Bill Gosper <billgosper@gmail.com> wrote:
This is precisely the tiling behind www.tweedledum.com/rwg/pentagonfill.pdf and http://gosper.org/pentfill.pdf . (And that stick-length illusion.)
Martin Gardner once fowarded me a set of ingenious but cryptic frac-tiles by Ammann. I don't know where they are, so I hope someone else has a copy. They all lead to spacefills, probably of the pentfill type, since they were based on algebraic numbers. Martin was intrigued by Ammann's constantly shifting return address, and repeatedly requested some biographical data. Ammann finally replied that he was a parking lot attendant. Uh-huh.
Here's an easy one with two equal tiles. Your hemispheres are not quite alike: www.tweedledum.com/rwg/hemis.gif .
I think I've finally figured out that pentagram snowflake S. Witham found (and my tutors rediscovered) in Minsky rug plots. Has anybody else worked on it? --rwg
Robert Munafo wrote: Fred lunnon wrote:
[...] Perhaps you might explain in more detail about what exactly you want to know about it?
Good question Fred.
I guess what I was looking for is a web site or a book where "my" tiling is described and it tells who originally discovered or invented it.
Mike Stay wrote:
This isn't really a tiling: you can take nearly any shape and "tile" the plane with it in the way you describe--given any unfilled region, just scale down your shape until it fits and recurse. See the Apollonian gasket, for example.
As far as I can tell, my tiling is no different in that respect from the Ammann tilings, for example. (See http://tilings.math.uni-bielefeld.de/substitution_rules/ammann_a3) So, like I said above, I want some book or website that explains how and why they are different.
Some kind of organized taxonomy for recursive substitution-systems for space-filling patterns. It should include everything on tilings.math.uni-bielefeld.de but should also include more information (that website seems to be an abandoned project)
On 9/5/10, Robert Munafo <mrob27@gmail.com> wrote:
The rules for my tiling can be seen here:
-- Robert Munafo -- mrob.com Your comments about tilings reminds me of some work of T. N. Thiele (1838-1910) who was a professor of Astronomy at the University of Copenhagen and an early writer in statistics and actuarial science. He was also interested in various numerical subjects such as the properties of integers and the mathematics of computation.
At a conference of scientists in Copenhagenin 1873, Thiele gave a paper titled "On patterns of numbers" in which he described a computational method using algebraic integers for making mosaic patterns. This paper was published in the Proceedings of the conference in the following year. I believe Steffen L. Lauritzen, who is a professor in the Dept. of Mathematical Sciences at Aalborg University in Aalborg, Denmark was written sometime recently. It was published by Oxford U. Press, however, I haven't seen it, only heard of it. I've seen pictures of a few of the mosaics that were obtained using algebraic integers based on cube roots of unity. That's all I know about the subject. Best, John Brillhart