Symmetry Gives Things Beauty

I know a lot of people don’t like spiders, but with the most recent conversation of symmetry we had in class, I can finally talk about them, and even show a picture of one! I specifically picked a very large species, shown below, which is the Giant Huntsman Spider, so called because they can reach a leg span of 12 inches, and they don’t make webs, but chase down (hunt) their prey. Aside from the incredible importance spiders have in keeping pest insect populations down, they are also symmetrical, as can be seen below.

Not only are they symmetrical, but they are also not chiral; their reflections would look exactly the same, and their original images could be superimposed on the mirror ones.  This perspective gives the spider a kind of beauty, in my eyes. So, in conclusion, it’s amazing how many cases of natural symmetry can be found, and yay, for something finally giving me a reason to post and talk about the Giant Huntsman Spider!

Symmetrical Mehndi Hand Designs

Similar to Mandalas, Mehndi hand designs are meant to be symmetrical in one way or another. For those who don’t know, Mehndi is a form of body art from Ancient India. The designs are made from a paste using dried powder from a Henna plant. Each Mehndi design has a significant meaning, much like mandalas. Many Indian women cover themselves on Mehndi for special events, such as weddings. The designs last from one to four weeks, depending on where you get the design. Here are some cool pictures some designs.

 

Here is a link to a website about Mehndi: http://www.mehndimama.com/info.html

Nature Mandalas

If you know me, you know that I’m a nature freak.  I always strive to be one with the Earth and feel the energies radiating off of its surface and all that stuff, I just find it so calming and interesting and it keeps me in the present. So obviously, I had to incorporate this into my blog post this week.

Natural mandalas can occur in so many places in nature, whether its in flowers, shells, spiderwebs, or even fruits.

Fruits hide a natural mandala in their core.  When it comes to citrus fruits, there are mandalas all throughout, but when it comes to fruits like apples, a perfect mandala is always formed right at the center.

Flowers can have a circular center blooming out to colorful outer rings that have layers of color.  Ferns can also be considered nature mandalas as well because the dewdrops on the leaves create symmetrical patterns.

Shells contain multicolored spirals throughout their entirety.  Spiderwebs, which I find the most intriguing and beautiful, create mandalas with a circular pattern beginning in the middle and working its way outward.  What makes them extra eye-catching is when the dewdrops (I don’t know why I’m focusing on dewdrops here but I guess I am) are glistening in the sunlight.  It just adds something extra to the whole image.

I could go on and on about this but instead, you can check out this link:

http://www.mandalasforthesoul.com/nature-mandalas/

If you’re as into this stuff as I am, I recommend checking out the rest of the website while you’re at it!

Food Mandalas

There is a theory out there that people find things that are symmetrical to be more beautiful in nature. This could be how we are drawn to objects we like, or people’s faces we are attracted to all based on symmetry. When we look at something and it looks so intriguing, do a little digging next time because chances are that what you’re looking it is symmetrical in a way. Our brains are drawn to it, some scientists believe.
The other day in class we got to color and draw our own Mandalas, and it was fun. I noticed when we were all showing our papers to the class, not one was remotely the same and that was very cool. Each of us had a reason why we chose to do what we did, places to start and what techniques we used. I came across some really pretty symmetrical food pictures and they are suppose to represent mandalas. They are very visually appealing to look at, and I wonder if that has to do with the fact if you sliced it down the middle or in any way rather, that it would be the exact same reflection on the opposite side. They are shown below

 

Symmetry in Videogames

Hey all. I’d like to relate the topic of symmetry we talked about in class to videogames. Specifically, Overwatch.

Symmetry in videogames is extremely important to keeping certain game modes fair. In Overwatch, there is a mode called control point. IN this mode, the teams compete to get to and hold a control point. If one side had an advantage over the other, such as a shorter run to the control point, that side would have an incredible advantage over the other.

This is an overhead picture of the control map Nepal. As you can see, the overall shape of the map has reflective symmetry to it. While the details may not be exactly the same, the general layout of each side is.

Each side has health packs in the same place. Each side has the same 3 pathways to get to the point. Neither spawn point is closer than the other. This gives the map dihedral symmetry, and makes it fundamentally even for both teams.

There are more maps like this in Overwatch and plenty of other games that also have symmetrical maps. This kind of symmetry sits at the heart of map creation for any game with this type of game mode. It is the only way to guarantee that the maps are dead even for everyone. This makes symmetry one of the most important math topics in game and map creation.

