Contents

• Panning & Zooming
• Symmetry
• Gamma
• Grid Size
• Fill
• Segments
• Download SVG
• Footnotes

Panning & Zooming

In the tiling view, use a two finger touchpad gesture or mouse wheel to zoom/scale. Click and drag to pan.

Symmetry

This is the nominal degree of rotational symmetry¹. For example, Penrose tiling has five-fold symmetry (or ten-fold, depending on how you count or whom you ask).

This value is currently limited to 40. Higher degrees of symmetry take longer to calculate and aren't necessarily more interesting.

Quasicrystal tiling is aperiodic and lacks translational symmetry. Rotational symmetry can be more easily visualized by creating a diffraction pattern of the tiling diagram (using image processing tools²).

Gamma

Generally a small number between zero and one.

This is the lattice offset used to minimize the possibility of more than two lines intersecting at the same point and screwing up the geometry. (These kinds of intersections would be called "degenerate", which you'd think would make them interesting, but they are not.)

Lower numbers (say, less than .01) make the perceived rotational symmetry increasingly obvious.

Grid size

This affects the number of tiles generated, hence the total extent of the tiling.

It's generally best to use smaller values (say, less than 20), otherwise things start to slow down quite a bit.

Technically, it's the number of lines per degree of symmetry used to produce the hypercubic lattice which is projected on to a plane to determine the eventual tiling (See deBruijn)...

Fill

The tiles can be colored based on the shape of the tile polygons, which is determined by the ratio of the distance between opposing vertices of the polygon. The number of unique tiles depends on the symmetry and is usually symmetry ÷ 2.

Color sets are generated randomly but you can then edit individual colors.

Color sets are not currently saved...

Segments

The tile polygons (which are rhombuses) can be segmented to produce interesting patterns. The tiles can be segmented in different ways based on the ratio of diagonals (how "fat" or "skinny" they are) and the type of segmentation.

Segments can created by joining the midpoints of the polygon edges or the vertices.

You can choose the ratio that determines whether a rhombus is "fat" or "skinny". There are a finite number of rhombus shapes/ratios for a given symmetry (usually symmetry divided by two).

Download SVG

You can download the tiling as an SVG file which can then be opened with a drawing program like Inkscape (or some rented Adobe product ³).