This page has ideas for books, journals, and web sites that may offer info useful to your nature study.

Feel free to send me links, suggestions or questions regarding resources.

...note that this page is a pretty ragged collection of links. Please forgive the mess.

Search on your Nature Study's subject — check non-art reference books, biology books, math articles, etc.

Every subject has been studied and restudied in great detail from many points of view — search morphology, general biology, chemistry, physics, medicine, ecology, etc.  Time spent reviewing the discoveries that others have made may save a lot of time discovering distinctive features that are easily overlooked.

Search for Web Sites on Design in Nature

Find an interesting web site which deals with design in nature.  Look for sites that have images and explanatory diagrams. 

When you find really helpful content, send an Email to GClayton@Harding.Edu with
a) a link to the site (the http address),
b) the title or name of the site
c) a brief description of the main topic of the site and
d) a description of whatever you found most interesting on that site — that is, why might other designers enjoy the site and its content? 

You might search for sites on:  Golden Mean, Phyllotaxy, Morphology,  Fibonacci series,  or anything interesting relating to design in nature.

The following web sites might provide ideas, resources, explanations--or distraction.

 

There are a lot of fields of study that are interested in design.  One of the fascinating things

about design is that there are so many points of view about it — artists may see things one way, but mathematicians might see the same thing another way, and botanists see it still another way — yet we all see compelling relationships.  Yet each group of observers uses its own language to describe what is interesting, so we often don't understand the relationships observed by the other, nor do we know why they are excited! Nevertheless, the insights of professionals trained in another field offers us an extra set of eyes— we can gradually see what they have seen, thereby expanding what we are capable of seeing.

It is, by the way, worth remembering that what we see is both limited by and illuminated by what we know— knowledge can be both a beam in the eye, and a magnifying glass.

The following are some sites on design in nature, the golden mean, Fibonnaci numbers, etc.

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html    ***

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html 

http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi.html

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html   ****
This page outlines many links on the fibonacci series in Art, Architecture and Design.
Its a good jumping off point.

Quite a few discussions of fibonacci series, golden mean, etc. Well outlined with fairly easy discussions. Includes some exercises for the interested reader.

Good reading for 2D Design course due to plenty of illustrated examples from nature.  Has other links as well.

Aloe plant tiling...code for tiling in Rhino 3d

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Intro and web resource links.

pw1.netcom.com/~merrills/fibphi.html ***
Well-organized with a wide range of topics related to the Golden Mean and Fibonacci numbers.

milan.milanovic.org/math/english/golden/golden.html ***
There are several pages of well-organized content and examples. Worth a look. (human body, Eyptian art, Greek art, etc.)

ccins.camosun.bc.ca/~jbritton/goldslide/jbgoldslide.htm **
A nice introduction to the golden mean in art and architecture. (check out the Mona Lisa applet)

http://community.middlebury.edu/~harris/Humanities/TheGoldenMean.html
Nicely organized intro from several points of view.

www.goldenmeangauge.co.uk/ *

[site has changed...there's not much content at present.]
An excellent site with lots of examples.  Author gets a bit carried away discovering the golden mean everywhere he looks.  But lots of good examples to think about.  This site belongs to the dentist selling the cute little golden-mean calipers.

Look, particularly, at the links to Art, Design, In Nature, History, (Handwriting), Architecture, etc.

This site is probably most helpful in generating ideas and possibilities for how to look for the golden ratio in natural structures.

www.infinitetechnologies.co.za/articles/geometry1.html **
General intro to golden mean, fibonacci, forms in nature and geometry.

mathworld.wolfram.com/GoldenRatio.html
Intro to the Golden Mean from a mathematical perspective. (Wolfram makes the computer program Mathmatica. What Photoshop, Illustrator and Autocad are to visual designers, Mathmatica is to mathmaticians.)

www.anselm.edu/homepage/dbanach/pyth4.htm ***
An historical narrative introduction to the golden mean. Has some useful discussion and diagrams dealing with the golden mean in relation to the design of Greekarchitecture, vases, and figure studies.

www.halexandria.org/dward103.htm An enjoyable intro that even ties in the Wizard of Oz.

www.makart.com/resources/artclass/golden.html A brief intro.

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Phyllotaxis -- an interactive site for the mathematical study of plant growth.

