Fibonacci in Grasshopper

http://www.grasshopper3d.com/forum/topics/fibonacci-square-sequence

Includes a link download a definition to form a Fibonacci spiral in GH

 http://www.grasshopper3d.com/photo/test-no1fibonacci-bridge?context=user

Another example of someone exploring how the Fibonacci sequence might manifest itself in a structure

 http://eat-a-bug.blogspot.com.au/2009/08/fibonacci-tiling.html

This page also includes a GH definition to create the pattern above. 

Generative art with Structure Synth

http://prideout.net/blog/?p=72

http://fab.cba.mit.edu/classes/MIT/863.10/people/hiro.tanaka/pages/page_02_ORSF_grasshopper_1.jpg

Development of Innovative Construction Systems with Glued Laminated Timber and Glass

In the last years, with collaboration of the architects Manuel García Barbero and Kiyanshid Hedjri (Klimark) and other collaborators in various fields, this Institute has been working in research projects related to timber structures and parametric architecture, such as “Development of Supporting Structures based on Technical Timber and Laminated Glass” and “Development of Innovative Construction Systems with Glued Laminated Timber and Glass”.


One of the aims of this project has been the development of an industrial and modular construction system for free forms with glued laminated timber and glass. To achieve this aim, software products as Rhinoceros for form-shaping and EvoluteTools for the tessellation of free forms in few families of triangles with the same length of sides, have been used. 

http://blog.rhino3d.com/2012/02/development-of-innovative-construction.html

Parametric Wood

"The Parametric Wood seminar is an advanced digital design research seminar focused on contemporary timber fabrication and long-span structures enabled through parametric design in Grasshopper."

Lots of information and resources on using Grasshopper to generate designs to be fabricated in wood

2D Branching Structures using RABBIT

The definitions show how to create 2D Branching Structures using RABBIT.
More about Branching Structures: http://algorithmicbotany.org/papers/abop/abop-ch1.pdf
The meanings of the symbols:

F move forward at distance L(Step Length) and draw a line
f move forward at distance L(Step Length) without drawing a line
+ turn left A(Default Angle) degrees
- turn right A(Default Angle) degrees
\ roll left A(Default Angle) degrees
/ roll right A(Default Angle) degrees
^ pitch up A(Default Angle) degrees
& pitch down A(Default Angle) degrees
| turn around 180 degrees
J insert point at this position
“ multiply current length by dL(Length Scale)
! multiply current thickness by dT(Thickness Scale)
[ start a branch(push turtle state)
] end a branch(pop turtle state)
A/B/C/D.. placeholders, used to nest other symbols

http://morphocode.com/work/rabbit/tutorials/2d-branching-structures-with-rabbit/