Mathematics and Digital Art, Spring 2017

Week 1

1 Mon, 23 Jan 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 Wed, 25 Jan 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.
3 Fri, 27 Jan 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 next 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.

Week 2

4 Mon, 30 Jan 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 Wed, 1 Feb 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 Monday'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 Wednesday, February 8.

And let's not forget Nick's office hours! We'll have a quiz soon.....
6 Fri, 3 Feb Here is today's Sage worksheet on affine transformations.

Don't forget about your quiz on Wednesday! 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 Monday. We will have a brief discussion on time management.

Remember: Nick's Office Hour is Monday, 6:30—7:30 at the fireplace in Lo Schiavo!

Here is a handy summary of affine transformations.

Week 3

7 Mon, 6 Feb Here is a Sage worksheet incorporating randomness for different color values.

Remember to add to the Discussion Board! You should submit a draft of each of your three pieces for comment. Please comment briefly on everyone's submissions!

Here is your affine transformation homework due Wednesday. ($\LaTeX$ code.)

Download a previous quiz on color values and coordinates.
8 Wed, 8 Feb 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 Friday.
9 Fri, 10 Feb Download solutions to Quiz 1.

(Here is the $\LaTeX$ code.)

Since we didn't have time to get to it last class, finish the Homework Assignment on affine transformations for Monday (which was posted on Wednesday).

Also, brush up on the unit circle!

Week 4

10 Mon, 13 Feb Here is your homework on matrix multiplication ($\LaTeX$ code). (Answers are included so you can check your work!)

Office Hours tomorrow: 10:30—11:30 due to a department meeting.

Download a blank copy of last semester's quiz. Be warned, there will be some different questions on your quiz!
11 Wed, 15 Feb 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.

Don't forget your quiz on Friday!
12 Fri, 17 Feb Recall how we discussed Question 4 on Quiz 2 from last semester. Here is the fractal you should make today when you're done with your quiz. Find the appropriate affine transformations needed to create an iterated function system which creates this fractal. Then make it in Sage!

Here are some homework problems for additional practice.

Assignment due Sunday, 26 February: 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 $45^\circ$). You should take a photo of your calculations involving your matrix multiplication(s), and include this in your file.

  3. Next, be as creative as you like. Just design the best fractal ever!

  4. Finally, upload drafts of all three fractals by noon on Friday, February 24. This is for a grade! I will be checking this before class next Friday. You will have time to give some thoughtful comments on each piece, and you will have plenty of time to revise as necessary before the Sunday due date.
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.

And you might want to be looking at the archives of the Bridges conferences for a 6—8-page paper of interest. I'll be giving you the formal assignment when we get back from break!

Week 5

13 Wed, 22 Feb For today's lab, first finish the fractal we started on Friday, if you haven't already. Then make the one of the three fractals you had to analyze for homework.

Then try another one involving rotations! 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.

Here's the formal Bridges paper presentation assignment!
  1. First, select a paper at least six 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 Monday 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 Friday, 3 March. I will use the random number generator in Sage during class to determine the order of presentations.
14 Fri, 24 Feb Remember the modified due dates. The Bridges paper selection and email is as scheduled. Upload your three drafts to Canvas by the beginning of class on Monday. (It will be late, but at least you will get credit for the assignment). The three-fractal assignment is now due Wednesday.

Remember, Monday is another lab day for working on iterated function systems!

Week 6

15 Mon, 27 Feb Reminder of things due:
  • Bridges paper selection and email to author(s): Monday night.

  • Iterated function systems assignment: Wednesday.

  • Presentation of Bridges papers: Friday.
16 Wed, 1 Mar Here is your homework on geometric series, due on Monday.
17 Fri, 3 Mar As a help, here are the answers to the geometric series problems (numbered 1—5 instead of (a)—(e)). Recall that in the formula $S=\dfrac{a(1-r^n)}{1-r},$ $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms you are adding. This is for a finite series. For an infinite series, the formula is just $S=\dfrac a{1-r}.$
  1. $1.$

  2. $\dfrac{255}{256}.$

  3. $-1640.$

  4. $2.$

  5. $\dfrac37.$

Week 7

18 Mon, 6 Mar Download the processing file used to make Koch curves which we explored in class today.

Download today's homework on geometric series and user/screen space.
19 Wed, 8 Mar Partial answers to the homework: 1) 2040, 2) 13,108, 3) 1/56, 4) 6250/243, 5) 4 and 15.

No homework other than to be prepared for your quiz on Friday. Feel free to experiment with L-systems as we did in class today.

For Monday, March 20, 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.)
20 Fri, 10 Mar Remember, your response paper is due Monday! Have a great Spring Break!

Week 8

21 Mon, 20 Mar 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?
REMINDER: Office hours from 10:40—11:40 ONLY tomorrow due to a department meeting.
22 Wed, 22 Mar Download solutions to the Quiz on Day 20.