Lots of well-illustrated applets of fibonacci numbers/spirals in nature. This is another good site for 2D exploration, but the biology and math emphasis limits how much is likely to be understood.

Most content involves mathematical discoveries/relationships related to fibonacci and golden mean.

Constructing the Golden Spiral:

Golden mean and pyramid construction. If you can explain this one, great!

http://www.mathsoft.com/asolve/constant/gold/gold.html

Best site (so far) for extensive slide-by-slide discussion of Parthenon, its design, and current efforts to restore it.

Fibonacci series and the Mandelbrot Set

http://math.bu.edu/DYSYS/FRACGEOM2/node7.html

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Book(s) on the Fibonacci Series

"Fibonacci Fun" by Trudi Hammel Garland (Harding Library)

The Golden Section in Architectural Theory
A fairly thorough introduction to the golden mean in architecture, spanning ancient to modern applications.
"...traces the Golden Section from the mathematical and rather theoretical character of Pacioli’s concept, the the treatises of Alberti, Serlio, and Palladio, to Adolf Zeising in the nineteenth century, and to theorist Matila Ghyka and the practitioners Ernst Neufert and Le Corbusier in the twentieth..."

 

http://www.vashti.net/mceinc/golden.htm **
The Golden Mean (or Golden Section), represented by the Greek letter phi , is one of those mysterious natural numbers, like e or pi, that seem to arise out of the basic structure of our cosmos. Unlike those abstract numbers, however, phi appears clearly and regularly in the realm of things that grow and unfold in steps, and that includes living things.

[glc -- Helpful content.  Math-oriented discussion and examples.  A couple of helpful graphics -- which need to be animations rather than stills. One interesting derivation based on y=x*x.]

goldennumber.net **

Good content on art and nature.

Overly wedded to new-age notions, but plenty of  interesting illustrations and applications. 

Some of the graphic/nature examples seem far-fetched -- what relevant features are we pointing to in these illustrations?

http://www.floweroflife.org/spiral01.htm

[glc--- heavy new age stance.  Interesting application, but highly philosophical/mystical, rather than being particularly concerned with formal design.]

[from the site] Although the Golden Mean Spiral is principally derived by utilizing mathematics, it is equally mystifying and intriguing to note that this mathematical spiral has additional properties that can be experienced by humans on a profound level that does not require an intellectual understanding of the mathematical principles.

Simply put, the Golden Mean Spiral is a doorway that weaves the ethereal and material dimensions together. In another context I would say that God left us one door of eternal mystery and exploration3⁄4 the Golden Mean Spiral or the door of love. In this article we will explore how, in fact, the Golden Mean Spiral is an expression of the basic energy of creation that we call love.

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Some nice animated graphics  (which are currently loading VERY slowly). 

Art, nature, and math are each addressed. Several graphic images programmed to use/depict Fibonacci spirals.

http://www.moonstar.com/~nedmay/chromat/fibonaci.htm

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Links to plant/botanical images:

http://www.botany.net/IDB/subject/botpics.html

http://plants.usda.gov

 

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Human/Facial Beauty

www.beautyanalysis.com
This an unusual site with an unsual premise. Basically they declare that they have discovered, or derived, a sort of map of beautiful faces -- if the placement of your features (eyes, nose, mouth, etc.) fits into the map, then your face is beautiful. If not, well, sorry. However far a face is from fitting this map, the less attractive we find it. Supposedly.
Its worth a look.

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Sites with a Mathematical Emphasis

Wolfram's Mathematica site is about as thorough as you're likely to find for exploring math-related topics.

http://mathworld.wolfram.com/GoldenRatio.html

http://mathworld.wolfram.com/search/?q=Golden+Ratio For a search on all sorts of mathematical series and geometric solids.

Sites with Extensive Coverage of Golden Mean Issues

www.goldenmuseum.com **
There is a great deal of content here, though much of it is mathematical in nature. There are some interesting pages on the golden section in painting, though the examples are rather unknown Russian painters.

This is a Russian site. The English translation is often poor.
www.goldenmuseum.com/index_engl.html A useful collection of links. (did you know that there is a Fibonacci Quarterly journal?)

golden mean, morphology, design, fibonacci numbers, golden rectangle, golden section, phyllotaxis, nature, architecture, art, human body

golden mean fibonacci