This page is available for you to provide your comments and to start a discussion on any topic about patterns in nature or other topics that are tangentially related.
16 Responses to “Your Comments”
Your Comments
Get my latest blogs
Featured eBooks
Recent Blog Posts
Hi, Bill – Thanks for visiting my blog, Complexity Simplified. I need to take some time to explore your interesting website. Very glad to see all these e-books you’re producing. I’ve been thinking of doing something similar with complexity science concepts.
I answered your comment/question over on my blog about the relationship between self-organization and self-similarity. While they both have the root word “self” in them, I don’t agree with whoever it is who is saying that self-organized systems are always self-similar (and vice-versa). This is simply not true. The mathematics of self-similarity are very well-understood and apply to chaotic systems and fractals, but self-organization often produces behavior that goes beyond these two states.
Anyhow, thought I’d leave a comment here to get us started. You might want to follow me on Google+ – I have a “Complexity and Emergence” circle there that might be useful for discussions. You can find me here: https://plus.google.com/108153055530371640578/about?hl=en
As an IT architect, I can see how natural patterns can be related to IT patterns, and as a biochemist I can see how the IT patterns we use are primitive and rigid. Even with our advanced system architectures, we establish patterns with the result of the patterns being known apriori. However, if we assume that we do not know how information is going to be used, then we have to rely on other patterns to predict what our systems will look like, and
I think the key word in your latest email is “predict”. A key idea in all patterns in nature is that they are unpredictable — particularly after a few iterations. However, I find that simulation can give us some answers. Complex systems (such as IT systems) are self-organizing and are driven by preferential attachment (“autocratic”). The work done by Barabasi and others has resulted in the definition of scale-free networks which nicely model the Internet and other complex systems. In turn, these systems can be defined by a constant power law exponent. I’m not sure if these ideas apply to your work, but it is now being shown by Geoffrey West, et.al., that there is a unity among many systems (including patterns in nature) that is defined by a power law exponent that is a multiple of 1/4. In that sense, there seems to be predictability. But, the predictability is a definition of the organizing principle and not a precise result.
I have been questioning the creation of artworks, (in terms of “chaos” theory) …As an artist/ human being can one remove the self to create truly random /chaos pattern?
Thanks for the great chapter on these topics. I will share with my design students, when we get to pattern/rhythm/order…
Hi Lee:
My apologies for a late reply. I’ve been moving and reorganizing my comments sections into my new blog at “blog.freshvista.com”.
Your comment is very interesting to me because I’m beginning to believe that nothing is truly random. Instead, there is “chaos” defined as highly complex processes where patterns are not always discernible. But yet, there is some order.
What do you think?
I’m studying communication design at art school, and I am so excited to find your website! My grad project is exactly along these lines of an interconnected world with a focus on nature. I would love to view these images on the patterns of nature. This would greatly enhance my design work! Thanks!
Hello Vanessa:
Thanks for viewing my Patterns In Nature website at
http://www.patternsinnature.org. I’d like to answer you on two issues,
my images and the subject of connectivity:
First, my images of just patterns in nature are at:
http://patternsinnature.org/galleryslideshow_PIN.html .
Or, if you prefer, you can see these and other images at
“gallery.freshvista.com”.
As to things being connected, it is a big subject that is just now
becoming important to Western science. May I suggest that you build a
consciousness in connectivity by examining everything you look at with
the question: How am I connected to this? It would be a wonderful
thing if the viewers of your art were somehow prompted to ask this
question with every one of your pieces. And, commercially powerful as
well. Perhaps your art could somehow lead the viewer to that question.
You might look at my blog at
http://www.patternsinnature.org/blog/?p=64 as well. This piece has an
aesthetic/spiritual bent. But, from an analytic viewpoint, you might
want to consider the study of networks and fractals. These are
representations of connectivity that could be utilized in your art.
Both fractals (self-similarity) and networks are covered in the draft
of my book. Both subjects have huge numbers of references if you were
to do a Google.
I’d love to keep posted on how you are doing — along with some
samples of your art.
