Assignment 3 – The Penrose

Project 3: The Penrose – Pattern, Materiality  (groups of 2)

Worth: 15%

Due: Beginning of week 8’s class (29th April 2010)


The objective of Project 3 is to introduce students to the SUBTRACTIVE 3D numeric fabrication processes, using a 3-axis CNC MILLING machine.  Students will create patterned 3D tiles in Rhino.

Working in pairs, students will use the same digital model to produce 2 routed models, one in foam and the other in timber, each using a different tooling technique.   The aim is to test what different effects can be achieved using one design but different materials and techniques.  (material:  foam, solid  Jelutong timber).

In terms of design, the intention of the assignment is to produce a large scale installation for the whole class, with each group contributing in the design and fabrication of two Penrose tiles (one in foam, one in Jelutong).  Students will be given specific geometric constraints in order to standardize the edges of the tiles, to allow for their connection in different arrangements.  Students are to explore pattern and tessellation methods to design their tiles – themes will be presented at the start of week 6’s class.  A setup file in Rhino will be provided to students to create their designs.   In addition to the weekly individual blog posts, students (in pairs) are to produce a short report on their design methodology for their pattern.

Each group of two will produce two Penrose tiles, to be assembled together to create a Penrose tiling.  A Penrose tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, who investigated these sets in the 1970s. Because all tilings obtained with the Penrose tiles are non-periodic, Penrose tiles are considered aperiodic tiles.

A Penrose tiling has many remarkable properties, most notably:

  • It is nonperiodic, which means that it lacks any translational symmetry. More informally, a shifted copy will never match the original exactly.
  • Any finite region in a tiling appears infinitely many times in that tiling and, in fact, in any other tiling. This property would be trivially true of a tiling with translational symmetry but is non-trivial when applied to the non-periodic Penrose tilings.
  • It is a quasicrystal: implemented as a physical structure a Penrose tiling will produce Bragg diffraction; the diffractogram reveals both the underlying fivefold symmetry and the long range order. This order reflects the fact that the tilings are organized, not through translational symmetry, but rather through a process sometimes called “deflation” or “inflation.”  [Penrose tilings:]

Penrose Kite and Dart Tessellation

Penrose Kite and Dart Tessellation

3 thoughts on “Assignment 3 – The Penrose

  1. hey,
    having trouble with circles.

    ive spent hours trying to figure it out, internet tutorials. it shows it but i just don’t understand.

    1: i can offset, only one circle at a time, don’t know how to offset all of them at once at a thickness of 3.

    2. don’t know how to put the surface onto the kite without stuffing up my design. the indents of the kite make it hard.

    • Amy,
      1: use the “Multi-Offset” script that I sent in a previous email.
      2: not sure what you mean by this. can you post up some screen shots?

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