Bathroom Math

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

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?

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

fibanocci sequence/Human body fractals

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

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.

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

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

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

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?

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

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

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

Exam Fun

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

This is a pretty funny video about the number zero.

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

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

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

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

"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

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.