Hicks’ Hexagon for Ceramic Tiles
... but 5 x 7 tiles? They're impossible to find.
The Primitive Cell is tiled to fill the image on the screen. This leads to tiling in the real world.
The standard "Shining" pattern could be reproduced using 5" x 7" ceramic tiles. That proportion is required to approximate the features of the pattern most accurately.
The Generator can show the Primitive Cell being subdivided into 4 tiles.
If the X and Y shift is chosen carefully (Auto Shift locks it in), then only 2 unique tiles are required.
If the grout colour is chosen carefully then the grout lines can be made least obtrusive. Here it was matched to the hexagon's colour.
Unfortunately 5 x 7 proportioned tiles are not usually manufactured. Instead the most common ones are square.
Producing Square Tiles
Ah... This is much more attainable. There are companies that can do custom printing on ceramic tiles.
To prepare for square tiles we need to use a different set of parameters all around.
First subdivide the Primitive Cell into a set of 6 tiles - 2 across and 3 down. If the tiles are to be square then the ratio of the Primitive Cell is 1.5 (height to width).
Generate a pattern that adheres to this new ratio of to 1.5 instead of the normal 1.4.
Line/Gap = 0.8, Cell = 6.4, and Hex = 1.9
Even though the line is now thinner and the room around the hexagon is larger, to the casual observer the pattern is still recognizable. Also notice that the hexagon is enlarged so that its left and right edges align with grout lines. This further reduces their visual distraction.
Careful X, Y shifts reduce the number of unique tiles to the minimum of 3.
The unique tiles are labeled A, B and C.
Also note that tile 'A' only requires 2 colour printing while B and C require 3. This may save costs.
These are the three unique tiles.
Here is the finished wall of square tiles. Again, grout colour was chosen to try to blend in with the pattern's colouring. When viewed from a distance they are hardly noticeable.
This was a proof-of-concept exercise. At present the Generator can only show a 4 tile subdivision. I may update it in the future to accommodate the 2x3 required for square tiles. I may also add 'save image' capability for individual (ceramic) tiles.
Revised 4 Apr 2020