Math, Art, and Design Course Blog

Bathroom Math

2008-12-19T10:29:00.000-08:00

i was in the bathroom appreciating the rosette patterns on the shower curtain and then i realized the tiles are a frieze pattern and the plant is a fractal... math is everywhere!

More Fractals

2008-12-16T17:16:00.001-08:00

http://www.youtube.com/watch?v=gXVj2SLSnSc&feature=related

So fractals and all the shapes they are in and can become have really started to amaze me. Here's another video showing how with simple manipulation, fractals can change from one thing to the next.

Huge Eggs?

2008-12-14T14:13:00.000-08:00

Speaking of scale, check out these huge eggs! I thought they were pretty funny.

fibanocci sequence/Human body fractals

2008-12-13T16:09:00.000-08:00

I came across this charm with the fibanocci sequence and never would of considered it a fractal until now. It fits its description and relates to more nature and patterns in everyday life, like in plants growth and in our body portions.

Human Body

If you are still not convinced that that fractals, being a math topic, are very important in real life, your opinion might change after finding out that you yourself are made of fractals!

THE LUNGS

The first place where this is found is rather obvious to anyone who knows fractals — in the pulmonary system, which you use to breathe. The pulmonary system is composed of tubes, through which the air passes into microscopic sacks called alveoli. The main tube of the system is trachea, which splits into two smaller tubes that lead to different lungs, called the bronchi. The bronchi are in turn split into smaller tubes, which are even further split. This splitting continues further and further until the smallest tubes, called the bronchioles which lead into the alveoli. This description is similar to that of a typical fractal, especially a fractal canopie, which is formed by splitting lines:

The endpoints of the pulmonary tubes, the alveoli, are extremely close to each other. The property of endpoints being interconnected is another property of fractal canopies.

THE ALVEOLI

Another supporting evidence that your lungs are fractal comes from measurements of the alveolar area, which was found to be 80 m² with light microscopy and 140 m² at higher magnification with electron microscopy. From the geometric method we know that the increase in size with magnification is one of the properties of fractals!

THE BLOOD VESSELS

Similarly to bronchial tubes, splitting can also be found in blood vessels. Arteries, for example start with the aorta, which splits into smaller blood vessels. The smaller ones split as well, and the splitting continues until the capillaries, which, just like alveoli, are extremely close to each other. Because of this, blood vessels can also be described by fractal canopies.

THE BRAIN

The surface of the brain, where the highest level of thinking takes place contain a large number of folds. Because of this, a human, who is the most intellectually advanced animal, has the most folded surface of the brain as well. Geometrically, the increase in folding means the increase in . Instead of 2, which is the dimension of a smooth surface, the surface of a brain has a dimension greater than 2. In humans, it is obviously the highest, being as large as between 2.73 – 2.79. Here’s another topic for science fiction: super-intelligent beings with a fractal brain of dimension up to 3!

MEMBRANES

The surface folding similar to that of a brain was found in many other surfaces, such as the ones inside the cell on mitochondria, which is used for obtaining energy and the endoplasmic reticulum, which is used for transporting materials. The same kind of folding was found in the nasal membrane, which allows sensing smells better by increasing the sensing surface. However, in humans this membrane is less fractal than in other animals, which makes them less sensitive to smells.

The fractal dimension of some anatomical structures are given below. Note that all dimensions are greater than you would expect them to be, and most are fractions, which automatically implies that the structures are fractal.

Anatomical Structure	Fractal Dimension
Bronchial Tubes	very close to 3
Arteries	2.7
Brain	2.73 – 2.79
Alveolar Membrane	2.17
Mitochondrial Membrane (outer)	2.09
Mitochondrial Membrane (inner)	2.53
Endoplasmic Reticulum	1.72

Fractals, in addition to the anatomical structures above can be found in the body on smaller scales in various molecules.

fractal inspired tattoos

2008-12-13T16:06:00.000-08:00

Any subject that I google, its almost positive that someone has it tattooed on themselves. Here are two fractal inspired tattoos, for your viewing pleasure.

create your own snow flakes/fractals/wallpaper patterns.

2008-12-13T16:03:00.001-08:00

I came across this drawing site and your able to create so many different types of images. check them out and try one yourself.
http://www.myoats.com/create.aspx.

more unique fractal art

2008-12-13T16:00:00.001-08:00

I did a general google search for fractal art and I came upon these, which i find very unique to the ones Ive come across so far. Enjoy.

Math Anxiety

2008-12-12T14:45:00.000-08:00

I found a site that helps a TON with coping with math anxiety, which is very helpful right before final exams.

TIps for dealing with math anxiety

2008-12-11T16:47:00.000-08:00

When I was searching for things to blog about, I found Pentomino, which are shapes each made of five squares attached to each other in varying ways. The blocks are then tiled on a plane to create really interesting and stimulating patterns.

The building blocks

A few basic designs

They really remind me of Tetris, mostly.

Fractal Cow?

2008-12-11T14:54:00.000-08:00

Just look at this!

Here you can find the blog dedicated to this cow.

This is what they are saying about it:

The Fractal Cow projects the contradictory vision of contemporary architecture that fractal spaces of nature are being replaced by the artificial fractal spaces of our society.

