Parquet Deformation Manually

This is not to explain the method, but to see the potentials. After we’ve studied regular, semi-regular, dual and truncated tessellations with students, Architectural Geometry course is now expecting them to develop a pattern deformation such as these shown below. These samples are taken from this website if you are also interested in other topics of tessellation.

They can all be drawn with simple commands, line, control point editing, trim, extend, and rotate. Their firing rule is so simple that maybe they don’t need a complex algorithms to model such structures. Instead, anyone can create them by hand. Again, sometimes it seems to be better that way. Yes, a script might speed up the process to see lots of different variations but at some point that would result a non-controlled, or a random choice, lack of a deeper reasoning.

Escher made repeated use of a family of metamorphosis techniques in his graphic work. Perhaps the most famous example of all of these techniques is his print Metamorphosis II.

A few decades later, architect William Huff began to assign his students the task of drawing “Parquet Deformations”, abstract designs depicting tilings that slowly evolve in space. The results are clearly related to Escher’s metamorphoses, though more abstract and mathematical. Parquet Deformations were popularized by Douglas Hofstadter in his Metamagical Themas column in Scientific American, later reprinted in the book of the same name.

Craig S. Kaplan (

Here are my Rhino tests utilizing above methods:

Here is the Rhino file, if you are still interested: [3dm: Rhino4]