Formula Tower

At digital matters, Tobias Wallisser from LAVA presented his Superformula Tower concept. Inspired by this beautiful idea, I created a grasshopper definition for towers based on a simpler formula.

The floor plate shapes are based on this formula:

(in polar coordinates)

r(φ) = 1 - a(1 + Sin(φ b))

FormulaTower.zip

Bricks

Inspiered by the work of Gramazio & Kohler, I plugged together a grasshopper definition, that generates a perforated brick wall from planar curves. Similiar studies in wood have been made recently at the Graduate School of Design, Harvard

Bricks.zip

(c) by Gramanzio & Kohler

Balmond's Sigma Code

The Search for the Sigma Code has a dense plot and relies on another imaginary narrator (not a monk this time, but) a boy called Enjil. If you have ever wondered why any prime number is greater than three will, when raised to the sixth power, leave a remainder of one when divided by nine, you will be at home with this book. -- Vanessa Thorpe, The Independent On Sunday - 13 September 1998

You get the sigma code of a given number n like this:
1. Calculate the sum s of all digits of n.
2. If s is smaller then 10, s is the sigma value.
3. Else set n=s and return to 1.
With this definition it is possible to calculate the sigma values of number sequences. The result of some simple sequences are beautiful patterns:

This diagrams you obtain from the Fibonacci and the Pell sequence by using (and modifing) the following script: SigmaCode.zip

More Geodesic Shells

Mårten Nettelbladt kindly adviced me of the Korkeasaari Lookout Tower, an example of a geodesic structure build of wood.

The Japan Pavillion at the expo 2000 by Shigeru Ban and Frei Otto is an example of an geodesic shell build of paper tubes.

Geodesic Shell

The structure of this shell is woven from isocurves and geodesic curves on a surface. Geodesic curves are also called plank lines, they can be build from straigth, but twisted planks. Mårten Nettelbladt studied them on his blog. Geodesic shells build in wood have been studied at the laboratory for timber construction of the EPFL.

Planks generated from lines on a surface with this script: TwistedBeams.zip


The (straight) bamboo strips of this chinese hat are following geodesic lines. Photo by drs2biz.

Surface Turtle

This is an implementation of a turtle walking around on a NURBS surface. If the turtle is going straight in small steps, the resulting path is close to a geodesic.

SurfaceTurtle.zip

In general relativity, the straight path in curved spacetime is a geodesic

Local Curvature

In this example, the turtle is connected with a graph, defining the local curvature of the resulting curve

CurvatureTurtle.zip

The relation between local curvature and the curve shape,

taken from S. Wolframs book, p. 418