Hey Bill…gymnastics coach here who has been trying to go beyond the raw physics we teach and connect with emerging neuroscience. In my quest I was led to Ginger Campbell and her Brain Science Podcast and have found much that I hope to incorporate. Understanding network systems and their topology has been driving my research lately. Your work popped up and it contains accessible and valuable knowledge. Good luck with your publication.
Hi Darryl:
I apologize for not getting back sooner. I’ve been changing my comments system and placing everything on my blog at “blog.freshvista.com”.
While I should have known better, I never explicitly connected neuroscience with patterns in nature. I’ve always though of it from the behavior point of view. Thank you for “yanking my chain” !!!
I’m studying architecture and i’m working on a project about using natural pattern in building structures and how we can inspire from these patterns for architecture!!
Somewhere deep in my brain I thought I had responded to you. But, maybe not. I have been moving my comments to a more central source inside my blog at “blog.freshvista.com”. My apologies for the confusion.
Your search for the use of natural patterns seems to be focused on fractals as indicated in another communication to me. I took a quick peek on Google and found many URLs coming up under the keywords “fractal architecture”. Once example is
http://www.fractalarchitect.com/index3.html .
Keep in mind that fractals are “self-similar” structures. Architecture exhibits self similarity all the time. And, self similarity is a key characteristic of most patterns in nature.
I am coming at this from the angle of epistemology – the study of knowledge. I have figured out a specific way I would organize knowledge. I have figured out a 2-dimensional way so far. But I am starting to wonder if there is a standard way to analyze nature. Something that might even be like a software algorithm. So your analytic aspect is what interests me. Do you have a section strictly to do with the analytical aspect ?
Hi Brad
Thanks very much for the comment you left at
http://www.patternsinnature.org. Thoughts like yours need to be
broadcast to a wider audience than a simple comments page. I’m just
starting to pull together my web site, a blog, and Facebook into a
coherent way to portray all information on patterns in nature. But, I
am struggling with how to set up a discussion forum on patterns in
nature. But, it will happen soon. You question is important and I will
eventually put your email and my answer into a blog or a discussion
forum of some sort.
My new eBook will be out in about a month and I will send you a free
copy. In many ways, this eBook addresses a “unity” in nature –
particularly in the epilogue. The epilogue in the web draft version is
incomplete and considerable editing has been done for the eBook
version.
But, in my view, it goes something like this.
Until recently, Western science has taken the worldview that any
knowledge can be gained by breaking something down to its lowest
common denominators and examining same by predictions using
mathematics. The process is called “reductionism”. It has resulted in
many “mathematical laws” that attempt to predict the actions of
components (Newton’s law, etc.etc.). In fact, most Patterns in Nature
books that I’ve read (typically written by mathematicians or their
advocates) insist that patterns can be described through mathematical
laws. That is a very incomplete point of view.
For centuries, a different view of nature has been held by the
Confucian “Li”. A very good explanation can be viewed at:
http://liology.wordpress.com/category/chinese-thought/the-li-series/ .
The Li says that nature is described by organizing principles rather
than mathematical laws. The Li emphasizes a profound truth in nature –
that everything is connected. Everything is a complex system. It goes
on to explain that nature needs to be described as a set of organizing
principles. (not as a set of mathematical laws as proposed by the
reductionist paradigm)
We’ve known for some time that the behavior of complex systems cannot
be predicted by mathematical laws. They can only be described
algorithmically where the final outcome is never predictable or known.
This gradual shift to a systematic paradigm by Western science has
taken place only in the last 20-30 years. But, if you are looking for
a way to analyze nature, I believe you’ll need to start by thinking
“simulation” rather than “computation”.