The conditions of our world's interconnected, hyperactive and dense space can be explored as we perceive it, with its inherent fractal dimensions and qualities exceeding the Cartesian concept of space that has dominated architecture and sculpture.

The underlying structure and labyrinthine networks of the city's architecture are artificial representations of the forms of nature and threaten to obliterate natural environments and vegetation at the same time.

Fractals in nature

2008-12-11T11:33:00.000-08:00

I have been looking at all kinds of fractals that occur in nature, and I thought that there were some very interesting finds, including:

Romanesco Broccoli

Trees and plants, specifically the Fern

blood vessels

Wear your Fractal

2008-12-10T19:14:00.000-08:00

I found a company that makes clothing and other oddities with fractal designs. They are actually pretty cool. Check it out here.

Exam Fun

2008-12-10T17:10:00.001-08:00

I thought everyone would appreciate a little animal humor from Wired Science during the busy week of exams. Enjoy! http://blog.wired.com/wiredscience/2008/12/top-10-incredib.html

2008-12-10T13:21:00.001-08:00

This is a pretty funny video about the number zero.

2008-12-10T13:18:00.000-08:00

This is a really cool fractal of a dragon. It's a really short video, but I enjoyed it.

2008-12-10T13:09:00.001-08:00

For those interested in Knitting and Crocheting, (Alyssa) I found this site which explains the correlation between knitting and math, and how some people use math to answer knitting problems, while some use knitting to answer math problems. On the right side of the site there is a mini-slide show that includes a picture of a mobius strip that someone knit.

Egyptian Fractals

2008-12-10T09:40:00.000-08:00

This image compares Egyptian architectural designs to the Cantor set, a fractal pattern. The Egyptian design is based on the symbol for biological recursion of the lotus flower. Perhaps this design influenced Cantor, who was fascinated with ancient Egypt.

Art and Fractals

2008-12-10T09:35:00.000-08:00

We coexist harmoniously with the fractal patterns in nature, our visual systems process thoughts that themselves have become fractalized, subconsciously in tune with the world around us. In so doing, we have inadvertently added this familiarity to our surroundings by letting fractals permeated our art, architecture, music, and even popular culture.
We can compare a 1920 Mondrain abstract composition with its use of rectangles to a Longone-Birni settlement in Cameroon to the first two stages of a fractal generated piece. This geometric style referred to as Neo- Plasticism, influenced many of architectural and sculptural designs that we now see in the modern world.

Fractal Poem

2008-12-10T09:33:00.001-08:00

"To see the world in a grain of sand,
And a heaven in a wild flower,
To hold infinity in the palm of your hand,
And eternity in an hour."

- William Blake¹, Auguries of Innocence, 1803

2008-12-10T08:04:00.001-08:00

Because da Vinci was obsessed with finding order in the universe, mathematics was a huge part of his life. He said, "the point is the first principle of geometry and no other thing can exist in nature or in the human mind from which the point can originate." He said other principles of geometry are the line, the body, and the body clothed by these surfaces.

2008-12-10T07:48:00.000-08:00

The golden ratio, or golden spiral, has been used in art for centuries to aid in establishing composition. The shape is also frequently seen in nature and various other places. Here is an example above.

2008-12-10T07:23:00.000-08:00

Art forgeries are often detected using mathematical techniques. Various equations were created based on time, age, decay, color retention, etc. This became a popular way to detect forgery with the issue between van Meegeren and Vermeer.

The entire article can be found here.

Angle Calculator

2008-12-10T07:09:00.000-08:00

I found this cool angle calculator online that negotiates focal lengths of lenses and film formats. Click

Math and Painting

2008-12-10T06:27:00.000-08:00

I found this interesting article about the relationship between mathematics and painting. There are a lot of great relationships made. The article discusses van gogh, kandinsky and fractals.

CLICK

Holiday Fractals

2008-12-09T20:49:00.000-08:00

Get 4 large shiny Christmas balls, some coloured wrapping paper, some lights from the Christmas tree, and you have you own fractal laboratory to amuse yourself with over the festive season.

The basic setup is four identical, highly reflective balls sitting is a pyramid formation so that each ball touches every other ball. You can look into the gaps between three balls and either shines light into all or one of the other gaps or places colored paper over the gaps and shines light into the same gap one is looking into (or variations of the above). The resulting of reflections, fractal, has what is known as the Wada property after the Japanese mathematician who studied these spatial divisions in 1917. The Wada property refers to cases when there are three basins of attractions so convoluted that every point on a basin boundary is also on the boundary of all other basins.

More Fun Self-Similar Shapes.

2008-12-09T15:52:00.000-08:00

http://www.youtube.com/watch?v=A4MZubCt87s

I found this video looking for more cool patterns created by self-similar shapes. Some of the patterns in here we have discussed like snowflakes, and other we haven't touched upon, like planets, leaves, and shells.