Monument Valley

During our class Thursday as we looked at various optical illusions,  I thought back to a smartphone game I used to play a few years ago.  The game is called monument valley, and it’s a puzzle game based on optical illusions.  The goal of the game is to shift the landscape of the levels to make a path to the exit.  The paths you make seem impossible, and they should be, but our perspective of the levels make them possible. 

What reminded me most about this game from class was when we made the origami Penrose Triangles and had to look at it from a certain angle to make the sides line up.  You have to use your mind the same way when playing this game to be able to complete the levels.

This is an example of what one of the levels looks like.  It doesn’t look like much of an optical illusion with a still image, so I’ll link a video too.

 

Skip to about 5:10 to get an idea of what this game is and how it uses optical illusions to entertain.  At one point during that level, there’s a clear Penrose Triangle that must be climbed to progress through the level.  I think Monument Valley is a great amount of fun and I recommend it!  It’s more difficult to figure out than the video suggests.

The Checker Shadow Illusion!

Optical illusions are really cool and fascinating. As I was doing research on optical illusions, I came across this amazing illusion called the Checker Shadow Illusion.

The Checker Shadow Illusion was created in 1955 by Edward H. Adelson, professor of Vision Science at MIT. 

 

 

In this visual illusion, the square marked with an A looks a lot darker than B, right? But in reality, they are the same shade of grey. 

Explanation of the Illusion:

Your brain makes a lot of assumptions when it’s processing visual information. The visual system uses several tricks to determine where the shadows are and how to compensate for them, in order to determine the shade of grey “paint” that belongs to the surface.

The first trick is based on local contrast. In shadow or not, a check that is lighter than its neighboring checks is probably lighter than average, and vice versa. In the figure above, the light check in shadow is surrounded by darker checks. Thus, even though the check is physically dark, it is light when compared to its neighbors. The dark checks outside the shadow are surrounded by lighter checks, so they look dark by comparison.

A second trick is based on the fact that shadows often have soft edges, while paint boundaries (like the checks) often have sharp edges. The visual system tends to ignore gradual changes in light level, so that it can determine the color of the surfaces without being misled by shadows. In this figure, the shadow looks like a shadow, both because it is fuzzy and because the shadow casting object is visible.

Part of the problem is where the squares are located. Most people know enough about checker or chessboards to know that a square will be the opposite color of all the adjacent squares. That means two squares that are next to each other, or separated by an even number of squares, should be different colors. Since squares A and B are two squares away, they logically should be different colors, and our brains really seem to want to think that as well.

Proof of the Illusion

 

The Checker Shadow Illusion In Real Life

The Checker Shadow illusion is one of the most stunning illusions, as it lets viewers perceive all the boxes as a different color when all of them are the same.

Please check out the links below for more information:

http://www.illusionsindex.org/ir/checkershadow

http://persci.mit.edu/gallery/checkershadow

Magic Eyes

Brad Wall

3/22/2018

Math 444.M1

Magic Eyes

On Tuesday we spoke about optical illusion and how they show up in parts of our culture. OK Go, uses optical illusions to make their videos fun and entertaining for their fans. I started to think about what aspect of my life have optical illusions come into play. While I was in high school I worked in a daycare. When I first started working there I taught the 4 year olds. Much of my time was spent doing fun things like arts & crafts, tag, and reading books. There was one book that always stood out however because it had no words. This book was called Magic Eye. In this book are pictures that look like a mess of color. However, if the reader focuses in just the right way then a 3D image appears.

The kids would take turns sharing the book trying to see what images would appear. It was a very fun past time and the kids enjoyed it.

The magic eyes book remind me of M.C. Escher picture that Professor Plant, showed in class.

If you read the Magic Eye book you see a 3D image appear like this.

The way Magic Eye works is they take a 3D object and produce an image of it. Next, they layer the image so that it can appear 3D. Finally they construct a 2D pattern and put it over the 3D image. Finally, the image is ready to be seen and published.

Magic Eye Website:

http://www.magiceye.com/client/city.html

 

Magic Eye Example:

https://www.google.com/search?q=Magic+EYe&client=firefox-b-1-ab&source=lnms&tbm=isch&sa=X&ved=0ahUKEwi51ZjeroDaAhXLhOAKHXXMDJ8Q_AUICigB&biw=1920&bih=929#imgrc=EqnHax8GcFK7lM:

 

M.C. Escher Example:

https://www.google.com/search?q=m.c.+Escher+sphere&client=firefox-b-1-ab&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjPkPuhr4DaAhXyYd8KHRl2BnsQ_AUICigB&biw=1920&bih=929#imgrc=0LqhP-xJaHD0vM:

Optical Illusions vs. Stephen Strange: FIGHT!

