Patterns in headgear?

Hello everyone! So this post has troubled me in a sense that I had a hard time finding any frieze patterns that were post worthy. As I looked around my room, I saw my green scarf hanging over my closet door. This is no traditional scarf, as it is actually called a Keffiyeh. This scarf is a traditional middle eastern headdress that is typical worn by Arab people around the world.  It is most commonly used in dry, arid, desert-like locations to protect the face and head from the sun. additionally to that, it can also serve to keep your head warm if need be. They have become more popular in the western world in the last few decades within the outdoor community.

 

The “shemagh” was given to by my interpreter while I was overseas and it has proven to be one of the most useful gifts I have received! I have used it to cover my face in a dust storm and also I have used it a few times while snowboarding. Its extremely useful on a blizzard-like day to cover your face from the harsh wind and whipping snow!

 

Now the fun part…..determining what patterns are displayed on the scarf!! Lets take a look at the two I zoomed in on below. The pattern shown on the left is a little difficult to isolate but if you focus on the tan color as your main “shape” then its a little easier to see. I believe it is an F2. It can not be vertically reflected because no matter where you try to reflect it, the shape can not land back on itself evenly. There is no horizontal reflection either, but there is a glide reflection, which would make this an F2 (I think). The pattern shown on the right, separated by the black vertical stripe, can be classified as F3. This pattern does have a vertical reflection this time, but there is no horizontal reflection. I was unsure if the pattern had a half turn symmetry but i decided it did not because if you flip it 180 degrees, the number of peaks pointing up would then be 2, rather than 3 as seen in the pattern. Please let me know if you see it differently than I do, as I may have missed something!

Rosettes you can eat!

Have you ever wanted to eat a rosette? Well, now you can! With some searching on the web, I have found that rosettes not only form in nature, but in the kitchen! The IOWA Public television station made cookies that were in the shape of rosettes. The ones being made in the video (Located below) are dihedral and have a rotational symmetry. It is very much like the snowflakes made in class. They represent snowflakes for the holiday usually made by families and other cooking experts. They seems to represent more than three lines of symmetry and have a horizontal and vertical line of symmetry within the cookie.

Here is the video to watch how to make them!

Puzzle Patterns

For the exercise we started at the end of last class, I decided that I would try to draw a puzzle, and I would see if I could create a pattern that would work with the instructions. Not the most creative idea, perhaps, but it certainly did work! Here is what I did in class:

This has no reflections, but it does have half-turn symmetry on each dot, making it an f4. While I discovered that not all puzzles have a repetitive pattern to them, I did find one in my house that does, at least in individual rows:

 

As you can see in this image, there are examples of horizontal refection with the line of reflection going directly through the puzzle pieces. If these rows were put together with the rest of the puzzle, the horizontal reflection would be lost, but these rows, individually, all have horizontal reflection, making the top two rows both f6.

I have zoomed in on the bottom row in the above picture. This one has vertical and horizontal reflection, with lines of reflection going through the centers of each piece, making it an f7:

 

When I set out to find frieze patterns in puzzles, I had expected them to be symmetrical going both vertically and horizontally, but I was surprised to find that most puzzles (or at least most of the puzzles in my house) had no obvious pattern, having pieces of varying sizes and shapes, and having little to no repetition across rows or columns.

#DormLife and Random Surprises

After our conversation in class about Frieze patterns and finding them in wallpaper, I was determined to find something I could use for this post. To my disappointment, I found that wallpaper is not a thing that exists in the dorm that I am staying in. You would think that art students would have something decorative in the means of wall paintings or pictures in my dorm, but sadly there is none of that. Anyway, when I asked a friend for her opinion, she told me to look at the pillows in the lounge area. When I did, I found that each one had its own distinct pattern, similar to the ones we have been talking about in class. Here are two of the pillows I was most drawn to and what patterns I found in them:

Pillow 1 is an example of a F2. There is no vertical reflections and no horizontal reflections, but there is glide. If you look closely at certain lines, the thin brown one or the green, then you can see it. It depends on which line you decide to focus in on.

 

Pillow 2 is a an example of a F3. There is vertical symmetry towards the left side of the pillow in that design along the center. There is no horizontal symmetry since the flower looking design would not match if it were reflected over the horizontal axis. There is half turn symmetry within the design as well, making the pillow design a complete F3.

I found it weird to stare at pillows for so long, but like I said I was determined to find a pattern that worked. I stare at these pillows everyday and honestly didn’t think their patterns would work, but was happy to see that they did.

Emma’s post about her pants also made me think about a pair of pants that I have that have similar Frieze patterns to hers. I always thought they just had the same pattern repeating over and over, but thanks to our conversations in class I was able to see that it has frieze patterns of F1, F2 and F4.  Its fun to find patterns in things as random as pillows and pants and see how there is more to everyday things than meets the eye.

