Mathematics and Digital Art, Fall 2016

Week 1

1 Wed, 24 Aug Download the course syllabus.

If you'd like to read more about the conferences mentioned in class today, click on Vienna or Finland.

Click here to watch some animated fractal movies using Processing. You'll be making movies like this in the second half of the course!

  1. Create a Sage account by clicking here. It's free, and we'll be using it frequently this semester.

  2. Read Day002 of my blog, Josef Albers and Interaction of Color.

  3. Go to the interactive color demo and copy it into a project of your own. You won't be able to change any code unless you do!
2 Fri, 26 Aug Here is the website on color codes we used in class today.

Homework (for real RGB values, round to the nearest thousandth):
  1. Convert $(250,69,227)$ to hexadecimal and real RGB values.

  2. Convert #FEDCBA to integer and real RGB values.

  3. Convert $(0.627,0.486,0.918)$ to integer RGB values and hexadecimal.

  4. You would to use an integer RGB color code, but you don't want any red in it, so you set the R value to 0. How many possible colors could you use?

  5. You color in a unit square with lower left-hand corner $(0,0)$ and upper right-hand corner $(1,1)$ so that a point $(x,y)$ is assigned real RGB values of $(x,1,1).$ Describe what the square looks like.

  6. You color in a unit square with lower left-hand corner $(0,0)$ and upper right-hand corner $(1,1)$ so that a point $(x,y)$ is assigned real RGB values of $(y,0,0).$ Describe what the square looks like.

  7. You color in a unit square with lower left-hand corner $(0,0)$ and upper right-hand corner $(1,1)$ so that a point $(x,y)$ is assigned real RGB values of $(1-x,1-x,1-x).$ Describe what the square looks like.

  8. You color in a unit square with lower left-hand corner $(0,0)$ and upper right-hand corner $(1,1)$ so that a point $(x,y)$ is assigned real RGB values of $(1-y,1,0).$ Describe what the square looks like.

Week 2

3 Mon, 29 Aug Here is the Sage worksheet on Josef Albers that we used in class today.

For Wednesday, read Day011 of my blog on on randomness and texture.

For Friday, create your first digital artwork!
  1. First, choose the dimensions of your image, a base color for the center rectangles, as well as ranges for the randomness in the red, green, and blue color values. You will use these dimensions, color, and set of ranges for all the images in this assignment.

  2. Next, create a set of five images using five different random number seeds. By clicking on the images, you can save these as .svg (scalable vector graphics) files. You can easily convert to any other file type using a program like Gimp (which is open source).

  3. Create a .pdf document with the following:

    • The five images, numbered 1—5;

    • A brief paragraph explaining your choice of color/randomness for these five images;

    • A paragraph explaining which of the five images has the most artistic value. Use whatever words come to mind, but try to be specific enough so that any other reader will be able to understand what you are saying without needing to talk to you!
Upload this to the appropriate assignment in Canvas. Use a name like (if it were me) "Matsko_Asst1.pdf".

Answers to Homework from Day 2:
  1. #FA45E3, $(0.980,0.271,0.890).$

  2. $(254,220,186),$ $(0.996,0.863,0.729).$

  3. $(160,124,234),$ #a07cea.

  4. 65,536.

  5. Click here to see what the square looks like.

  6. Click here to see what the square looks like.

  7. Click here to see what the square looks like.

  8. Click here to see what the square looks like.
4 Wed, 31 Aug Here is the color and texture worksheet we'll be using in class today.

The course on Canvas is published! Please add a comment to the discussion, maybe even post a draft of your work for others to comment upon. When you comment on another's work, be respectful, but don't be afraid to be critical. The least useful response to an artist's work is "it's nice." What does that mean? Write a comment that you would be comfortable receiving if someone else wrote it to you.

Finish your assignment for Friday! An assignment is set up on Canvas, so submit it there. You do not need to print anything out.

Also, read the blog post on color gradients.
5 Fri, 2 Sept Here is the Sage worksheet we'll be using in class today to work with color gradients.

Your second assignment will consist of three images and descriptions. You should create one image using the ColorSquare function, one image using the TextureSquare function (both from Wednesday's class), and one image using the Evaporation function (from today's class). For each image, give a complete list of parameters, and a discussion of why you chose those parameters, just like with the last assignment. Put this all in a .pdf file, with your last name included in the file name.

I will read over your descriptions from the last assignment, and give you feedback before the next one is due. The due date is Saturday, 10 September.

Week 3

6 Wed, 7 Sept Here is today's Sage worksheet on affine transformations.

Don't forget about your quiz on Friday! It will cover color codes, basic coordinates in two dimensions, and generating random numbers (like you needed to do for your previous assignment). Know how to make cyan, magenta, yellow, white, and black! Bring a hand-held calculator; no phones or computers!

