## Digital art by Eric Hayes

I received this email yesterday from Eric Hayes. I like what he's up to so I thought I'd give him a plug. Good luck, Eric.

My name is Eric Hayes, and I am a programmer and digital artist. I have written a software application called "Commander Crayon" which translates the elegance of mathematics to the beauty of art. Every image I create is a direct translation of sets of mathematical equations embedded within a program. To use an analogy of music, I am the composer (programmer) who writes the musical score (the program) that the band plays (Commander Crayon) to produce the music (picture) the audience hears (sees).

To get a preview of some of the images I have created, please go to my website.

I am writing you to announce the publication of the four volume series of my work called "Art, Love, and Mathematics." I hope that you will find the art contained within the books compelling and beautiful. Each book in the series contains over 100 images. The art explores mathematical topics such as Chaos Theory, Fractals, Iterated Function Systems, Strange Attractors, Nonlinear Equations, Statistical Distributions, and Geometry. I have included links to the ebooks below.

**Author Website**

**Author Pages**

**Bookstore Links**

**Art, Love, and Mathematics (Volume 1)**

iBook

Kindle

Nook

**Art, Love, and Mathematics (Volume 2)**

**Art, Love, and Mathematics (Volume 3)**

**Art, Love, and Mathematics (Volume 4)**

## 80 pencils

Check out the great pictures in this blog post by Cory Poole at An Ocean of Knowledge an Inch Deep.

It's the middle of April and this next week all students at University Preparatory School, where I teach, will be taking the California standardized tests. So I decided to design and build a sculpture that I'm calling "Standardized Testing And Reporting" or "STAR", which is what the California testing program is named. The sculpture is made up of 80 pencils and is held together with a variety of glues.

## Great article about Vi Hart in the New York Times

Check out Bending and Stretching Classroom Lessons to Make Math Inspire at the New York Times. It's a great interview with Vi Hart. You'll need a free account at the New York Times to read the article.

I didn't know that Hart graduated with a degree in music and never took a math course in college. Just two years after graduating she has produced amazing work!

## Rolling regular n-gons on catenary “roads”

Here's an interesting exploration, illustration courtesy of Mathematica:

There's a nice animated illustration at Mathematica.

A particularly interesting case of a roulette is a regular n-gon rolling on a "road" composed of a sequence of truncated catenaries, as illustrated above. This motion is smooth in the sense that the geometric centroid follows a straight line, although in the case of the rolling equilateral triangle, a physical model would be impossible to construct because the vertices of the triangles would get "stuck" in the ruts (Wagon 2000).

## Have you seen asciiTeX?

Here's a very geek way to impress your geek friends. asciiTeX!

Like the name says, asciiTeX takes input similar to that for LaTex and renders mathematical equations in plain ASCII. Wow!

Check it out at Sourceforge.net.

## Granddaddy of fractals on TED

From TED:

At TED2010, mathematics legend Benoit Mandelbrot develops a theme he first discussed at TED in 1984 -- the extreme complexity of roughness, and the way that fractal math can find order within patterns that seem unknowably complicated.

Here's some biographical information on Mandelbrot:

Studying complex dynamics in the 1970s, Benoit Mandelbrot had a key insight about a particular set of mathematical objects: that these self-similar structures with infinitely repeating complexities were not just curiosities, as they'd been considered since the turn of the century, but were in fact a key to explaining non-smooth objects and complex data sets -- which make up, let's face it, quite a lot of the world. Mandelbrot coined the term "fractal" to describe these objects, and set about sharing his insight with the world.

The Mandelbrot set (expressed as z² + c) was named in Mandelbrot's honor by Adrien Douady and John H. Hubbard. Its boundary can be magnified infinitely and yet remain magnificently complicated, and its elegant shape made it a poster child for the popular understanding of fractals. Led by Mandelbrot's enthusiastic work, fractal math has brought new insight to the study of pretty much everything, from the behavior of stocks to the distribution of stars in the universe.

And, here's the 17 minute presentation:

## Fractal Foundation fun

In my neck of the woods in northern New Mexico, the Fractal Foundation lives the mission of inspiring interest in science, Math, and Art through the beauty of fractals. The Foundation puts on fractal-related programs in schools and takes them on the road. The Foundation also sponsors a very popular First Friday Fractals night, on the first Friday of the month, for locals and tourists at the planetarium of the New Mexico Museum of Natural History and Science in Albuquerque.

At the Foundation's website are some nice fractal-related resources, many of them free.

- The Fractal Software page has a great fractal viewer (runs on Windows and Mac) that lets you pick from 23 different fractal patterns and zoom in. This one is great fun.
- On the same page there is also a program called "Electric Sheep" that seems to be like the SETI At Home project, but for fractals. For those of you who don't know, SETI At Home is a collaborative effort among millions of PCs to find extraterrestrial life by using some of the compute power in each cooperating PC to analyze signals from space looking for patterns. The idea is that when your computer is idle, like at night, it can give some computer time to the SETI project. Well, Electric Sheep does something similar for fractals. I've not downloaded it but the idea of collaborative fractal building sounds fascinating.
- And, there's "Fractal Grower" (same page) that lets you create certain kinds of fractal patterns.
- There are a half dozen fractal videos at the Fractal Video page. I downloaded the first one, named Glomey, which is 3 minutes 20 seconds long and found the video plus accompanying music to be absolutely mesmerizing.
- The Fractal Art page has some beautiful fractals.

Check out the site. There's a fractal store, a page on chaos theory, and more.

Have fun!

## Phi: It’s everywhere you look

Phi, also known as the golden ratio or the divine proportion, is one of the great mathematical constants. It is equal to a little more than 1.6 and is a most interesting irrational (but not transcendental) number. Phi has a fascinating connection with the Fibonacci series, it can be derived by solving a simple quadratic equation, and it reveals itself in simple but deep geometric constructions.

http://goldennumber.net provides the familiar background material on Phi and then goes much deeper, showing startling examples of how the golden ratio appears in art, architecture, music, poetry, proportions of the human body, and other surprising places.

A fun example of Phi appearing in unexpected places is in the dimensions of a credit card. The ratio of the two sides is very close to Phi.

Another surprising example, at the microscopic level, is the DNA molecule. Each double helix spiral is in the proportion of the golden ratio.

Check out http://goldennumber.net for more than you could every want to know about Phi, all beautifully illustrated.