Twisted Beams on Surface

Twisted beams with custom cross-section curve aligned normal to a given surface.


Download the gh-definition here.

Graphic Statics

The french mathematician Pierre Varignon (1654-1722) introduced the funicular polygon and the polygon of forces in his work Nouvelle Mecanique ou Statique. He describes a way to construct the form of a hanging rope with attached weights graphicaly. Based on this principle, a technique called graphic statics has been developed in the 19th century. The basic principle of graphic statics is the reciprocal relation between force polygon and funicular polygon. Recomended books: Luigi Cremona: Graphical Calculus (1890) and Edward Allen,Waclaw Zalewski: Form and Forces (2009)

This grasshopper definition generates a funicular polygon for uniform loading. Download here.

Lorenz Attractor

The Lorenz attractor has chaotic behaviour, named for Edward N. Lorenz. The movie shows the changing of the attractor with increasing Prandtl number.



Downlad definition here

Istanbul Street Parametrics

Spirograph toys for sale at the Sultan Ahmet station in Istanbul,Turkey.

Spirograph patterns generated with grasshopper.

Download the definition here

Cairo Attractor

A diamond grid locally distorted by a cairo attractor


The moving attractor

Download the definition here

Tracking with Processing and Grasshopper

I threw a marble in an iron wok and tracked the motion, using brightness tracking in processing. Then I sended the coordinates of the marble via udp as a list to grasshopper.

The path remindes me of harmonograph curves.



Download the files here. The grasshopper definition is based on Luis Fraguada's work, I used his grasshopper udp receiver and adapted it.

Fibonacci Tiling

Aloe plant, the leaves are arranged in the form of a golden spiral, based on Fibonacci numbers
Picture from CSSNZ

A Fibonacci tiling of the plane

Grasshopper definiton of the tiling for download

I found this picture of Nicholas Grimshaw's Eden project on Katie Bednarz's blog

Chemnitz Stadion

Winning competition entry for the Chemnitz Stadion, Germany, 1995, Peter Kulka with Cecil Balmond





The roof structure is based on a spirograph curve, sketches by Cecil Balmond, from his book "Informal", p. 159

Spirograph.zip generates spirograph curves with grasshopper

Busan Towers

This project is the competion entry of UNStudio for the World Business Centre in Busan, South Korea, 2006. The geometry of the floor plates is based on rolling curves.
Pictures (c) by UNStudio

Rolling curves are also known as spirograph curves.

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

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

Turtle Graphics

This VB.Net module calculates a turtle path

Read an introduction to Turtle Geometry here

Turtle.zip

An analog turtle build by Grey Walter in the fifties

Map Lines

Maps straight curves from the xy plane on a surface
The mapped lines change length, but remain straight

MapLines.zip

Harmonograph

A nice example from the
Science Museum



















Harmonogram generated with grasshopper
More about the harmonograph on Paul Bourke's page

Harmonograph.zip

Isocurve Wireframe

NURBS curves on surface generated with grasshopper
Number of curves in u- and v-direction is separately adjustable

Isocurve.zip