Disclaimer: Not designed for touchscreens. Not tested on touchscreens.

Tile(1,1)

This is Tile(1,1), a non-convex polygon whose angles are indicated below:

All edges have the same length if you consider that the edge marked 2 is in fact two edges making an angle of 180°.

David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss proved in May 2023 that, if you prevent reflections, it can tile the whole plane, but only aperiodically. This is the first proven example and it has many more interesting properties that you can discover in their article.

Controls

Turn the tile by a multiple of 30° with either: the mouse wheel; the left/right arrow keys while the cursor is above the canvas; the turn buttons.
There are 5 tools, you can select them by clicking on their buttons or cycle through them by a right click or the up/down arrow keys while the cursor is above the canvas: place new tile, move tile, delete tile, paint tile, pan/zoom.

Missing features

Tiling generation should come when I have time to implement it.

Overlap is not prevented

There is no overlap checking implemented. A priori I do not think this is necessary: visual inspection shall be enough and it may be interesting to allow overlaps for experimental/temporary purposes.

Magnet (snapping)

The vertices of the already placed tiles are used to snap the current tile being placed: this tile is translated according to the closest vertex pair, provided their distance is below some threshold.

Custom tile

Each color can be individually replaced by a custom tile given by an image in a standard web browser image format (PNG, GIF, SVG, etc. but --not-- PFD, EPS, etc.) with a certain amount of freedom in the choice of its shape. The format JPEG will cause problems since it does not handle transparent pixels.

Format

Specification: Image should be oriented and framed as below, the top tip should be in the middle of the top side of the central box image and the bottom-most vertex should lie on the bottom side of the central box. The image frame should be scaled-up version of the central box by a factor of 2, scaled about its centre. It is important that the image has transparent background since the applet won't apply cropping. This is to allow you to change the shape of the outline.

Again: the image does --not-- get cropped to the outline of Tile(1,1), so: use transparency or SVG.

The program lays out a non-drawn outline of Tile(1,1) over the image using the specification above to place it precisely. Then the vertices of this outline are used in the magnet feature.

The tile above results in

Spectres are possible too!

The tiles above result in

More examples here.

Saving/Loading tilings

Saves a data file containing position and color of tiling. Does not save the custom images if there are, but instead the coulour that the image replaced.

A few examples of tilings saved as data files can be found near the end of the examples page.