Fractals built Temples

2008-12-09T09:22:00.000-08:00

I was researching the Indian temples of Khajuraho when I came across a scholarly article that said fractal geometry was the underlining structure for the building of these temples. To be honest, I was surprised! Here is a photo of one of the temples.

flower patterns

2008-12-08T20:25:00.000-08:00

i found this pretty cool program where you can make flower patterns. it reminded me of the wallpaper symmetry groups.

Math in Motion

2008-12-08T17:53:00.000-08:00

I found this fun little animation called the chaotic pendulum. It is made with two springs, and the motion of one pendulum keeps the other one moving in a circle. Check it out!

Sumo paint

2008-12-08T16:13:00.000-08:00

I stumbled on this website that has an art-making program kind of like paint. The difference is that the brushes are cooler, and it has a symmetry tool (the one that looks like a snowflake). The symmetry tool allows you to create a rosette, kind of like the programs we used in class earlier in the semester. I used the symmetry tool to make some cool pictures. Give it a try!

cactus

2008-12-08T15:48:00.000-08:00

I have a grafted cactus on my windowsill and it reminded me of fractals. Many flowers follow the fractal and Fibonacci sequence patterns. Sunflowers are also known to be true to this fact.

2008-12-08T15:33:00.000-08:00

This escher fractal drawing is called "Fish and Scales" and was completed in 1959. Here we see the scales of the large fish developing into fish. The occurs from both sides.

Angles and Focal Lengths

2008-12-08T15:23:00.000-08:00

This chart demonstrates different angles of view from lenses of different focal lengths. On a camera, lenses of different focal lengths distort and manipulate the image in various different ways depending on how long or wide it is.

Aperture and Math

2008-12-08T15:18:00.000-08:00

Aperture is a space through which light passes in a photographic instrument. Light gathering power is determined by the area of the lens or mirror. The area of a circle equals pi times the radius squared.

Bellows Extension Compensation

2008-12-08T15:07:00.000-08:00

When doing close up work in large format photography, there are several mathematically based formulas to figure out how to compensate for the extra space that the light has to travel. Because the light has to travel further to hit the film plane, typical light meter exposure has to be adjusted. Here are a few formulas:

BE=bellows extension FL=focal length

Zero to Infinity in Nothing Flat

2008-12-08T14:33:00.000-08:00

On helasculpt.com, you can see the sculpture of Helaman Ferguson, who expresses mathematical equations through sculpture. His process is equally weighted with the mental (mathematics) and the physical (sculpture).

2008-12-08T14:23:00.000-08:00

I found this artist, Eric Hammel, who makes digital art from fractal dimensions. A writer of military history books, Hammel became interested in this type of art when Kai's power tools plug in was first released for windows photoshop. Now he uses applications such as Ultra Fractal and Apophysis. A 8.5 x 11 print sells for $75!

2008-12-07T15:48:00.000-08:00

http://www.youtube.com/watch?v=J-fcRzvRBqk&feature=related

Infinity + mirrors = fractals

2008-12-07T07:55:00.000-08:00

I just moved into this nice new apartment- already furnished and with several large mirrors hanging. I just realized last night that two big mirrors face each other at either end of the main hallway- you can basically look into infinity in either one although they're only about 15 ft away from each other. The images are self-similar and repeat endlessly...
It reminded me of this famous Dutch painting although i guess Jan Van Eyck's mirror doesn't repeat endlessly- BUT while i was searching for the image i also found this intersting image/info about another mirror.
Tibetan, 17th Century
Divination Mirror of the State Oracle of Tibet
"Seven metal" silver alloy, gold, and turquoise.
"When advising the Dalai Lama, the State Oracle wears an elaborate costume, including this mirror on his chest. In deep trance, he looks into the mirror, not directly, but through another mirror held by an assistant in front of him. Through this doubly distant vision he foretells the future and gives advice."

Lego Sculptures

2008-12-06T22:26:00.000-08:00

These mathematical lego sculptures were made using computer code, which reminded me of what we've been learning about fractal computer programs in class. I think these are especially impressive because the shapes are so curvy even though they are made up of lots of small rectangular blocks. Also, legos are awesome.

the social aspect of art

2008-12-06T19:49:00.000-08:00

this is to comment on kcantor's comment on the email conversation that David Thorne had about the drawings. this is a piece that speaks to the very soul on the topic of how can one price art. the worth of this piece to begin with is about 27 million or something. it has diamonds all over it. the point trying to be made by the artist is art has an imaginary number on it. the amount of art is never specified to something like the tools used or how much paint was used but rather it just had a random number placed on it, and yes people thought about the time and effort placed onto their piece and gage that for the amount. however with this piece there is automatically a price tag on the piece, without time placed on making it and the effort of the artist. so as you can see art is less of substance anymore its more about the name behind the piece of late. so what is the true problem today. society or one's self as an artist?

foreign fruit

2008-12-06T06:09:00.000-08:00

Ever seen a califlower like this before? I typed in fractals in nature and this was one of the first images it presented. It looks almost alien to actually eat this.

Pruning

2008-12-01T20:24:00.000-08:00

So i was thinking about fractals and trees. These are an obvious example that we see all the time (especially now that the leaves have fallen the shape of the tiny twigs are so clear and resemble the trunk and main limbs)
so Pruning trees... what does that do to the fractal structure? how do trees compenate for this interference in their natural pattern?
Also Strawberries are amazing and the way they propagate is to send out runners which then take root and grow up to be big enough to send off their own runners. In this way, they are self-similar and continue in an endless fractal-like pattern of growth (more strawberries for everyone!)