Download the revised processing file used to make Koch curves which we explored in class today.

Here is your work for the in-class lab today:
  1. Create a nice, centered image of the fractal with angle parameters of $90^\circ$ and $-210^\circ.$

  2. By altering the parameter which determines the number of lines drawn, find the minimum number of line segments which need to be drawn to complete the figure.

  3. Create a centered image of the fractal with angle parameters $53$ out of $336$ parts, and $189$ out of $336$ parts.
Remember, response papers for Monday's talk and late iterated function systems assignments due today!
23 Fri, 24 Mar No homework other than to make sure you download the Python packages for work on projects next week (if this applies to you).

Week 9

24 Mon, 27 Mar Download your homework assignment for Wednesday.
25 Wed, 29 Mar Here is the revised L-systems code in Processing which allows you to use different colors for the background and line segments.

For your next assignment, you will be using this code to create some digital artwork! Here is what to do.
  1. Create two pieces using the results we learned in class. Be sure to include values of $P,$ $q,$ $k,$ $\alpha_0,$ and $\alpha_1$ with your figures. I should be able to reproduce them if I want to.

  2. Create one piece which does not close up. Be creative! No constraints here. Just be sure to include the angles you use along with your image.

  3. Post drafts of your work by next Wednesday at the beginning of class. You will comment on each others' work during lab next Wednesday.

  4. Your final drafts should be uploaded to Canvas by next Friday.
There are still a few of you who have not submitted response papers for Stacy Speyer's talk. Please email them to me!
26 Fri, 31 Mar Keep working on your fractal assignment!

Week 10

27 Mon, 3 Apr Your response paper for today's talk by Gwen Fisher is due Friday.

Please make sure drafts of your work are uploaded to Canvas by class on Wednesday.

Remember your Homework Quiz Wednesday!
28 Wed, 5 Apr Here is my blog post on Processing we discussed today. Start making this movie in class today!

Don't forget that your response paper is due Friday.

Also, remember that your draft images are to be uploaded by Friday, and your FINAL drafts with commentary are to be uploaded to Canvas by Monday. The commentary should be similar to comments you made previously — provide a brief narrative for each piece explaining your choice of parameters, colors, etc.

Homework: Finish making the movie by Monday if you have not already done so. Come prepared to work on your projects Friday!
29 Fri, 7 Apr Don't forget the assignment due on Monday! Also, finish the movie if you haven't already. I'll be checking!

Week 11

30 Mon, 10 Apr For today's lab, you'll be making 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.

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.
31 Wed, 12 Apr Presentations on Bridges papers will be next Wednesday, so get prepared!

Here is the prompt for your movie project. It's not due for a few weeks yet, but you might want to start thinking about it.
  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 Friday, April 28, at midnight.

Week 12

32 Mon, 17 Apr Download the movie we'll be discussing in class today.

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. These must be exact!

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 Bridges paper by today! Remember to copy me on the email.
33 Wed, 19 Apr Remember, due to technical difficulties.... Presentations are moved to Friday, and Monday will be a project day!
34 Fri, 21 Apr Be prepared for a project day on Monday.

Also, in advance of the assignment due next Friday, have a draft of your video ready for next Wednesday's class!

Week 13

35 Mon, 24 Apr Don't forget to have a draft of your movie ready for Wednesday!
36 Wed, 26 Apr Remember that your movie is due on Friday at midnight. Please reread the prompt on Day 31 and make sure you submit appropriately.

Also, be prepared to work on your projects on Friday!
37 Fri, 28 Apr Continue working on your projects. Monday will be a project day!

Week 14

38 Mon, 1 May Project Day!
39 Wed, 3 May Project Day!
40 Fri, 5 May Project Day!

As you make final preparations for your presentations, please keep the following in mind. The presentations will be a little more formal than our other ones.
  1. You presentation should be between 7 and 10 minutes long.

  2. Other guests will be invited to hear you. So be sure you include any necessary introductory material necessary. Don't just say "remember when we.....". Provide an example.

  3. Be sure to talk about your creative process. What inspired you? What obstacles did you confront and overcome?

  4. Credit images you use from the internet or other sources.

  5. Include Title, Acknowledgment, Future Work (in other words, where you could see your project going if you had more time), and References slides.

  6. No need to dress up, but please dress "casually nice."

Week 15

41 Mon, 8 May Presentations today!

The semester is almost over! There is not much else to do, but here is what I need from you.
  1. Email me a copy of your last presentation.

  2. Assemble a folder containing your Final 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 Monday, May 15. You narrative should be brief (250—500 words). 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. 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.

    5. Please comment on whether Sage should be replaced with Processing, and why or why not.

    I will create an assignment on Canvas to upload your response. This is due Wednesday, May 17.
42 Wed, 10 May Final Project Presentations!

Thanks for a wonderful semester, and have a great life!