MATH ART
" It
is certain that the real function of art is to increase our self-consciousness;
to make us more aware of what we are, and of what the universe in which we live
really is.
And since
mathematics, in its own way, also performs this function, it is not only
aesthetically charming but profoundly significant. It is an art, and a great
art." . . . (John W.N. Sullivan)
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I suppose
the classic examples are the Mandelbrot Set and the work of M. C. Escher, which
is very mathematical and based on the theory of infinite series. The Mandelbrot
Set was the first example of what are called "fractals" in art: it is
an interesting and extraordinarily complex mathematical object (but with an
extremely simple description), and pictures of it, or of parts of it, are very
beautiful.
Fractals
are now commonly used in many computer graphics applications. Fractal art makes
"natural" looking things, mathematically creating realistic trees,
rocks, or mountain ranges for instance.
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Your assignment is to create a piece of
"mathematical art" for our classroom (I, for one, was getting a
little tired of looking at those health class collages). And when I say that "you will create
it" I mean by your own two hands (it especially cannot be a picture that
you simply printed off of a computer). I
want to see some of your natural-born talent on display, and I know that you
guys (and gals) have a lot of that.
So what is Math Art? I believe that the name should say it
all. It is some form of art that can be
related to mathematics in some way. Some
examples are Escher drawings, origami, quilts, some Native American designs,
and computer generated Fractals. All of
these have some pattern built into them, and you know how those crazy
mathematicians like to find patterns.
And where can you see some of this art? Well, I've included in this handout a few web
sites for you to peruse and get some ideas.
This page will also be available for you to access on ServerTwo ("Math Art" folder). These sites mainly focus on Escher drawings
and Fractals, but there are also a few links to other topics. And you can always do a search yourself for
"mathematical art". I'm sure
that you know how to do this Internet work a bit better than me, so I won't
make too many suggestions.
You will be graded on your originality, your
creativity, your neatness, and your ability to relate your artwork to some
aspect of mathematics. This means that
you must also type up a short
(1 or 2 page) explanation relating the art to mathematics. You will also have to give a quick oral
presentation (2 to 5 minutes) about your artwork and explain how it relates to
mathematics (essentially restating what you wrote…but NOT reading what you
wrote to the class).
A few quick notes:
Your piece of artwork can be no larger than 1 piece of poster board and
no smaller than 1/2 of a piece of poster board.
Also, I can't reiterate enough how much I value creativity and
originality of thought. Also, to those
of you who are afraid of trying to be an artist, all I ask is that you give it
your best. I can tell when you have
truly made the attempt.
Good luck, and I look forward to seeing the finished product!
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MATHEMATICAL ART WEBSITES
Visual
Mathematical Art:
http://www.mi.sanu.ac.yu/vismath/fath/
Examples
of Art in Math:
http://wwwpa.win.tue.nl/wstomv/math-art/
Mathematical
http://www-sop.inria.fr/safir/SAM/Izic/images.html
Art in
Mathematics:
http://www.sinc.sunysb.edu/Stu/rhenken/Robin'sEzine.html
(has
some good links to sites about all kinds of “mathematical art”)
Maple Art:
http://www.mapleapps.com/categories/graphics/gallery/mathart.shtml
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MC Escher Sites
http://www.mathacademy.com/pr/minitext/escher/
“The Mathematical Art of M.C. Escher” Great site. Lots of explanations (some may be a bit too
involved). Good links.
“The Official M.C. Escher Website” A few good links. Some pictures. Some explanations.
http://www.djmurphy.demon.co.uk/escher.htm
A personal webpage. Lots of
images!
“The Site for Everything Escher” Check out the
“GALLERY” link for lots of Escher drawings.
While on the Gallery page, go to the “Escher from the Internet” link for
Escher-like images
created by other people.
Many
sites related to M. C. Escher can be found.
An Escher sketcher can also be downloaded. I found a link at the following site: http://www-sphys.unil.ch/escher/
("Download
Escher Web Sketch"), but I’m sure that there are other sites (as well as other
programs) available.
FRACTAL WEBSITES
What is a
Fractal?: http://www.glyphs.com/art/fractals/what_is.html
A basic history of fractals. A general overview of what fractals are. A few images.
What are
Fractals?: http://math.rice.edu/~lanius/frac/
A teacher's step-by-step
explanation of Fractals and how they are created.
What is a
Fractal?: http://www.ccinet.com/~rob/fractal/what.html
More explanation and examples of basic fractals.
The Spanky Fractal Database:
http://spanky.triumf.ca/
!!! GREAT SITE FOR LOTS OF
EXAMPLES!!! This is a really nice place
to start looking at Fractals. I didn’t
check all the links, but it seems to have a large collection of fractal related
materials (esp. “fractal images at other sites” link…I checked out the Flying
Frog and the Fractal Bugs links, and they were pretty cool!)
THE SPANKY FRACTAL DATABASE, a collection of fractals and
fractal related material. Includes includes the following links:
·
What's
New in Fractals
·
An
index of Fractal material at Spanky.
·
Some
General information about Spanky.
·
Some
info about the fractal images stored at Spanky.
·
Welcome
to the Fractint Web Pages at Spanky.
·
Fractal
documents at other sites.
·
Fractal
images at other sites. (highly recommend this link)
·
Fractal
programs at other sites.
·
Interactive
Fractal Explorers at other sites.
·
Miscellaneous
Fractal material at other sites.
·
Chaos
and Nonlinear Dynamics at other sites.
·
Near
Subject Related material at other sites
For more information on the basics
of Fractals, search Google with "what is a
fractal".
Fractal Freeware:
Flarium24
Flarium24 is an interactive fractal generating
program. Many sites to download this
program can be found.
Fractint
Fractint is
a freeware fractal generator created
for IBM PC's and compatible computers. It is the most versatile and extensive
fractal program available for any price
(can be found at http://spanky.triumf.ca/www/fractint/fractint.html)
Fractal Tutorial: http://life.csu.edu.au/complex/tutorials/tutorial3.html
good explanations of fractals, nice
examples of fractals in real life
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