2008-12-01T08:50:00.000-08:00

Our group could have so made this if we had enough time and bigger sheets of cardboard.

2008-12-01T08:38:00.000-08:00

I was wondering why we should learn about fractals so I decided to search online to see if it had any relavcence or daily use. To me the images look a little silly and I didnt understand how the Math could be used. But I found this web site that talked about technology that was made through the knowledge of fractals to monitor fluid movements. I don't really understand all of what they say but check it out.

www.arifractal.com

Web Cams

2008-12-01T07:36:00.000-08:00

Hey! I am looking for a web cam to be able to communicate with volunteers in Africa. It has to be suitable for a Mac computer. Does anyone have any suggestions?? I am clueless.

Thanks!

New Wind Turbine Design

2008-12-01T07:29:00.000-08:00

A more attractive wind mill design has been made for rural and urban environments. It is pretty cool and definitely eco-friendly. One of these towers can provide 25-30% of the electricity needed to run a house!

2008-11-30T17:36:00.000-08:00

If you haven't read this, do yourself a favor and do so:

Below is the complete email conversation that Adelaide man David Thorne claims he had with a utility company chasing payment of an overdue bill.

From: Jane Gilles
Date: Wednesday 8 Oct 2008 12.19pm
To: David Thorne
Subject: Overdue account

Dear David,
Our records indicate that your account is overdue by the amount of $233.95. If you have already made this payment please contact us within the next 7 days to confirm payment has been applied to your account and is no longer outstanding.

Yours sincerely, Jane Gilles

From: David Thorne
Date: Wednesday 8 Oct 2008 12.37pm
To: Jane Gilles
Subject: Re: Overdue account

Dear Jane,
I do not have any money so am sending you this drawing I did of a spider instead. I value the drawing at $233.95 so trust that this settles the matter.

Regards, David.

From: Jane Gilles
Date: Thursday 9 Oct 2008 10.07am
To: David Thorne
Subject: Overdue account

Dear David,
Thankyou for contacting us. Unfortunately we are unable to accept drawings as payment and your account remains in arrears of $233.95. Please contact us within the next 7 days to confirm payment has been applied to your account and is no longer outstanding.

Yours sincerely, Jane Gilles

From: David Thorne
Date: Thursday 9 Oct 2008 10.32am
To: Jane Gilles
Subject: Re: Overdue account

Dear Jane,
Can I have my drawing of a spider back then please.

Regards, David.

From: Jane Gilles
Date: Thursday 9 Oct 2008 11.42am
To: David Thorne
Subject: Re: Re: Overdue account

Dear David,
You emailed the drawing to me. Do you want me to email it back to you?

Yours sincerely, Jane Gilles

From: David Thorne
Date: Thursday 9 Oct 2008 11.56am
To: Jane Gilles
Subject: Re: Re: Re: Overdue account

Dear Jane,

Yes please.

Regards, David.

From: Jane Gilles
Date: Thursday 9 Oct 2008 12.14pm
To: David Thorne
Subject: Re: Re: Re: Re: Overdue account

Attached

From: David Thorne
Date: Friday 10 Oct 2008 09.22am
To: Jane Gilles
Subject: Whose spider is that?

Dear Jane, Are you sure this drawing of a spider is the one I sent you? This spider only has seven legs and I do not feel I would have made such an elementary mistake when I drew it.

Regards, David.

From: Jane Gilles
Date: Friday 10 Oct 2008 11.03am
To: David Thorne
Subject: Re: Whose spider is that?

Dear David, Yes it is the same drawing. I copied and pasted it from the email you sent me on the 8th. David your account is still overdue by the amount of $233.95. Please make this payment as soon as possible.

Yours sincerely, Jane Gilles

From: David Thorne
Date: Friday 10 Oct 2008 11.05am
To: Jane Gilles
Subject: Automated Out of Office Response

Thankyou for contacting me. I am currently away on leave, traveling through time and will be returning last week.

Regards, David.

From: David Thorne
Date: Friday 10 Oct 2008 11.08am
To: Jane Gilles
Subject: Re: Re: Whose spider is that?

Hello, I am back and have read through your emails and accept that despite missing a leg, that drawing of a spider may indeed be the one I sent you. I realise with hindsight that it is possible you rejected the drawing of a spider due to this obvious limb ommission but did not point it out in an effort to avoid hurting my feelings. As such, I am sending you a revised drawing with the correct number of legs as full payment for any amount outstanding. I trust this will bring the matter to a conclusion.

Regards, David.

From: Jane Gilles
Date: Monday 13 Oct 2008 2.51pm
To: David Thorne
Subject: Re: Re: Re: Whose spider is that?

Dear David, As I have stated, we do not accept drawings in lei of money for accounts outstanding. We accept cheque, bank cheque, money order or cash. Please make a payment this week to avoid incurring any additional fees.