Recall that we ultimately want to be able to create fractals like the Sierpinski triangle. Make sure you review translations, scaling (both in the x and y directions), and reflections about the x- and y-axes.

Bring due dates for ALL major assignments in your classes on Friday. We will have a brief discussion on time management after the quiz.

Also, be sure to post on the Discussion Board for the second assignment. This is for a grade!
7 Fri, 9 Sept Here is the Sage worksheet (thanks to Andrew for the suggestion) incorporating randomness for different color values.

Remember to add to the Discussion Board (this will be graded!), and to turn in your digital art assignment by tomorrow night. Please reread the instructions carefully — some of you did not not submit the correct assignment last time.

Email me by Sunday at 11:59 p.m. the next major assignment in ALL your classes. Look at your course syllabi for the necessary details! If there is no major assignment listed, be sure to explicitly say so.

Here is your affine transformation homework due Monday. I will want to see the work done in your notebook! ($\LaTeX$ code.)

Download today's quiz on color values on coordinates. Here is the $\LaTeX$ code.

Week 4

8 Mon, 12 Sept Download solutions to Quiz 1.

Here is the Sage worksheet on iterated function systems we'll be using today.

Here is today's homework. ($\LaTeX$ code.)

Also, read Day034, Day035, and Day036 of my blog for Wednesday.

Also, email me due dates for major assignments if you have not already done so!
9 Wed, 14 Sept Here is your homework on matrix multiplication ($\LaTeX$ code). (Answers are included so you can check your work!)
10 Fri, 16 Sept Here is the fractal we discussed today. What affine transformations would you use in an iterated function system to create this fractal?

For today's lab, create a fractal using two affine transformations. For the first, rotate by $45^\circ,$ then scale the $x$ by $0.6$ and the $y$ by $0.4,$ and finally move to the right $1.$ For the second transformation, rotate $90^\circ$ clockwise, scale both $x$ and $y$ by $0.5,$ and then move up $1.$ To check that you've done it correctly, click to see what this fractal looks like.

Assignment due Sunday, 25 September: Create three fractals using iterated function systems.
  1. First, create a morphed Sierpinski triangle, based on the code in the Sage worksheet. The idea is to have your fractal look like it was derived from a Sierpinski triangle, but just barely. Someone looking at it should wonder about it, and maybe after 30 seconds or so, say "Hey, that looks like a Sierpinski triangle!"

  2. Next, create a fractal using just two affine transformations. One of the transformations should involve a rotation (though not using a multiple of $90^\circ$). You should take a photo of your calculations involving your matrix multiplication(s), and include this in your file.

  3. Finally, be as creative as you like. Just design the best fractal ever!
Your .pdf should include a picture of each fractal, a brief description of your creative process for each one, as well as a pic of your work for the second one.

Here is today's homework.

Week 5

11 Mon, 19 Sept For today's lab, first finish the fractal we started on Friday.

Now let's try another one. Create a fractal using two affine transformations. For the first, rotate by $60^\circ,$ then scale the $x$ by $0.6$ and the $y$ by $0.5.$ For the second transformation, rotate $60^\circ$ clockwise, scale the $x$ by $0.5$ and the $y$ by $0.6,$ and then move to the right $1.$ To check that you've done it correctly, click to see what this fractal looks like.

When you finish this, recreate one of the fractals you had to analyze for homework.

The only homework is to study for Wednesday's quiz!
12 Wed, 21 Sept We will have our first round of presentations beginning next Wednesday. Here is what you need to do.
  1. First, select a paper at least four pages long from the Bridges Archive.

  2. Next, post the title and author of your paper on the Discussion board dedicated to this topic. No paper may be presented twice, so you might want to choose early to get the paper you want. (You can't choose Nick's or my papers.)

  3. By Sunday night, email the/an author of the paper with a question you have about the paper, and copy me on the email: Make sure you proofread your email carefully!

  4. Prepare a five-minute presentation on your paper. You may need to look at the references in the paper, or search online for other sites which address the topic(s) in your paper. Be ready to present next Wednesday, 28 September. I will use the random number generator in Sage during class to determine the order of presentations.
Download today's quiz on affine transformations. Here is the $\LaTeX$ code.
13 Fri, 23 Sept

Week 6

14 Mon, 26 Sept Many of you did not send emails about your papers (or you forgot to copy me on them). Please take care of this today!

Remember, everyone needs to be ready for Wednesday. I'll use a random number generator before class to determine the order of presentations.

Be looking for scissors, a straight edge, and maybe some glue for next week. We'll be building polyhedra!
15 Wed, 28 Sept Download solutions to Quiz 2 from Day 12.

Download the rubric for class presentations.
16 Fri, 30 Sept Please read this chapter on the Platonic Solids for Monday. We'll go over the algebra in detail next week.

