Spiral trees

Trees are the great form of nature and this the shape made many inspiration for numerous artists of mathematical art. I've posted several collections of fractal trees and pythagoras trees. And we've also met with combination of tree-like shape with spiral. Spirals are one of basic mathematical shapes and they are harmoniously match to branchy tree figure. Also spiral is the shape that very close to fractals.

Below, you can see several spiral shapes, which look very interesting for me. They are not true fractals, but they make sence of great curly figures. Click on images to see them in better quality.

Black spiral tree 

 © Willy Deganello

Logo of the site The Spiral Tree 

Curly cone tree from article of Cameron Browne about spiral space filling  

Spiral dotted tree 

by baggingspam

A fractal-like spiral tree. Smaller branches repeat their parent branch.

Images were found at

• http://ru.depositphotos.com/6475327/stock-illustration-black-spiral-tree-.html
• http://www.thespiraltree.co.uk
• http://www.cameronius.com/graphics/spiral-packing-figures/
• http://baggingspam.deviantart.com/art/Spiral-dot-tree-win-ver-52496424
• http://www.dragonartz.net/2009/09/03/curl-tree-design-vector/

Fibonacci spiral in nature

Fibonacci spiral is a line, which is created by drawing arcs connecting the oppposite corners of the squares in Fibonacci tiling, which is constructed of squares whose sides are successive Fibonacci numbers in length.

Fibonacci tiling

Fibonacci spiral

Fibonacci spiral exists in many objects of wildlife. It's one ob the basic curve, which you can see in small shells of nautilus and even in spirals of galaxies.

Arrangement of seeds in sunflower is an example of Fibonacci spiral among plants.

Hurricane is one of the most destructive power on Earth.

You can see Fibonacci spiral even in shapes of galaxies.

Although Nautilus shell looks very similar to Fibinacci spiral, it does not. Ivars Peterson in his article Sea Shell Spirals proved this fact. Nevertheless, Nautilus shell is one of examples of fractals in nature.

Fibonacci spiral inspired some artist to use it in their artworks. Below you can see an artwork by Petar Milivojevic named Gaia's gift.

Printgallery

M.C. Escher "Printgallery" (1956)

Printgallery is one of the most fascinating image of M.C. Escher. We see a young man which stands before print on the wall in print gallery. We see ships and seaside town with many houses on it. One house is closer to us than others and there's print gallery on the first floor. Then we look through the window of the print gallery and see young man looking at print. So we returned to beginning. It's a looped image, and we can infinitely look on it and never find the end.

But artist leaved center of the image empty and placed his sign there. What is under this blank spot? We don't know if Escher knew it. In 2002 this puzzle was solved and it's proved that reduced and rotated copy of the source image should be behind the spot.