Yours sincerely, Jane Gilles

From: David Thorne
Date: Monday 13 Oct 2008 3.17pm
To: Jane Gilles
Subject: Re: Re: Re: Re: Whose spider is that?

I understand and will definately make a payment this week if I remember. As you have not accepted my second drawing as payment, please return the drawing to me as soon as possible. It was silly of me to assume I could provide you with something of completely no value whatsoever, waste your time and then attach such a large amount to it.

Regards, David.

From: Jane Gilles
Date: Tuesday 14 Oct 2008 11.18am
To: David Thorne
Subject: Re: Re: Re: Re: Re: Whose spider is that?

Attached

Attention Art Students: Free Photoshop Brushes

2008-11-24T16:12:00.000-08:00

These Fractals Like Nebula Photoshop Brushes are made by Ali Sutter (Female-USA). These are Fractals and Nebula's that looks like fractals. The folder contains 15 PhotoShop brushes and 15 PNG images for 7.0 user to convert into brushes if these don't work for 7.0. Ali Sutter has done some good works and you can see them at her gallery.

And if you go to the link, u can download the set for free, their awesome.
http://photoshop-freebies.blogspot.com/2007/09/fractals-like-nebula-brushes.html

DIY Cardboard Furniture

2008-11-24T16:08:00.000-08:00

We're now looking at all the large cardboard boxes in a new light after seeing these impressive DIY furniture creations made by the Parisian artist collective known as the Cartonnistes. Founder Eric Guiomar began creating cardboard furniture after looking for affordable and lightweight seating, and now offers classes in the construction technique he developed...

The materials used are readily available and easy to find. Add a few dollars worth of glue, paints, pigments and water-based varnishes, buy another $50 worth of tools and you are ready to start production as an art, a hobby or a business.

You can check out a real life project following the Cartonnistes' technique here; looks like a lot of trial and error but a fun project if you have the time and space. Order your own instructional DVD here.

And it looks like New Yorkers will have the opportunity to participate in cardboard furniture workshops from September 20th-28th. We can only hope the La Compagnie Bleuzen decide to make a west coast trip in the near future.

Cardboard Artwork

2008-11-24T16:01:00.000-08:00

Chris Gilmour is an Italian artist that creates life-size sculptures out of cardboard and glue.
He uses no supporting structure, and no wooden or metal frames. He

uses cardboard to show that extravagant artwork can be created from everyday household materials.

In an article written by Guido Bartorelli, he says that Chris Gilmour “compares his sculptures to drawing, a way of seeing objects by observing and measuring them. There is a process of deconstruction, followed by the actual construction process. It is in this process of making, in an almost instantaneous and immediate construction, as if Gilmour was using a pencil on a piece of paper, that the subtlety of diversity is embodied.”

Back to Tesselations Artwork

2008-11-24T15:53:00.000-08:00

I stumbled upon this artist, the other day. Yehrin Tong is an illustrator/ graphic designer and creates a lot of album and advertisement work all around images that repeat and rotate around itself. Much of the work becomes fashion fabrics, something I personally would buy because of its uniqueness and originality. The website to see more is

Andy Goldsworthy

2008-11-22T13:58:00.001-08:00

As artists, most of us know of Andy Goldsworthy's work. He is a very respected artist for making installations using nature's materials in the landscape. After creating these beautiful pieces, he then allows nature to take over. The installations often fall apart almost immediately, and some over a longer period of time. It amazes me how he is able to make this work. Here are a few images.

Scale in Google SketchUp

2008-11-22T13:56:00.001-08:00

I don't know if I am the only one, but I still find Google SketchUp to be kind of confusing. I stumbled upon this video about the scale tool in the SketchUp program. I hope ya'll find it as useful as I did!

Look Around You

2008-11-19T16:20:00.000-08:00

My friend told me about these funny, joke math videos making fun of those videos we had to watch in high school that were seriously out of date and lame. It's pretty good.

http://www.youtube.com/watch?v=drE5cHe6c3s

Senior Thesis Show and Book

2008-11-18T16:24:00.000-08:00

My senior thesis show has been scheduled and I have published a book to go with it! I hope to see you all there!

Exhibition Dates:
December 15 - 20th, 2008
Reception:
Friday, December 19th 6 - 8 pm
Location:
601 Newbury Street Boston, MA

also showing: Ariele Hertzoff and Chris Villano

PUNCH OUT STYLE CHAIRS

2008-11-17T09:14:00.000-08:00

What better time than now to show this? This 'Cardboard punch-out' design stool comes complete with its own hang sell. Easier than a three year old's jigsaw puzzle, the pieces pop out of the frame to create a simple yet stylish stool.

see you guys in class!

a landscape with dreams

2008-11-17T08:50:00.001-08:00

i know this chair isn't cardboard, but i was looking into cardboard chairs researching kind of for this project, and i stumbled on this blog all about chairs. they had all kinds of chairs, for airplanes, for lounging, and even one that could be twisted into a lounge chair, a study chair, or an everyday chair. but i thought the one below was the best, it said it was a lounge landscape. and it definatly is in my opinion. it creates this air around the lady making her seem as though she is larger than any human being. i love the way it cuts into the space so deliberatly and yet you just flow through it. it plays on depth and comfort which is so odd but extremly appealing. it's exciting what you could do with ideas.