Frieze Pants

Today as I was searching for the perfect Frieze pattern to post about, all I could find were rosettes. My house is quite literally full of them. Following in Peter’s footsteps, I headed over to my instagram to check if I had any hidden Frieze patterns there. To my surprise I did in fact find something! I found this photo taken a few years ago and it’s a Frieze pattern goldmine!

These pants are actually my favorite pair that I own and I believe I’ve worn them to class before. As you can see there are several different Frieze patterns on the pants, I chose to define three of them.

This first pattern would be an F7

The second is an F6

The last pattern is also an F6

From far away, patterns 2 and 3 could have been mistaken for F7’s, but when you look closely you can see that there are actually small differences in the pattern.

I’ve always been drawn to fun patterns like this. I own so many pairs of fun pants and leggings and now I realize that they all have Frieze patterns! Makes me realize that I’m probably drawn to them because of the satisfying symmetry. I was so stressed out trying to find Frieze patterns around my house… I didn’t even think to look at my clothes and it was actually fun realizing how they are all around me without me noticing!

Panera

This week, I went to Panera after one of my classes. The homework from class Monday and Wednesday was running through my mind, nonstop. For the homework, we had to find a picture of a frieze pattern and write a blog post about it. I was frantically searching everywhere to try and find a frieze pattern. I thought I couldn’t do it.

Until I went to Panera.

Here is the photo I took when I looked at the booth across from me:

Let’s take a closer look to just two rows, so it’s clearer.

As you can see, this frieze pattern has no vertical symmetry. Does it have horizontal symmetry? Nope. Does it have a glide reflection? Yes! The red circle on top reflects to the downward position, then shifts forward. In the end, that specific frieze pattern is a F2.

It was awesome to discover this pattern! This further proves that math is everywhere, whether you like it or not.

cyclic pattern I found while walking my dogs

Alright so I wanted to somehow be able to count the amount of rotations that are in this cyclic rosette but I failed miserably to do so due to the quality of the image. Anyways I have to admit that this post isn’t very recent as it was taken over the summer and uploaded to my instagram (shoutout to @ptropavlsk for those interested)

I found this one of the trails I take my dogs on every day while my parents are at work. They need to get off leash and it’s a decent form of moderate exercise for me. Plus it lets me let off some steam and just relax. I try not to focus on my phone and just take in my surroundings. It’s therapeutic.

Anyways, I digress. I found this photo to be beautiful. I was sort of just walking through the fields and taking odd photos of flowers and when I saw this pattern it kind of brought happiness to my day. I know I sound like a #420 #luvnature #freespirited kind of guy by saying that, but I’m not really hahaha. I just found it to be really beautiful. Just a lot of intricate detail in such a small object. Makes me think a lot about the beauty of nature and the different patterns that make up the world.

anyways, let me know what you all think

-peter

Wallpaper designs, magic?

When I was growing up in the late eighties, early nineties; Magic Eye books were the rage. If you crossed your eyes or smashed your face against the page and drew back slowly, a 3-D image would appear, floating in space. It was great. There was always that one friend that couldn’t ever get it, which made it even more fun.

When we were in class Tuesday, discussing wallpaper patterns, I kept thinking about Magic Eye. I had to investigate if there was any relationship between what we were learning and the secret behind creating these crazy images.

The images in the book are autostereograms. There are different types but the one that is most like what we have been talking about is the wallpaper autostereogram.

Here are a few examples:

When you stare at the image with crossed eyes or from a wall angle, 3D images are revealed. It takes some time and practice but it’s pretty mind blowing when it happens the first time. As demonstrated by my dear friend, Markice:

It was great.

So basically, and without going into the physiology of the eye and brain, the repeating images create a pattern that establishes different visual planes. When viewed from wall-end view, the brain distinguishes between these different planes and certain parts of the image stick out or push in, giving a 2D image, a 3D perspective. Try it! You can see that a few of the images I posted show several of the characteristics we have discussed including reflection, translation, and rotation.

Where are all the rosettes?

When we were first tasked with finding rosettes in our everyday life, I though to myself, “This’ll be easy.” Especially after Dr. Plante showed us all the images he gathered in 10 minutes. Yet here I am scratching my head wondering where all the rosettes are. I was so determined to find something that no one else would post about, and perhaps that was my downfall in this assignment.

But don’t you worry… I did find rosettes. Nothing too spectacular. In fact what you’re about to see is a pretty normal sight for some.

Above you see a 25lbs plate. If we ignore the words on this bad boy, we are looking at a Dihedral 3 with a Rotational Symmetry of R120.
Woooh! Someday I’ll find a rosette worth your while, and it’ll probably happen when I don’t have a camera on me.