Crocheting the Lorenz Manifold

In 2003, Hinke Osinga and Bernd Krauskopf from the Bristol Centre for Applied Nonlinear Mathematics produced the first real model of the Lorenz Attractor surface by knitting.






















Download the paper by Osinga & Krauskopf here.

For more information on this topic please visit The Home of Mathematical Knitting

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

Cairo Tiling

This pentagonal tesselationis called cairo tiling.

3D2REAL: A wall based on the cairo tesselation, designed and build by ILEK students.

Extension of the congress center Davos, currently under construction. The roof structure is based on the cairo tesselation. By Degelo Architekten, Engineer: Dr. Schwartz Consulting

The cairo pattern seems to be a blend of a diamond pattern and a chinese pattern.

Download the definition here.

Sun-Shade Machine

Inspired by Frei Otto's sun-shade machine, this grasshopper definiton generates the shadow of mesh objects for a given geographical location, date, and time. North is in positive y-direction.

Download the file here

"The sun-shade machine, [...] is an extremly flexible tool for determining in the first phase of planning the areas of insolation and shade. [...] the sun-shade machine offers an infinitely variable adjustment for three parameters: geographical location, month, nd time of the day." IL 30 Vela, Toldos, sun and shade (1986)

Armillary Sphere

An armillary sphere is a model of the celestrial sphere. The drawing is from Christoph Clavius commentary on the book De Sphaera from 1581.

This grasshopper definition generates the position of ecliptic and sun for a given time, timezone and date at a given position on earth. The real position of the sun deviates from this position by approx. +/- 15 min. The reason is the eccentricity of the earths's orbit around the sun. (see equation of time).

Download the grasshopper definition here

Dreidle Urbanism

Tracking the tip of a dreidle with processing, and then sending the coordinate data via udp to grasshopper.

Dreidle City in time lapse. Inspired by parmetric urbanism.



Download the definition files here. Udp sending and receiving based on Luis Fraguada's definition.

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.

Mesh Deformer

Inspiered by the IXth chapter of D'Arcy Thompson's On growth and form I build a definition for the deformation of mesh models. The reference surface should be in the XZ plane.

The fish model is from planit3d

Download the grasshopper definition here

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

Parametric Sculpture

Design by Kyle Scherzing and Lee Farmenter at the AA dLab 2009.

initial experimental setup



volumetric model of the motion path

Reverse Dynamism

Project for a bridge by Elora Brachmachari, Pierluigi D’Acunto, and Ed Pearce at the AA dLab 2009.

conceptual studies

structure

final rendering

Parametric War

Design for a suit of armour by Kobpong Khomson, Soo Hyun Jin, and Tji Young Lee at the AA dLab 2009.

folded collar








grasshopper definition of the collar

Physico-Logical Design Workshop

Toni Kotnik and Lorenz Lachauer will lead a design studio at the AA Summer dLab 2009, 3 - 14 August. In the workshop the process of abstraction of physical phenomena will be exemplified by an investigation into patterns of movement of bodies in space and the architectural utilization of these patterns by means of parametric and geometric variation.

A motion sequence by Eadweard Muybridge

The movement of a drummers hand performing a single stroke

Read Colors From File

The RGB chanels ploted as surface

The input image

This VB script component reads the RGB values from a jpeg file
Download the grasshopper definition ColorSurface.zip here

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.