Hey guys,

This is your friendly neighborhood lady nerd here! My nerd senses legit screamed as soon as we watched the Inception clip in class. As much as I love watching that movie until my brain melts, I’m also a sucker for a happy ending and a tie-in to the largest movie franchise since everrrrr (I was gonna say since Disney but I can’t anymore…)

Anyways, what if we took all of the visual effects of Inception, made them uber-colorful, added magic, mystery, ?drugs?, and BENEDICT FRIGGIN CUMBERBATCH?

What you have is this (start at about 20 seconds):

If you don’t know, that’s incredibly wealthy surgeon Stephen Strange after about an hour and a half of texting and driving leading to a car crash, seeking out some mystic healing, getting the WiFi password, and then studying his butt off to become the Sorcerer Supreme so he can help the White Witch save the world from Hannibal Lecter/whatsherface’s dad from Rogue One.

The film’s VFX supervisor Stephane Ceretti says the effects team analyzed the physical impossibilities of M.C. Escher’s drawings, the forced-perspective motion of the mobile game Monument Valley, the unnatural realism of light-painting photography, and the mathematical psychedelia of fractals. (http://www.vulture.com/2016/11/what-inspired-doctor-stranges-visual-effects.html)  Ceretti was surprised and impressed to find things that looked like them in the pencil-and-ink artwork of comics writer/artist Steve Ditko, who co-created Doctor Strange in 1963: “[Ditko’s] use of colors and shapes was pretty uncommon at the time,” he says. “And actually, today, we can only do those things on the computer. Even some of the design that he did looked like fractals, which were not even invented at the time.”

Here are some images from the original comics (which began in the early 1960’s)

It’s just illusions and writers that were probably trippin’ and COLOR. SO MUCH COLOR.

Said Cerreti: “When you start to play with fractals, it’s very mathematical so its process intensive. But you cannot choreograph it very well because it reacts in a very procedural way. So, with this film, we had to create the different deformations, change of shapes and the use of fractals that we’re doing. You need to do that to direct the scene and have what you want in the shot. And because we had four different visual effects vendors working on the film and all working together to match together, they worked as a group to figure out the best way to go about choreographing and controlling the fractals for what we wanted.” (https://www.awn.com/vfxworld/stephane-ceretti-and-vfx-doctor-strange)

For the super technical among you, these articles (one from a math blog!) go into more details on the types of math/fractals that people picked up on:

  • https://lifethroughamathematicianseyes.wordpress.com/2016/11/13/great-math-in-doctor-strange/
  • https://www.framestore.com/doctorstrange
  • https://www.fxguide.com/quicktakes/bonus-luma-pictures-new-tools-for-doctor-strange/

So ends our journey into interdimensionality for today! See y’all tomorrow, weather permittin’.

🙂

Illusions

I thought what we talked about in class the other day was pretty cool considering I had never really associated math with fun optical illusions. As we studied different ones I would have to say that the music videos were probably my favorite because it incorporated music, which I love, as well as the fun music video with tons of different things going on including illusions, various colors, and patterns. I’ve always found myself interested in colors and patterns, as I work at a daycare I find myself almost always accidentally pushing my kids to create some sort of color pattern for my own pleasure. So I did some further research about illusions and some popular one’s that you all may or may not have seen.

This one was interesting to me because it was all about trying to decide if the horizontal lines were sloped or parallel to each other. We are so focused on if the black and white lines are parallel to each other in terms of being vertical together that it would appear that the horizontal lines are crooked, which they really aren’t.

This is a more simple one. Because our eyes automatically focus on the black dot in the center and it makes it seem as though the black lines are curved,  it therefore makes the two purple lines curved. The illusion it plays on us begins with the black dot in the center, do you think it’s curved or straight? I feel that some people will see it differently but I think that they are in fact straight.

This last one is an old yet effective one. I remember seeing this back when I was way younger in some of the Nintendo DS games, it was part of a series of games. The object is to try and focus on saying the actual color you see not the color the word says. For example, green, red, blue, yellow, blue, black, etc. It may seem easy at first but after a couple times try to speed it up a little to add more difficulty.

 

Overall I find optical illusions really interesting. Honestly, sometimes some of the hardest ones are the most simple and not that difficult to solve we just end up getting into our own heads too much and convince ourself that it’s more complicated than it really seems. I’m excited to see what the rest of the semester holds with colors, shapes, and illusions like these because I actually think they’re much more interesting and fun than taxes stuff we did. (Nothing personal, I just like hands on stuff more than notes and quizzes)