time, the random numbers added to the heights are scaled down."
    • You never introduced what part of this model corresponds to the height, and how so.
    • In addition to your next sentence, which is good, further explain how scaling down the magnitude of the random number as the iterations increase creates a form that has a bumpiness that is on the same scale as the part of the surface it takes up. Namely, features that impact a large portion of the form are large, while the bumps that impact only a small fraction of the form are small.
  • Htasoff 15:35, 20 June 2011 (UTC)last paragraph could use some more explanation. It made sense to me, but I can see it being clearer if more things are explained, and if you go through the process a bit more slowly.
    • Explain that the z-axis is the up and down direction.
    • Explain what is being done with the trig and calc: perhaps: "trig and calc are used to rotate the form so it is viewed side-on, rather than from above, then it is projected, turned into a 2D image, etc. ..."
Kate 23:12, 6 July 2011 (UTC): I can't answer this question, the source doesn't say.
Kate 23:14, 6 July 2011 (UTC): I'm just going to interpret this as being that I need to rewrite this section, and hide the specifics.

Why It's Interesting

  • Chris 7/13/11 In a way, Anne Burns is doing two very different things in her work. The first you get at in your topic sentence, which is to reveal the mathematical elements in certain natural phenomena, such as the fractal patterns of some plants. The second you get at later, which is that she is creating something new using mathematics. It resembles nature and it is natural looking but it is scripted in a very intentional, not quite natural, way. Your paragraph is good; I'm wondering if it makes sense to clearly delineate these two different things she's doing somehow.
Kate 14:46, 14 July 2011 (UTC): I don't really see these things as being quite so distinct as you see them, so to me it doesn't really make sense to try and delineate them more clearly. I'm open to any suggestions you have about changing the wording in this section, though.

  • Htasoff 15:35, 20 June 2011 (UTC)Also add that, "Burns' images reveal the fractal geometry behind many natural phenomena."