M.C. Escher inspired tattoo

2008-11-16T13:03:00.000-08:00

Cool video to check out if your either:

A) Into tattoo's

or

B) into M.C. Escher.

enjoy.

triangles vs. I's

2008-11-12T09:15:00.000-08:00

I was thinking about corrugation and kind of realizing that it is just like a set of triangles put next to each other and also lie on top of each other. the distribution of weight for a triangle is what makes it so efficient and so if you put a bunch of triangles together they would be even more strong since you are setting up three points in which weight can be distributed. cardboard is strong because of corrugation which is strong because of the triangular form it has inside and triangles are strong because they have three solid walls that place weight on two opposite ends of the bottom wall. however i was wondering why most construction companies use the I form beams to build building since they seem to be the least efficient beams, and i realized space plays a part in buildings. I beams you don't need many to sustain a lot of weight since we realized they hold the most weight. you just need a few distributed correctly and the space saved and the weight managed makes it somewhat more efficient to the building itself.

tesselating leaves

2008-11-10T18:29:00.000-08:00

every time i walk down a street with an oak tree i think about tessellations. I keep feeling like these leaves could tessellate, or maybe a few different types of leaves could fit together and continue endlessly... there's just all this really great positive and negative space in these leaves...

2008-11-10T16:16:00.000-08:00

Check out these crazy cardboard pieces of furniture. Can you believe people pay this much for them?

CURVY CORREGATED CARDBOARD CHAIR

by Jill Fehrenbacher

Frank Gehry made design history in 1972 when he designed a whole set of curvy modern furniture out of cardboard. You’ve more than likely seen Gehry’s classic Wiggle Chair hanging out around stylish offices and design spaces - showing off the strength, durability, and organic comfort that is possible with layered corrugated cardboard…

You can buy the classic Gehry wiggle chair from many mid-century modern design shops (like Moss) for 850 bucks, which isn’t too bad for a classic design icon. However, we’ve just discovered that there is now a cheaper and more eco-friendly knock-off of the same thing at cardboardchair.com.

We are not exactly sure what is going on with the intellectual property here, but we do know that the business looks perfectly legit and Cardboardchair’s version of the Wiggle chair is about half the price of the original ($430) - AND is made with 30% recycled cardboard:

$850 - Gehry Wiggle Chair at Moss

$430 - Curvy Side chair at Cardboardchair.com

In addition, the Cardboard chair company seems to have surpassed their original point of inspiration, because they’ve come up with a whole new set of designs for tables, stools and even shelves that are really clever and beautiful - designs that would probably make papa Gehry proud (if he isn’t mad about his classic chair getting ripped off…)

4-Petal Table - $430

Cadence Shelves - $490

Uderwater exploration.

2008-11-09T18:57:00.001-08:00

http://www.ted.com/index.php/talks/graham_hawkes_flies_through_the_ocean.html

Flying underwater machine

2008-11-09T18:36:00.000-08:00

Amazing cardboard work!!!........check it out

Columns and Beams

2008-11-02T09:59:00.000-08:00

my house on cape cod was an old barn but was restored by my father, but as you can see it still has the old barn style beams and columns, they haven't buckled on us or collapsed in any way so from my experience the octagon shaped column and the square shaped beams work great...

Soicety

2008-10-27T16:11:00.000-07:00

Why do societies fail? With lessons from the Norse of Iron Age Greenland, deforested Easter Island and present-day Montana, Jared Diamond talks about the signs that collapse is near, and how (if we see it in time) we can prevent it.

http://www.ted.com/index.php/talks/jared_diamond_on_why_societies_collapse.html

frieze patterns in earthen art

2008-10-23T07:07:00.000-07:00

I have been studying a lot of eco-art therapy. I have this wonderful book "Dig Your Hands in The Dirt: A Manual for Making Art out of Earth" by Kiko Denzer I was reviewing some of the material in this book to get inspiration for a project to do with the kids I work with at CitySprouts.
I noticed that a lot of the tile patterns he uses to make mud mosaic murals are made into frieze patterns. He describes how to make your image more simplified, create a pattern out of it and reverse and repeat the image. The work he does is beautiful and full of symmetry!
P.S. we're trying to start some mud mosaic murals as a part of the eco-expressive therapies group at Lesley- let me know if you're interested!

another escher master piece

2008-10-21T17:29:00.000-07:00

I found this by Escher. Its a more complete illustration by him displaying his artistic skills in composition set up and use of the gray scale very effectively. His talent in creating a metamorphosis' are amazing.

origami tesselations

2008-10-21T17:26:00.000-07:00

folding paper lamp by Kouichi Okamoto

This beautifully unique lampshade is expertly handcrafted from Denguri paper found locally in the Shikoku region of Japan. The honeycomb paper diffuses the light creating a soft, gentle glow.
It is designed by Kouichi Okamoto, and manufactured by Kyouei Co. Ltd., Japan.
He’s got some rather impressive and unique design concepts- you can see some more information on his designs here.