What makes all of this very interesting, Brad, is that a guy named
Geoffrey West has been recently suggesting that there is a “unity” in
nature (he never dares to couch it using that term) that can be
described using a mathematical law that we know as a power law. He
suggests that many interrelating natural phenomena, at a systems
level, are interrelated by their scaling power law exponent which is
some multiple of “1/4”. He goes on to explain that the proposed
reason is that natural systems are all connected and require some form
of network architecture to be connected. He suggests that these
networks are scale-free and have a dimension of “1/4” or a multiple of
that. Much of this can be described with the Pareto Distribution which
is a power law distribution. None of this is “exact”!! None is
predictable. But it may now be explainable.
To quote West: “… biological systems obey a host of remarkably simple
and systematic empirical scaling laws which relate how organismal
features change with size over many orders of magnitude. These include
fundamental quantities like metabolic rate (the rate at which energy
must be supplied to sustain an organism) , time scales (like lifespan
and heart rate) and sizes (such as the length of the aorta or the
height of a tree trunk). It is remarkable that all of these can be
expressed as power law relationships with exponents that are simple
multiples of ¼ (e.g. ¼, ¾, 3/8) . They appear to be valid for all
forms of life whether it be mammalian, avian, reptilian, unicellular
or plant-like. These “laws” are clearly telling us something
important about the way life is organized and the constraints under
which life has evolved. ”
To me, in your search of a way to analyze nature or to organize
nature’s “information”, you are dwelling in a very important field.
Unlike Western science’s reductionism, however, with West’s ideas you
are on a path where your “analysis” would be by examining nature’s
organizing principles instead of trying to predict nature through
impossible mathematical laws.
In the course of your work, I would be looking strongly at
self-organizing systems (emergence), self-similarity (fractals),
network theory (particularly scale-free and small-world networks), and
scaling (power law growth and change).
Below are some references (to name only a few) that I’ve found useful:
http://complexityblog.com/papers/aaron/Amaral-Complex%20Networks.pdf
http://research.yahoo.com/files/w_ARS.pdf
http://www-personal.umich.edu/~mejn/courses/2004/cscs535/review.pdf
http://hep.ucsb.edu/courses/ph6b_99/0111299sci-scaling.html
http://www.npr.org/templates/story/story.php?storyId=12877984
Google “Geoffrey West” where there are at least two of his lectures on
YouTube where he talks about the idea of a universal scaling (power
law) exponent. West is the “man” on this subject.
http://www.alliancemagazine.org/en/content/interview-geoffrey-west
http://video.google.com/videoplay?docid=7108406426776765294#
http://www.youtube.com/watch?v=Obpjv5FtWxk
http://people.ccmr.cornell.edu/~ginsparg/Phys446-546/gbwscl99.pdf
Google “Strogatz”, “Duncan Watts”, or “Albert-Laszlo Barabasi” for all
sorts of material on netwoks.
http://www.ted.com/talks/lang/eng/steven_strogatz_on_sync.html
http://en.wikipedia.org/wiki/Self-organization
Many more. But, this should give you a start.
I want to create realistic Sheep Horns, that retain the property of producing a beautiful tone when blown, like the Jewish shofar. So I am looking for a simple iterative algorithm that can do this, or at very least, a good mathematical description of the sheep horn. Logarithmic spiral is a start…
Hi Ted:
As promised, I’m getting back to you on the construction of a logarithmic spiral. I’m not sure how you intend to transpose a 2D representation into your 3D horn. But, I enclose some URLs for the
construction of the 2D version. The logarithmic spiral goes by various names including the “equiangular spiral” and the “Fibonnacci Spiral”.There are different ways to construct the spiral as shown in the four URLs below:
http://xahlee.org/SpecialPlaneCurves_dir/EquiangularSpiral_dir/equiangularSpiral.html
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phi2DGeomTrig.html#spiral
http://www.maa.org/projectwelcome/calculus%20in%20action/librarya/spiral/pdf/calculus7_5.pdf
http://etc.usf.edu/clipart/61200/61291/61291_logspirals.htm
Hope this helps. I am VERY interested in hearing how your project progresses. Please keep me informed. I will send you a free copy of one of my eBooks in a week or two as soon as I finalize the document.
Hi Again Ted:
You might enjoy this:
http://www.youtube.com/watch?v=kkGeOWYOFoA