FRACTAL
AND PHOTO
Images
from Math and Nature |
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Mathematicians
have long known that patterns can form when certain types
of mathematical equations are iterated millions of times over
and the results are graphed. The process of iteration is where
the result of a solved equation is plugged back at the starting
point and solved again. A modern PC is able to perform this
iteration very quickly. Using colorizing software these patterns,
called fractals, can readily be generated and appreciated.
This
website features galleries of fractal images that I have generated;
it also features photographs of nature scenes that I have
taken. These two sets of images may seem very dissimilar,
but there is a real connection.
I first learned about fractals when I recently took up nature
photography. Fractals often show self-similarity. This is
where a small portion of the fractal resembles or is identical
in form to the whole. Self-similarity is also seen in nature.
Examples include the contours of coastlines, the branching
of trees and river systems, cloud formations and the shape
of galaxies. It was a book of photographs by the late nature
photographer Eliot Porter called “Nature’s Chaos”
that alerted me to these relationships. The text of that book
was written by James Gleick, who wrote a book called “Chaos”
that explained in fascinating detail a theory called the Chaos
Theory. Fractal images are but a small part of this theory
that assigns a non-Euclidean geometry to many of nature’s
forms and offers a new way of looking at our world. Both books
are highly recommended.
The nature photographs on this site are varied. Many do not
show nature’s fractal patterns. Along with photos of
local scenery and flora there are however some that feature
subjects with a fractal geometry. Examples are the structure
of a fern, ice formations, river turbulence as evidenced by
foam and drainage patterns in beach sand. I hope to present
more images of this type with updates to this site. I also
enjoy nature images with an abstract or painterly aspect to
them. I hope I am successful in here sharing with you nature’s
patterns of form and color.
I hope that you enjoy the images on this website. Feel free
to save them on your hard drive. The fractal images are sized
to allow their use for monitor wallpaper. The images are,
however, copyrighted and are not to be used for any commercial
venture without my approval.
High quality prints of the images on this site are available
for sale.
I wish
to thank Stephen Ferguson for creating his freeware program
Tierazon. All fractals were generated with this software.
No images were added to the fractals by post processing.
Thanks also go out to Joe Mulvey for the design and construction
of this web site, and to Scott
Whittemore, my photography mentor.
Special thanks also to Noel Lion for first recognizing, and
helping to bring out, the artist in me.
Bob Janules
Email: janules@worldnet.att.net
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