2008-10-20T08:49:00.000-07:00

I just thought that this video pertained to what we were doing in class. Just some cute and creative tessellations http://www.youtube.com/watch?v=Aq6eLQihh2M&feature=related

A new look at everything

2008-10-19T20:39:00.000-07:00

http://www.ted.com/index.php/talks/garrett_lisi_on_his_theory_of_everything.html

2008-10-19T12:00:00.001-07:00

While brainstorming ideas for the Tessellation project I checked out some work done from artists all around the world. Here's a link to a Tessellation artist data base, http://tessellation.info/?open=general/artistinfo.php&lang=english&style=default.

Looking at this work will help you form a piece of your own.

Wordle

2008-10-15T07:35:00.000-07:00

My 10-year-old sister showed me this site! Wordle is a toy for making "word clouds" from text that you enter. The words you want to put into patterns are arranged randomly by an ingenious program designed by an IBM programmer. The arrangements are unique in different sizes, fonts, colors and shapes. (It takes a little while to load so be patient!) Here is one I made. I have also posted one someone made using Barack Obama's 2004 speech.

Yann Arthus-Bertrand

2008-10-15T07:29:00.000-07:00

Photographer Yann Arthus - Bertrand is aiming to inspire people to think globally about sustainable living. He has been photographing our planet from above since 1994. His images are amazing! Click here to see more.

Digitized books

2008-10-13T18:01:00.000-07:00

I was just looking around and found this very interesting. Rice University professor Richard Baraniuk explains the vision behind Connexions, his open-source, online education system. It cuts out the textbook, allowing teachers to share and modify course materials freely, anywhere in the world.

http://www.ted.com/index.php/talks/richard_baraniuk_on_open_source_learning.html

Math and art

2008-10-13T12:45:00.000-07:00

I found this website which shows a project that I thought looked pretty cool. From what I gathered, they made this whole structure out of a bunch of hexagons arranged in different shapes. The final result is pretty big and impressive.

Tessellation project

2008-10-13T09:14:00.000-07:00

I wikipedia(ed) tessellations and through clicking links i came upon Tiling with Regular Polygons.
There were a lot of different cool graph paper-ish ideas that could be helpful for the project we have. If you click on the image there is a bigger version that you can print and doodle on. I thought this pattern could be really interesting to try and make a design with.

Tessellation Program

2008-10-07T09:41:00.000-07:00

I found a program that makes tessellations for you, like Kali makes wallpaper patterns. It is fun and definitely useful. Here it is!

Pattern Artists

2008-10-07T07:06:00.000-07:00

I found these two portfolio websites this summer of illustrators who do patterns. If you go to the pattern sections of their portfolios you can see that many of them were actually purchased and printed on merchandise. Many of the patterns don't have reflection or rotation, just translation. They are, however, really cute.

Julia Rothman

Helen Dardik

Tessellation in class

2008-10-06T13:44:00.000-07:00

So during class today we were all tessellating with rectangles, parallelograms and triangles. that was easy enough, but when question 6 asked us to use a shape that was a little weirder it was really a challenge. I admit that instead of paying attention to what came next in class i continued to work on this shape. I was going to make it work. And i did! check it out! (look only at the dark blue lines)

James Nahtwey

2008-10-05T23:07:00.000-07:00

This is important. http://www.ted.com/index.php/talks/james_nachtwey_fights_xdrtb.html

Wallpaper artists

2008-10-05T19:57:00.001-07:00

I was stumbling around the internet and I came across this website full of wallpaper design artists.....there are some unique designs and some terrible ones but there are many artists to choose from with multiple pieces, check them out.....they also show some images of the machines used to print the paper. here's the link "http://www.wallpapersbyartists.com/"

MC Escher

2008-10-03T07:07:00.000-07:00

This web page has a few short videos about Escher and his work. The videos show a slightly different view of his patterns than what we are doing in class. The interviews are in black and white and subtitled, but I suggest you watch them just to see Escher's silly beard. In one interview he talks about how he was supposed to be an architect but he chose to be a graphic artist instead. There is even a video of him making a wood carving for one of his prints, which I thought was very cool.

The many ways and shapes to math.

2008-10-01T22:00:00.000-07:00

so i was searching online for something cool and interesting to put onto my post, and i finally stumbled upon this site. basically it's what we have been doing in class just interpreted in a diffrent way, and with a different flow chart (which was what i think the teacher was saying that there are a bunch of different ways to categories frieze patterns and so many mathematicians use these other types of charts to decipher frieze patterns). So i tryed it and it is pretty difficult since i'm used to the p-_ _ _ system. But it's fun to see what you get out of this system, don't try too hard cause this should just be fun. And also it shows different types of patterns for different cultures, time periods etc. Its an interesting little article not too long take a look.

http://www.phschool.com/atschool/math_activity_library/frieze_frames_s.html

Russian Constructivism

2008-09-30T06:02:00.000-07:00

I found this website showcasing one of my favorite design movements, Russian Constructivism (correct me if it is actually another -ism, they aren't labeled but I'm pretty sure). Design 1- Design 8 shows a bunch of examples. Constructivist design is based very heavily on geometric shapes, as well as the use of angled figures and typography to create movement in the composition. This was a huge breakthrough in design at the time, because static text and realistic images were replaced with flat and very expressive geometric-based compositions.

