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/

New set of fractal trees - 2

Today, I represent a small but nevertheless interesting set of fractal trees of various kinds.

Two mystical fractal trees by Jacob Ankney (Jeddaka).

A new variation of Pythagoras tree with curl as base figure for duplication in fractal, which was created by IDeviant.

And, in conclusion two fractal images from Shutterstock. The first can be bought here, the second is no longer represented there.

New set of fractal trees

A new set of fractal trees open images by Nirolo. Nice gradients give mystical glow to trees. Probably, these trees should grow in the foresests of the elves. Curved branches look very unusual for fractals.

Fairy Tree

A tree of Fire and Ice

The next tree is like a lightning. Branches have rough outline like real lightning. But it still variation of Pythagoras tree. The image was created by Cory Ench. Author also created several variations of this fractal.

The last image show us apocalyptic sunset with a fractal tree of very regular form. The image was created by George13.

Fractals by Manny Lorenzo

Some time ago I've published one fractal by Manny Lorenzo in the post about Pythagoras trees. Today I would like to show some his fractals.

Let start from new kinds of Pythagoras trees. He created a tree with spheres and a very strange kind of Pythagoras tree, which has infinity symbol as a base part of fractal. It looks unlike Pythagoras tree, but it is true.

Also he created a set of wonderful fractals of Nautilus shells. Nautilus shell is one of known examples of fractals in nature. 

Except these ones he created another fractal shells.
Visit Manny's Flickr phostostream to see more beatiful fractals.

Fractal trees

Some time ago we have talked about Pythagoras tree, which represents simple fractal structure consisting of squares. Also, there are many variations of fractal trees, which are consist of lines and curves.

The three-dimensional fractal tree above is constructed from lines. It belongs to L-system class of fractals. Associated as trunk and branches brown lines of the tree are elements of low generations of the fractal. Green lines are elements of higher generations of the fractal. They remind us leafs. So, the whole fractal structure resembles real tree.

The rainbow fractal Julius tree below was crated with help of the computer program Fractal Imaginator. The tree reminds rounded Pythagoras tree, where squares were replaced to thin rectangles. The tree fractal can be created not only with help of straight lines or rectangles, but also with help of curves and spirals. Below, you can see a title for the High School Course "Gödel, Escher, Bach: A Mental Space Odyssey" by Justin Curry and Curran Kelleher, where curved fractal tree is used. The spiral was chosen as base element for this fractal, which gives many elegant curls.

Pythagoras tree

The Pythagoras tree is a plane fractal constructed from squares. It's named after Pythagoras because each triple touching squares encloses right triangle, traditionally used to depict Pythagorean theorem. If triangles of the tree have equal sides, the Pythagorean tree is symmetric, as you can see above, otherwise the tree is asymmetric. The illustration above shows eight iterations of tree construction progress.

Below it's shown asymmetric Pythagoras tree.

The shape of the tree can be used for creation of infinite impossible figure. Some parts of the fractal can be replaced to impossible triangles or squares. Illustrations below show symmetrical and asymmetrical impossible fractal tree.
Flemish artist Jos de Mey created many artworks with Pythagoras tree as main motif. Below you can see his artworks.

Three dimensional effect can be applied to the Pythagoras tree. Illustrations below by Koos Verhoeff shows trees with applied various parameters.

Below you can bronse sculpture of Pythagoras tree which also created by Koos Verhoeff. the sculpture based on computer sketch above right. 

Upd 25.11.2008.

A very nice Pythagoras tree was created by hyperion_00001. Note, that younger leaf generations are located below older ones, which increase convexity of the figure.