# Elegant Fractals

### J. C. Sprott

I am writing a book entitled "Elegant Fractals:
Automated Generation of Computer Art" in which I discuss the
methods I have used over the years to produce computer art. It
would include examples of images produced by the repeated
iteration of simple systems of equations. Thus I propose a
discussion of what constitutes "elegance" and why certain images
have more aesthetic appeal than others.

Accordingly, I have written a computer program that calculates the
solutions of millions of equations and plots several thousand of
those that meet certain mathematical criteria. I have looked through
those images and selected 144 examples that I found most visually
interesting and put them into a Google Photo Album.
I ask that you view them, select ones that you find most elegant (or
most aesthetically appealing) and tell me in the comments what you
like about them. You can also comment on any that you think are
"inelegant" and why. Your comments will form the basis for our
discussion. One goal is to improve the computer program so that it
is a more refined critic of its own art.

For anyone interested in the mathematical details, all these images
were produced by about 10 million iterations of the following
equations:

* x*_{new} = *ax* + *bx*^{2}
+ *cy* + *dy*^{2} + *ez* + *fz*^{2}
+ *gu* + *hu*^{2} + *iv* + *jv*^{2}
+ *kw* + *lw*^{2}

*y*_{new} = *x*

*z*_{new }= *y*

*u*_{new} = *z*

*v*_{new} = *u*

*w*_{new }= *v*

where (*x*, *y*, *z*) is the position of each
point, (*u*, *v*, *w*) are the red, green, and blue
components of its color, and (*a*, *b*, ... *l*)
are the parameters that the computer chooses randomly over the range
-1.2 to 1.3 to obtain the different images (which are technically
called "strange attractors").