The Divine Proportion and DESIGN!

2008-09-28T14:27:00.001-07:00

This is continuation from my last comment about the Divine Proportion. I found out that the design process should also follow this "natural language". The Golden Section, or the Divine Proportion is a visual representation of a number called Phi. Phi is a number produced by bisecting a line at a particular point (see above.) Phi is 1.618033988749895, or by the numerical sequence called the Fibonacci sequence. If you use the Divine Proportions in creating your compositions it will improve the communication of the design. I think an example would be paper. Anyone want to figure that one out?

2008-09-28T14:19:00.001-07:00

New Technology! touch screen and intuitive keyboards.

Baman vs. Piderman

2008-09-28T14:19:00.000-07:00

This video doesn't have much to do with Math but it is full of epic artness check it out!

paper folding architecture

2008-09-28T07:54:00.000-07:00

I stumbled upon this website about using geometry to fold paper into architectural forms. Here is a quote from the page about how they were created:
The original form was generated by radiating the hexagonal grid of a geodesic sphere and trimming the resultant surfaces with an inner and outer cube. The resulting network of cells gives the impression of a sphere caught within a cube.

http://roryhyde.com/pavilion.htm

tessellations

2008-09-26T07:02:00.000-07:00

http://www.mathpuzzle.com/Tessel.htm
this website classifies different types of tessellations. it also gives examples of translation, rotation and reflection.

Math can even make things absurd.

2008-09-25T07:21:00.000-07:00

http://www.alaska.net/~clund/e_djublonskopf/Flatearthsociety.htm

Contraptions

2008-09-24T19:28:00.000-07:00

This game lets you create contraptions to move shapes to their goals. You learn a lot about the structure and strength of different shapes. It also allows users to save and show off their contraptions and the way they chose to solve puzzles. You don't need an account to play though either. Enjoy, it's fun!

http://fantasticcontraption.com/

Geometry and Symmetry at its Best

2008-09-24T08:45:00.000-07:00

The Symmetry of Man by Leonardo Da Vinci is distinctively geometry and symmetry. This type of symmetry is called relfectional symmetry. There are five points (looks like a pentagon) which is said to be "the five points of living things." Da Vinci illustrates the form with two positions of both arm and legs. This depicitingg symmetry and proportion of the human figure.

2008-09-22T18:42:00.000-07:00

http://www.ted.com/index.php/talks/robert_lang_folds_way_new_origami.html

Applied math to make crazy origami figures, relating origami to every different type of math such as quantum mechanics in simplicity, where simple laws govern the entire subject. Break down into the simplest form and move from there, shape related to square is equal to origami. The movement in origami is related to science and moving large objects into space by folding them, and finally to saving lives. Very Very interesting.

Math Magic

2008-09-22T18:32:00.000-07:00

http://www.ted.com/index.php/talks/arthur_benjamin_does_mathemagic.html

Arthur Benjamin is a truly amazing mathematician who does HUGE math equations in his head, it is almost a performance. Enjoy his math magic.

article on rosette patterns

2008-09-22T08:34:00.000-07:00

so i found this article online on rosette patterns and thought it was pretty interesting and thought you guys should have a look http://www.jstor.org/pss/1576515

2008-09-22T07:54:00.000-07:00

So I wikipedia-ed mathematics and art, and found something kind of interesting about platonic solids and polyhedrons being used frequently in western art. "In geometry, a platonic solid is a regular convex polyhedron. These are the three-dimensional analogs of the convex regular polygons...They are unique in that the faces, edges and angles are all congruent" (wikipedia).

These shapes appear in, to name a few, Dali's "The Last Supper", da Vinci's book The Divine Proportion, and Albrecht Durer's "Melancholia".

Rosette Patterns- -Spider Web

2008-09-21T20:05:00.000-07:00

While i was playing with some rosette patterns on Kali, i was reminded of this spider web i once saw.
(the setting- we were in the jungle and my friend was nursing a crazy infection that prevented him from walking...)
I walked in to my friends room to check on him and when i looked in the corner, I was kind of shocked, mostly in awe of this beautiful spider web. When i commented on the intricate and unique pattern, my friend smiled and said "yeah... i watched him make it"
The pattern is amazing to me as is the thought of Joe sitting there all day watching the spider move back and forth through space to weave this web...
Just like we criss cross and set points with the mouse in the Rosette program on Kali, this spider built his web building thread upon thread in this pattern he knew to create...

pattern game

2008-09-21T17:26:00.000-07:00

i came across this game that reminds me of the patterns you can make with kali.
it's fun and it's based on symmetry and patterns.
patchworkz!

2008-09-21T11:26:00.000-07:00

We talked about Robert Smithson in my critical theory class...a lot of his work is mathematically based. The drawing of his, "A Heap of Language", which was made in 1966, is widely talked about in art historical circles. It uses a traditional grid format that was typical in the 50s and 60s. He also does some cool geometrical earthworks.

Here's a link to his website: Robert Smithson