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Hi---I generally enjoy your articles. As a biologist it's nice to see someone writing with clarity about interesting aspects of the natural world. However I must point out that fractals are NOT the product of chaotic behavior---they are not random in the least. By definition chaos cannot be organized. Your title is a little misleading.
Thanks for your comment. The title would be misleading were this a scientific dissertation, but instead the title refers to the inclusion of the study of fractals in what is known as "chaos theory", which to me would also be a misnomer. I agree that fractals are not chaotic; furthermore, in my opinion an argument could be made that true chaos does not exist. This is due to the fact that every phenomenon in the universe has some kind of organized influence, if only by virtue of the nature of matter itself (organized particles/waves). Even in something as seemingly chaotic as the explosion of a sun or collision of galaxies, apparent disorganization reorganizes as new stars are born and systems develop. Possibly, the universe can display only chaotic characteristics, not pure chaos.
I read "Complexity" by MIchael Waldrop, in which he describes the work of scientists at the Santa Fe Institute and elsewhere. The thesis is that complexity occurs at the border or interface between chaos and order, and that is where life occurs.
Life is not viable in conditions of too much order or too much chaos. A fascinating idea and a new way of understanding the divine act of creating order out of chaos... an ongoing project rather than something that happened a long time ago.
The book is outdated (1992), however, and I'm sure there are more recent books on the subject.
Thank you, i injoyed your article so very much. It's been a long time since i've been into fractals. The most beautiful art in the universe.
I keep things very simple in my mind. and fractals are the epitamy of simplicity out of the chaos of the universe and beyond.
Vickie
