These girih tiles may have been used to generate a wide range of complex tiling patterns on major buildings from medieval Islam, including mosques in Isfahan, Iran, and Bursa, Turkey; madrassas in Baghdad; and shrines in Herat, Afghanistan, and Agra, India.
Dr. Lalvani has been developing tiling patterns for decades, and holds patents on a few.
In the 1970s, Sir Roger Penrose, the Oxford University mathematical physicist, created "aperiodic" tiling patterns that never repeated themselves, work that he suspects was inspired by Kepler's drawings.
The ratio of numbers of kites to darts in any sufficiently large P2 Penrose tiling pattern therefore approximates to the golden ratio φ.
This tiling pattern consists of rows formed by triangular features comprising three bright lobes.
Another is to use a pattern of circular arcs (as shown above left in green and red) to constrain the placement of tiles: when two tiles share an edge in a tiling, the patterns must match at these edges.
Previously, we described the first use of a human gene promoter tiling microarray platform to identify genome-wide DNA methylation patterns in a human breast cancer cell line model of metastasis [4].
Methyl-DNA immunoprecipitation in combination with a CpG island tiling array was used for profiling methylation patterns in un-treated zebrafish liver and hepatocellular carcinoma (HCC) samples.
We found that identification of co-expression patterns by tiling array experiments was helpful in operon prediction.
Tiling array analysis provided further information on expression patterns in different growth phases.
Tiling thus helps in handling curved edges.