For Monday, write a brief response — about one page, double-spaced — addressing the following questions:
  1. How do I think differently about mathematics after six weeks of this course? About art? About programming?

  2. What are one or two significant things you learned so far?

  3. What do you like best about the course?

  4. What do you think can be improved? Please give specific suggestions.
This is not an essay, but just a record of your thoughts. Be informal, and honest! (This is a completion grade — you will not be assessed on content.)

Remember we'll be building polyhedra in the next few weeks! So feel free to surf the internet to find interesting polyhedra nets — and email links to me so I can determine whether they're possible to build in a reasonable amount of time.

Week 7

17 Mon, 3 Oct Solve each of the following equations. Do not do more work than necessary — you may use any previous results we derived in class. There will be a notebook check at the beginning of Wednesday's class! Assume $p, q, e$ are all integers, and $e>0.$
  1. $\dfrac1p+\dfrac1q=\dfrac12+\dfrac1{6e},\quad p,q\ge3.$

  2. $\dfrac1p+\dfrac1q=\dfrac12+\dfrac1{5e},\quad p,q\ge3.$

  3. $\dfrac1p+\dfrac1q=\dfrac12+\dfrac1{e},\quad p,q>0.$

  4. $\dfrac2p+\dfrac1q=\dfrac12+\dfrac1{e},\quad p\ge5,\quad q\ge3.$ Hint: You should find twelve solutions.
18 Wed, 5 Oct Finish Monday's homework!
19 Fri, 7 Oct Your project proposal is due Sunday at midnight. You should include as detailed a description as you can! We will be working on these in class during Weeks 9—14 (approximately one day each week), with presentations during Week 15 (which is right after Thanksgiving break). So you should indicate intermediate goals for each of the six weeks we'll be working on projects during class.

Your project may evolve as you learn more about making movies with Processing, and that's OK. You may submit an updated proposal whenever you feel necessary.

Keep in mind that we will be using Processing to make movies with iterated function systems in class, so your project can not also be to make movies with IFS.

REMINDER: Bring in both your dodecahedron and icosahedron on Monday! We will need them in our discussion of duality. This is just a completion grade.

Also, finish the last case analysis from #4 on Monday's homework.

Week 8

20 Mon, 10 Oct Please resubmit your Project Proposals. Of those who actually submitted a proposal, only one was done correctly!

Here is the chapter about polyhedra and graph theory. For Wednesday, do problems #1, 3, and 6.
21 Wed, 12 Oct Remember, you have a Homework Quiz on Friday! Also, finish building your rhombic dodecahedra.
22 Fri, 14 Oct No homework over the break except to do what you need to in order to prepare for our in-class Project workday next Friday.

Week 9

23 Wed, 19 Oct Your homework is to write a short response paper (one page, double-spaced is fine) about today's talk! You may address anything at all, but here are a few suggestions if you're not sure where to start.
  • What did you learn from the talk?

  • How is mathematics/computer science used to create art in a way you didn't know about before?

  • How are you inspired to learn more about some aspect of art or sculpture?

  • What would you like to learn more about after hearing the talk?
This is due Friday at midnight. Please write a full page! Some of the response papers from the previous assignment were too short.

Also, bring anything you need to work on your project on Friday! We'll devote the entire day to projects.

Download solutions to Quiz 3.
24 Fri, 21 Oct Here is the link to the dual gradient worksheet in Sage.

Week 10

25 Mon, 24 Oct Our first day with Processing! You'll be making this movie in class today.

Homework: You decide to make a movie in Processing which is 1024 x 768 pixels (a 4/3 ratio). So you want a user space with upper right corner (4,3) and lower left corner (-4,-3). As we did on Day039 of my blog, find the screen space in terms of the user space. If the center of a square is at (-1,0) and the upper right corner has coordinates (1,2) in user space, what are the coordinates of the corners of this square in screen space?
26 Wed, 26 Oct Homework: Finish making the movie if you have not already done so. Come prepared to work on your projects Friday.!
27 Fri, 28 Oct Now that we've had two weeks of project work, you should have a fairly clear idea of how you would like to proceed. Some original proposals were very sketchy, others had more details. Submit a revised proposal by Sunday at midnight. If you wrote a more detailed proposal at the beginning, you might not have to revise much at all. You must include a weekly list of goals!

Also, make this movie! Your screen should be 500 pixels wide (as before), and the dots should always be 25 pixels from the edge of the screen. Colors are the usual red, orange, green, blue. Large dots are 200 pixels wide, and small dots are 100 pixels wide.

