Jeff's Non-Periodic Skimboard

Copyright 2004 Jeffrey Valjean Cook

In 1996 I installed the first version of my website at jeffcook.com. Back then, I made this statement: "An esoteric longer-term hobby [of mine] is marketry and ceramic tiling using non-periodic infinite tilings of the plane." I haven't gotten around to these specific hobbies yet, but I have created something that incorporates non-periodic elements in its design. The result is shown below, with a description of the important elements at the bottom of this page. (My interest in non-periodic tilings and non-periodicity in general is due to the intriguing visual patterns that appear when using these techniques, and only incidentally to the mathematics involved.)

Move cursor over Front and Back descriptions below to toggle photo → Front view of skimboard with Mika     Back view of skimboard with Mika     Click on the links above for full-size images. The photos on this page were taken on Venice Beach just south of the Venice Pier, in front of my house, on 31 May 2004.

Skimboard "in action."     Click on the link above for a full-size image.
Skimboard detail (top front).     Click on the link above for a full-size image.

The following three design elements appear on the front of the skimboard, the second and third of which are examples of non-periodic constructions:

(A) the top of the board consists of a word-phrase that outlines a triangle, written in a circle-based font invented by my daughter, Mika (the identity of the word-phrase is left as an exercise for the reader, as is its starting point);

(B) within the triangle is an illustration of a portion of an infinite spiral tiling constructed using a single type of tile, taken from page 515 of Grünbaum and Shephard's "Tilings and Patterns"; and

(C) the bottom of the board shows a non-periodic pattern based on Rule 30 from Wolfram's "A New Kind of Science." (On looking back through Wolfram's book, I have discovered that my hand-generated illustration of Rule 30 contains a mistake, but which does not, in my opinion, detract from the pleasing visual quality of the resultant pattern. The first 50 iterations of Rule 30 are shown on page 25 of Wolfram's book.)

Notes: The Escher tiling (interlocking lizards) used as the background image on this page was obtained from http://scientium.com/drmatrix/puzzles/progchal.htm, which posts the following challenge: Create a Windows program that allows us to explore the properties of Penrose tiles (a special type of non-periodic inifinite tiling discovered by Roger Penrose in 1974). The replies to the challenge, including the contents of an email I sent to the site concerning the topic of non-periodic tilings and my non-periodic skimboard, can be found at: http://scientium.com/drmatrix/puzzles/progchalreplies.htm