Friday, March 9, 2007

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.


12 comments:

Kora said...

magnificent! fantastic, really

Dirk said...

Een leuk initiatief! Waar zijn de 3D ontwerpen te bekijken?

Vlad Alexeev said...

>> Een leuk initiatief!
>>Waar zijn de 3D ontwerpen te bekijken?

Excuse me, but I don't understand Dutch language. Could you post your question in English.

Anonymous said...

What an excellent way to express fractals in art!

Juan mimi said...

I do really love fractal art, and the way you can get such beauty just by using mathematics.

Anonymous said...

are the yellow ones pythagoras trees, or just fractal trees?

Coalescence said...

See: http://flickr.com/photos/32286042@N00/3050945484/

http://flickr.com/photos/32286042@N00/3046359411/

Vlad Alexeev said...

>> are the yellow ones pythagoras trees, or just fractal trees?

I think, it's true Pythagoras tree with impossible triangle as basic shape.

>> 2 Coalescence
Thank you for the link. I've updated the post with this image.

nooodl said...

>> >> Een leuk initiatief!
>> >>Waar zijn de 3D ontwerpen te >>bekijken?
>>
>> Excuse me, but I don't >>understand Dutch language. Could >>you post your question in English.

He said:
"What a fun initiative!
Where can I find the 3D-designs?"

Manny Lorenzo said...

Vlad,

I have added additional Pythagoras at:

http://flickr.com/search/?w=32286042@N00&q=Pythagoras&m=text

and at:

http://strangeartifacts.smugmug.com/gallery/2005576_6RsiZ#250623133_2sNSg

Melinda said...

These kind of art is very crappy, nothing like the inspiration of a artist

Melinda Robinson

knee anatomy

Nikolay Vyatkin said...

Спасибо! Интересный пост:)