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! Homework: Create a Sage account by clicking here. It's free, and we'll be using it frequently this semester. Read Day002 of my blog, www.cre8math.com: Josef Albers and Interaction of Color. 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): Convert $(250,69,227)$ to hexadecimal and real RGB values. Convert #FEDCBA to integer and real RGB values. Convert $(0.627,0.486,0.918)$ to integer RGB values and hexadecimal. 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? 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. 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. 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. 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! 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. 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). 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: #FA45E3, $(0.980,0.271,0.890).$ $(254,220,186),$ $(0.996,0.863,0.729).$ $(160,124,234),$ #a07cea. 65,536. Click here to see what the square looks like. Click here to see what the square looks like. Click here to see what the square looks like. Click here to see what the square looks like.

Week 2

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. 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!" 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. Next, be as creative as you like. Just design the best fractal ever! 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! First, select a paper at least six pages long from the Bridges Archive. 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.) By Monday night, email the/an author of the paper with a question you have about the paper, and copy me on the email: vjmatsko@usfca.edu. Make sure you proofread your email carefully! 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 $S=\dfrac a{1-r}.$ $1.$ $\dfrac{255}{256}.$ $-1640.$ $2.$ $\dfrac37.$

Week 7

 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: Create a nice, centered image of the fractal with angle parameters of $90^\circ$ and $-210^\circ.$ 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. 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).