Week 11

28 Mon, 31 Oct Download the movie we'll be discussing in class today.

Next week is our second Presentation Week! By the beginning of class Wednesday, please choose the paper(s) you would like to present on, and post them to the Discussion Board to avoid duplication.
29 Wed, 2 Nov Here is the movie we'll be working with in lab today. Try to duplicate this as closely as possible. The starting fractal is one we did for homework earlier in the semester, so you know where to start — you just need to figure out where to end! Also, you don't need to match the colors in the movie, use whatever colors you like.

The size of screen space is 800 x 500 pixels, and the fractal itself is 600 x 300 pixels.

You can download this sample movie which shows how to work with different colors for the different transformations.

Don't forget to email the author of your paper by Friday! Remember to copy me on the email.
30 Fri, 4 Nov Your response paper to Friday's talk is due Monday! Do not use four lines of your paper with your name/date/class or rewriting the prompts. Many of the last papers were too short. I will be more strict with grading this assignment.

Also, make sure all movies we worked on in lab are done Monday! And be ready for your presentations....

Week 12

31 Mon, 7 Nov Remember, if you did not present today, be prepared for Wednesday!
32 Wed, 9 Nov Be prepared for a Project workday on Friday.

Also, complete any unfinished assignments. There will be a late penalty, but anything not completed and submitted by Friday at midnight will turn into a 0!
33 Fri, 11 Nov Please email me all major due dates and Final Exam dates by Tuesday so I can discuss them with you individually during lab on Wednesday and Friday of next week.

Week 13

34 Mon, 14 Nov Here are a few Processing tricks you might want to incorporate into your assignment.

Here is the code for Evaporation in Processing.

Your movie in Processing is due before you leave for Thanksgiving break (Wednesday at midnight).
  1. The subject of the movie is up to you. You may incorporate any of the ideas we used so far this semester. Be creative!

  2. There is no length requirement. I am interested in what happens in the video, not how long it takes. It is very easy to make a longer video by just increasing the frameCount. Quality, not quantity!

  3. You should incorporate linear interpolation in at least four different features of your movie. Note that using color only counts as one, even if you use interpolation on R, G, and B values. Also, position counts as one, even if you use interpolation on $x$ and $y$ values.

  4. You should write a brief narrative on your use of linear interpolation, as well as discuss artistic choices you made. This need not be long — a rough guideline is between one-half and one page in length. This should be uploaded to Canvas.

  5. You should also email me a copy of your .pyde file at The time stamp should be before Wednesday, November 23, at midnight.
35 Wed, 16 Nov Be prepared to work on your Projects on Friday!
36 Fri, 18 Nov Remember that your movies are due next Wednesday by midnight!

Week 14

37 Mon, 21 Nov Your repsonse paper to today's talk is due next Monday. Please do not forget!

Remember, we have an Open Lab period on Wednesday morning. Hope to see you there!

We will start Project Presentations next Friday. When we come back from Break, we will use Monday and Wednesday as in-class work days.
38 Wed, 23 Nov Have a great Thanksgiving Break!

Week 15

39 Mon, 28 Nov Presentations begin Friday! Here is the complete prompt.
  1. Your presentation should be 7—10 minutes long. Keep in mind that I am inviting math and art faculty, so your presentation should include enough introductory material so that someone who hasn't been in the class can follow along. Feel free to use any of the materials on the course website. But all images which are not your own should be properly referenced! This is a formal presentation!

  2. You should also write a 250—500 word narrative about your project. I want to keep the form fairly loose, but here are some items you should address somewhere in your narrative:

    • What was the motivation for your project?

    • What were your biggest obstacles/successes?

    • Did you learn something unexpected along the way that you didn't think would come up while working on your project?

    • Do you feel satisfied with the level of progress you made on your project?

    • Do you plan to continue working when the class is over?

  3. Finally, assemble a folder containing your presentation, narrative, Processing/Python files, and images (if appropriate; drafts as well as final images). Make sure the folder is named with your name, and upload it somewhere and send me a link. This is due Wednesday, December 7.
40 Wed, 30 Nov Be prepared for Project Presentations on Friday!
41 Fri, 2 Dec Project Presentations.

Week 16

42 Mon, 5 Dec Project Presentations.
43 Wed, 7 Dec Your final assignment (as there is no Final Exam!) is to write a response paper about your experience in Mathematics and Digital Art. The prompt is essentially the same as the prompt for the first response paper, but you've had the rest of the semester to develop as a digital artist.... Your paper should be at least one page, double-spaced, not counting name, title, etc. Remember, this is not a formal essay, but an informal reflection on you experience. Please address the following points, and add any other comments you would like:
  1. How do I think differently about mathematics after this course? About art? About programming?

  2. What are the most significant things you learned?

  3. What did you like best about the course?

  4. What do you think can be improved? Please give specific suggestions.
This is due Friday at midnight. I hope you enjoyed the course as much as I did!